TSTP Solution File: SWW244+1 by Otter---3.3

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SWW244+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n025.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 13:22:15 EDT 2022

% Result   : Unknown 15.31s 15.23s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SWW244+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n025.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Jul 27 02:58:45 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 15.31/15.18  ----- Otter 3.3f, August 2004 -----
% 15.31/15.18  The process was started by sandbox on n025.cluster.edu,
% 15.31/15.18  Wed Jul 27 02:58:45 2022
% 15.31/15.18  The command was "./otter".  The process ID is 22971.
% 15.31/15.18  
% 15.31/15.18  set(prolog_style_variables).
% 15.31/15.18  set(auto).
% 15.31/15.18     dependent: set(auto1).
% 15.31/15.18     dependent: set(process_input).
% 15.31/15.18     dependent: clear(print_kept).
% 15.31/15.18     dependent: clear(print_new_demod).
% 15.31/15.18     dependent: clear(print_back_demod).
% 15.31/15.18     dependent: clear(print_back_sub).
% 15.31/15.18     dependent: set(control_memory).
% 15.31/15.18     dependent: assign(max_mem, 12000).
% 15.31/15.18     dependent: assign(pick_given_ratio, 4).
% 15.31/15.18     dependent: assign(stats_level, 1).
% 15.31/15.18     dependent: assign(max_seconds, 10800).
% 15.31/15.18  clear(print_given).
% 15.31/15.18  
% 15.31/15.18  formula_list(usable).
% 15.31/15.18  all A (A=A).
% 15.31/15.18  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).
% 15.31/15.18  class_Rings_Oidom(t_a)->v_c____!=c_Groups_Ozero__class_Ozero(t_a).
% 15.31/15.18  class_Rings_Oidom(t_a)-> -(all B_z (B_z!=c_Groups_Ozero__class_Ozero(t_a)->hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z)=c_Groups_Ozero__class_Ozero(t_a))).
% 15.31/15.18  class_Rings_Oidom(t_a)-> -(all B_z (B_z!=c_Groups_Ozero__class_Ozero(t_a)->hAPP(c_Polynomial_Opoly(t_a,v_p),B_z)=c_Groups_Ozero__class_Ozero(t_a))).
% 15.31/15.18  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)))).
% 15.31/15.18  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)))).
% 15.31/15.18  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)).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)))).
% 15.31/15.18  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)))).
% 15.31/15.18  class_Rings_Oidom(t_a)-> (-(all B_z (B_z!=c_Groups_Ozero__class_Ozero(t_a)->hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z)=c_Groups_Ozero__class_Ozero(t_a)))-> (exists B_k B_a (B_a!=c_Groups_Ozero__class_Ozero(t_a)& (exists B_q ((v_cs____=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))->c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fe_qual(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (v_cs____!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))->c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fe_qual(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,v_cs____)))& (all B_z (hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),B_z))))))))).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  all V_pa_2 V_a_2 T_b (class_Groups_Ozero(T_b)-> (c_Polynomial_OpCons(T_b,V_a_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))<->V_a_2=c_Groups_Ozero__class_Ozero(T_b)&V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_n_2 V_k_2 V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(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)).
% 15.31/15.18  all V_n_2 V_m_2 V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(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)).
% 15.31/15.18  all V_n_2 V_m_2 (hAPP(hAPP(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)).
% 15.31/15.18  all V_m (hAPP(hAPP(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)).
% 15.31/15.18  all V_n (hAPP(hAPP(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)).
% 15.31/15.18  all V_n_2 V_m_2 V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)<->V_m_2=V_n_2).
% 15.31/15.18  all V_k V_n V_m (hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))).
% 15.31/15.18  all V_n V_m V_k (hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))).
% 15.31/15.18  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).
% 15.31/15.18  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).
% 15.31/15.18  all V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(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))).
% 15.31/15.18  all V_q T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(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))).
% 15.31/15.18  all V_n_2 V_m_2 (hAPP(hAPP(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))).
% 15.31/15.18  all V_n V_m (hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))).
% 15.31/15.18  all V_n V_m (hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))).
% 15.31/15.18  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,hAPP(hAPP(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))))).
% 15.31/15.18  all V_y V_x (c_Nat_OSuc(V_x)=c_Nat_OSuc(V_y)->V_x=V_y).
% 15.31/15.18  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).
% 15.31/15.18  all V_n (c_Nat_OSuc(V_n)!=V_n).
% 15.31/15.18  all V_n (V_n!=c_Nat_OSuc(V_n)).
% 15.31/15.18  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).
% 15.31/15.18  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).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  all V_q_2 V_b_2 V_pa_2 V_a_2 T_b (class_Groups_Ozero(T_b)-> (c_Polynomial_OpCons(T_b,V_a_2,V_pa_2)=c_Polynomial_OpCons(T_b,V_b_2,V_q_2)<->V_a_2=V_b_2&V_pa_2=V_q_2)).
% 15.31/15.18  all V_q_2 V_pa_2 T_b (class_Int_Oring__char__0(T_b)&class_Rings_Oidom(T_b)-> (c_Polynomial_Opoly(T_b,V_pa_2)=c_Polynomial_Opoly(T_b,V_q_2)<->V_pa_2=V_q_2)).
% 15.31/15.18  all V_m (c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.18  all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m)).
% 15.31/15.18  all V_nat_H_1 (c_Nat_OSuc(V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.18  all V_m (c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.18  all V_nat_H (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_nat_H)).
% 15.31/15.18  all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m)).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  all V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 15.31/15.18  all V_n (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_pa_2 T_b (class_Groups_Ozero(T_b)-> (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_b,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_x V_q V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x)=hAPP(hAPP(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))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_x V_n V_p T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n)).
% 15.31/15.18  all V_pa_2 T_b (class_Int_Oring__char__0(T_b)&class_Rings_Oidom(T_b)-> (c_Polynomial_Opoly(T_b,V_pa_2)=c_Polynomial_Opoly(T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))<->V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))).
% 15.31/15.18  all V_q V_p V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q))).
% 15.31/15.18  all V_n V_m V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 15.31/15.18  all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))).
% 15.31/15.18  all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))).
% 15.31/15.18  all V_n V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)).
% 15.31/15.18  all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))).
% 15.31/15.18  all V_n V_a T_a (class_Power_Opower(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 15.31/15.18  class_Rings_Oidom(t_a)-> (v_c____=c_Groups_Ozero__class_Ozero(t_a)-> (exists B_k B_a (B_a!=c_Groups_Ozero__class_Ozero(t_a)& (exists B_q ((c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))->c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fe_qual(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (c_Polynomial_OpCons(t_a,v_c____,v_cs____)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))->c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fe_qual(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))))& (all B_z (hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),B_z))))))))).
% 15.31/15.18  all V_n T_a (class_Power_Opower(T_a)&class_Rings_Osemiring__0(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_OSuc(V_n))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.18  all V_n_2 V_a_2 T_b (class_Power_Opower(T_b)&class_Rings_Omult__zero(T_b)&class_Rings_Ono__zero__divisors(T_b)&class_Rings_Ozero__ne_q__one(T_b)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b)&V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c))!=c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d))))).
% 15.31/15.18  all V_y_2 V_x_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(T_b)<->V_x_2=c_Groups_Ozero__class_Ozero(T_b)&V_y_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.18  all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)).
% 15.31/15.18  all V_k V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))).
% 15.31/15.18  all V_r V_q V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r))).
% 15.31/15.18  all V_n (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.31/15.18  all V_m_2 V_x_2 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_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)|V_x_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.31/15.18  all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)).
% 15.31/15.18  all V_ry V_rx V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry))).
% 15.31/15.18  all V_ry V_rx V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry)).
% 15.31/15.18  all V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx))).
% 15.31/15.18  all V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly)).
% 15.31/15.18  all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)))).
% 15.31/15.18  all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry))).
% 15.31/15.18  all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry))).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  all V_n V_m V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n)).
% 15.31/15.18  all V_q V_p V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q))).
% 15.31/15.18  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.18  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.18  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).
% 15.31/15.18  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).
% 15.31/15.18  all V_a_2 V_b_2 T_b (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)-> (V_b_2=c_Groups_Oplus__class_Oplus(T_b,V_b_2,V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.18  all V_z V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z))).
% 15.31/15.18  all V_d_2 V_ca_2 V_b_2 V_a_2 T_b (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)-> (V_a_2!=V_b_2&V_ca_2!=V_d_2<->c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2))!=c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)))).
% 15.31/15.18  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 15.31/15.18  all V_b V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m)).
% 15.31/15.18  all V_z_2 V_x_2 V_y_2 V_w_2 T_b (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)-> (c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2))=c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))<->V_w_2=V_x_2|V_y_2=V_z_2)).
% 15.31/15.18  all V_n V_a T_a (class_Rings_Oring__1__no__zero__divisors(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)!=c_Groups_Ozero__class_Ozero(T_a))).
% 15.31/15.18  all V_n V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 15.31/15.18  all V_n V_b V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))).
% 15.31/15.18  all V_q V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q))).
% 15.31/15.18  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))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q)))).
% 15.31/15.18  all V_a_2 V_pa_2 T_b (class_Rings_Oidom(T_b)-> (hAPP(c_Polynomial_Opoly(T_b,V_pa_2),V_a_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|c_Polynomial_Oorder(T_b,V_a_2,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.31/15.18  all V_k V_j V_u V_i (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k)).
% 15.31/15.18  all V_n_2 V_m_2 V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(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).
% 15.31/15.18  all V_b_H V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H))).
% 15.31/15.18  all V_y V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y))).
% 15.31/15.18  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 15.31/15.18  all V_b V_a_H V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b))).
% 15.31/15.18  all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya))).
% 15.31/15.18  all V_c V_b V_e V_a T_a (class_Rings_Osemiring(T_a)->c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c)).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_b V_a T_a (class_Rings_Ono__zero__divisors(T_a)-> (hAPP(hAPP(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))).
% 15.31/15.18  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)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a)))).
% 15.31/15.18  all V_b_2 V_a_2 T_b (class_Rings_Oring__no__zero__divisors(T_b)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b)|V_b_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.18  all V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.18  all V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.18  all V_a T_a (class_Rings_Omult__zero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.18  all V_y T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.18  all V_b T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.18  all V_a T_a (class_Rings_Omult__zero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.18  all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_a_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.18  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).
% 15.31/15.18  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).
% 15.31/15.18  all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (c_Groups_Ozero__class_Ozero(T_b)=c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.18  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).
% 15.31/15.18  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).
% 15.31/15.18  all V_pa_2 V_a_2 T_b V_z_2 V_f_2 T_c (class_Groups_Ozero(T_c)-> (hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_c)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c))),V_z_2)=V_z_2->c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,c_Polynomial_OpCons(T_c,V_a_2,V_pa_2))=hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,V_pa_2)))).
% 15.31/15.18  all V_ca_2 V_pa_2 T_b (class_Rings_Ocomm__semiring__0(T_b)-> (c_Polynomial_Osynthetic__div(T_b,V_pa_2,V_ca_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))<->c_Polynomial_Odegree(T_b,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.31/15.18  all V_n V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(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))))),V_n))=V_n).
% 15.31/15.18  all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a).
% 15.31/15.18  all V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a).
% 15.31/15.18  all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a).
% 15.31/15.18  all V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a).
% 15.31/15.18  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)).
% 15.31/15.18  all V_x_2 T_b (class_Groups_Oone(T_b)-> (c_Groups_Oone__class_Oone(T_b)=V_x_2<->V_x_2=c_Groups_Oone__class_Oone(T_b))).
% 15.31/15.18  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)))).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a).
% 15.31/15.18  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a).
% 15.31/15.18  all V_n T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a)).
% 15.31/15.18  all V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_a).
% 15.31/15.18  all V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_x).
% 15.31/15.18  all V_n (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)=V_n).
% 15.31/15.18  all V_n_2 V_m_2 (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(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)).
% 15.31/15.18  all V_n (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n).
% 15.31/15.18  all V_n_2 V_m_2 (hAPP(hAPP(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)).
% 15.31/15.18  all V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_m,V_m)=hAPP(hAPP(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)).
% 15.31/15.18  all V_a V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m))=hAPP(hAPP(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)).
% 15.31/15.18  all V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m)=hAPP(hAPP(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)).
% 15.31/15.18  all V_a T_a (class_Power_Opower(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a)).
% 15.31/15.18  all V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a)).
% 15.31/15.18  c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  all V_n V_m (V_m=hAPP(hAPP(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)).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  all V_n T_a (class_Power_Opower(T_a)&class_Rings_Osemiring__0(T_a)-> (V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a))& (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Ozero__class_Ozero(T_a))).
% 15.31/15.18  all V_x_2 T_b (class_Groups_Ozero(T_b)-> (c_Groups_Ozero__class_Ozero(T_b)=V_x_2<->V_x_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.18  all V_c V_b V_a T_a (class_Groups_Oab__semigroup__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_ca_2 V_b_2 V_a_2 T_b (class_Groups_Ocancel__semigroup__add(T_b)-> (c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_b_2)=c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_ca_2)<->V_b_2=V_ca_2)).
% 15.31/15.18  all V_ca_2 V_a_2 V_b_2 T_b (class_Groups_Ocancel__semigroup__add(T_b)-> (c_Groups_Oplus__class_Oplus(T_b,V_b_2,V_a_2)=c_Groups_Oplus__class_Oplus(T_b,V_ca_2,V_a_2)<->V_b_2=V_ca_2)).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  all V_z V_y V_x (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z))).
% 15.31/15.18  all V_z V_y V_x (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z))).
% 15.31/15.18  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))).
% 15.31/15.18  all T_b V_z_2 V_f_2 T_c (class_Groups_Ozero(T_c)-> (hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_c)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c))),V_z_2)=V_z_2->c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c)))=V_z_2)).
% 15.31/15.18  all V_pa_2 V_a_2 V_f_2 V_z_2 T_b T_c (class_Groups_Ozero(T_c)->c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,c_Polynomial_OpCons(T_c,V_a_2,V_pa_2))=hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_If(T_b,c_fe_qual(V_pa_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c))),V_z_2,c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,V_pa_2)))).
% 15.31/15.18  all T_b (class_Power_Opower(T_b)->c_Power_Opower__class_Opower(T_b)=c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b))).
% 15.31/15.18  all V_p V_c T_a (class_Rings_Ocomm__ring__1(T_a)->c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(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).
% 15.31/15.18  all V_x V_p V_n T_a (class_Rings_Ocomm__ring__1(T_a)->hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,c_Groups_Oone__class_Oone(T_a),V_n)),V_p)),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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)))).
% 15.31/15.18  all V_n V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(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))))),V_n)),V_n)=c_Groups_Oone__class_Oone(T_a)).
% 15.31/15.18  all V_q V_a V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)))).
% 15.31/15.18  all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)))).
% 15.31/15.18  all V_b_2 V_a_2 T_b (class_Groups_Ogroup__add(T_b)-> (c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)=c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)<->V_a_2=V_b_2)).
% 15.31/15.18  all V_b_2 V_a_2 T_b (class_Groups_Ogroup__add(T_b)-> (c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)=V_b_2<->c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)=V_a_2)).
% 15.31/15.18  all V_b_2 V_a_2 T_b (class_Groups_Ogroup__add(T_b)-> (V_a_2=c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)<->V_b_2=c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))).
% 15.31/15.18  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).
% 15.31/15.18  all V_w V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))).
% 15.31/15.18  all V_z3 V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3))).
% 15.31/15.18  all V_w V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w))).
% 15.31/15.18  all V_z2 V_z1 V_w (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))).
% 15.31/15.18  all V_w V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)).
% 15.31/15.18  all V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z).
% 15.31/15.18  all V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)=V_z).
% 15.31/15.18  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)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n))).
% 15.31/15.18  all V_b_2 V_n_2 V_a_2 T_b (class_Groups_Ozero(T_b)-> (c_Polynomial_Omonom(T_b,V_a_2,V_n_2)=c_Polynomial_Omonom(T_b,V_b_2,V_n_2)<->V_a_2=V_b_2)).
% 15.31/15.18  all V_y_2 V_x_2 T_b (class_Groups_Ozero(T_b)-> (c_Polynomial_Ocoeff(T_b,V_x_2)=c_Polynomial_Ocoeff(T_b,V_y_2)<->V_x_2=V_y_2)).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_q_2 V_pa_2 T_b (class_Groups_Ozero(T_b)-> (V_pa_2=V_q_2<-> (all B_n (hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),B_n)=hAPP(c_Polynomial_Ocoeff(T_b,V_q_2),B_n))))).
% 15.31/15.18  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)).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_n)).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  all V_a_2 T_b (class_Groups_Ogroup__add(T_b)-> (c_Groups_Ozero__class_Ozero(T_b)=c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)<->c_Groups_Ozero__class_Ozero(T_b)=V_a_2)).
% 15.31/15.18  all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (V_a_2=c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.18  all V_a_2 T_b (class_Groups_Ogroup__add(T_b)-> (c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.18  all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)=V_a_2<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.18  all V_b_2 V_a_2 T_b (class_Rings_Oidom(T_b)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)<->V_a_2=V_b_2|V_a_2=c_Groups_Ouminus__class_Ouminus(T_b,V_b_2))).
% 15.31/15.18  all V_b V_a T_a (class_Rings_Oring(T_a)->hAPP(hAPP(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))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 15.31/15.18  all V_b V_a T_a (class_Rings_Oring(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 15.31/15.18  all V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))).
% 15.31/15.18  all V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 15.31/15.18  all V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x))).
% 15.31/15.18  all V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 15.31/15.18  all V_b V_a T_a (class_Rings_Oring(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b)).
% 15.31/15.18  all V_b V_a T_a (class_Rings_Oring(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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).
% 15.31/15.18  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).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_p)).
% 15.31/15.18  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).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))).
% 15.31/15.18  all V_q V_a V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))).
% 15.31/15.18  c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  all V_b_2 V_a_2 T_b (class_Groups_Ogroup__add(T_b)-> (V_a_2=c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)<->c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.18  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)).
% 15.31/15.18  all V_x T_a (class_Rings_Ocomm__ring__1(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x)).
% 15.31/15.18  all V_x_2 T_b (class_Rings_Oring__1__no__zero__divisors(T_b)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)=c_Groups_Oone__class_Oone(T_b)<->V_x_2=c_Groups_Oone__class_Oone(T_b)|V_x_2=c_Groups_Ouminus__class_Ouminus(T_b,c_Groups_Oone__class_Oone(T_b)))).
% 15.31/15.18  all V_pa_2 V_a_2 T_b (class_Rings_Oidom(T_b)-> (c_Polynomial_Osmult(T_b,V_a_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))<->V_a_2=c_Groups_Ozero__class_Ozero(T_b)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Polynomial_Osmult(T_a,V_a,V_p))).
% 15.31/15.18  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).
% 15.31/15.18  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)).
% 15.31/15.18  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)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))).
% 15.31/15.18  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)))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_n_2 V_a_2 T_b (class_Groups_Ozero(T_b)-> (c_Polynomial_Omonom(T_b,V_a_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  all V_n V_a T_a (class_Rings_Oring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_a_2 V_times_2 V_one_2 T_b (hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_one_2).
% 15.31/15.18  all V_n_2 V_a_2 V_times_2 V_one_2 T_b (hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2))=hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),V_n_2))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_pa_2 T_b (class_Groups_Ozero(T_b)-> (hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),c_Polynomial_Odegree(T_b,V_pa_2))=c_Groups_Ozero__class_Ozero(T_b)<->V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))).
% 15.31/15.18  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)))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_x V_n V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))).
% 15.31/15.18  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)))).
% 15.31/15.18  all V_n V_b V_m V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))).
% 15.31/15.18  all V_q V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(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)))=hAPP(hAPP(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)))).
% 15.31/15.18  all V_y_2 V_x_2 T_b (class_Rings_Oidom(T_b)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))<->V_x_2=V_y_2|V_x_2=c_Groups_Ouminus__class_Ouminus(T_b,V_y_2))).
% 15.31/15.18  all V_y_2 V_x_2 T_b (class_Groups_Ogroup__add(T_b)-> (c_Groups_Oplus__class_Oplus(T_b,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_y_2=c_Groups_Ouminus__class_Ouminus(T_b,V_x_2))).
% 15.31/15.18  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)))).
% 15.31/15.18  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),hAPP(hAPP(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),hAPP(hAPP(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))).
% 15.31/15.18  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),hAPP(hAPP(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))).
% 15.31/15.18  all V_p V_a T_a (class_Rings_Oidom(T_a)->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(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)).
% 15.31/15.18  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)))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.31/15.18  c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.31/15.18  all V_z (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z))=V_z).
% 15.31/15.18  all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.31/15.18  all V_w V_z (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))).
% 15.31/15.18  all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.31/15.18  all V_n (c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n)=V_n).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Rings_Odvd__class_Odvd(T_a,V_a,V_a)).
% 15.31/15.18  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)))).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  all V_y_2 V_x_2 V_k_2 T_b (class_Fields_Ofield(T_b)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_k_2,c_Polynomial_Opoly__gcd(T_b,V_x_2,V_y_2))<->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_k_2,V_x_2)&c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_k_2,V_y_2))).
% 15.31/15.18  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))).
% 15.31/15.18  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))))).
% 15.31/15.18  all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)=V_z).
% 15.31/15.18  all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z).
% 15.31/15.18  all V_w V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)).
% 15.31/15.18  all V_z V_y V_x (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z))).
% 15.31/15.18  all V_z3 V_z2 V_z1 (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 15.31/15.18  all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))).
% 15.31/15.18  all V_k V_b V_a T_a (class_Rings_Odvd(T_a)-> (V_a=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)->c_Rings_Odvd__class_Odvd(T_a,V_b,V_a))).
% 15.31/15.18  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)->c_Rings_Odvd__class_Odvd(T_a,V_a,V_c))).
% 15.31/15.18  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)->c_Rings_Odvd__class_Odvd(T_a,V_b,V_c))).
% 15.31/15.18  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))))).
% 15.31/15.18  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)).
% 15.31/15.18  all V_y_2 V_x_2 T_b (class_Rings_Ocomm__ring__1(T_b)-> (c_Rings_Odvd__class_Odvd(T_b,V_x_2,c_Groups_Ouminus__class_Ouminus(T_b,V_y_2))<->c_Rings_Odvd__class_Odvd(T_b,V_x_2,V_y_2))).
% 15.31/15.18  all V_y_2 V_x_2 T_b (class_Rings_Ocomm__ring__1(T_b)-> (c_Rings_Odvd__class_Odvd(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_x_2),V_y_2)<->c_Rings_Odvd__class_Odvd(T_b,V_x_2,V_y_2))).
% 15.31/15.18  all V_n V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)->c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)))).
% 15.31/15.18  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)))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_y_2 V_x_2 T_b (class_Fields_Ofield(T_b)-> (c_Polynomial_Opoly__gcd(T_b,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))<->V_x_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))&V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))).
% 15.31/15.18  all V_b_2 V_ca_2 V_a_2 T_b (class_Rings_Oidom(T_b)-> (c_Rings_Odvd__class_Odvd(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))<->V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2))).
% 15.31/15.18  all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Oidom(T_b)-> (c_Rings_Odvd__class_Odvd(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))<->V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_q_2 V_pa_2 V_a_2 T_b (class_Fields_Ofield(T_b)-> (V_a_2!=c_Groups_Ozero__class_Ozero(T_b)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_pa_2,c_Polynomial_Osmult(T_b,V_a_2,V_q_2))<->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_pa_2,V_q_2)))).
% 15.31/15.18  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)))).
% 15.31/15.18  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)))).
% 15.31/15.18  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)))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_h_2 V_pa_2 T_b (class_Rings_Ocomm__semiring__0(T_b)-> (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_b,V_pa_2,V_h_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))<->V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))).
% 15.31/15.18  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)).
% 15.31/15.18  c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.18  all V_q_2 V_pa_2 V_a_2 T_b (class_Fields_Ofield(T_b)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),c_Polynomial_Osmult(T_b,V_a_2,V_pa_2),V_q_2)<-> (V_a_2=c_Groups_Ozero__class_Ozero(T_b)->V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))& (V_a_2!=c_Groups_Ozero__class_Ozero(T_b)->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_pa_2,V_q_2)))).
% 15.31/15.18  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))).
% 15.31/15.18  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)))).
% 15.31/15.18  all V_ca_2 V_pa_2 T_b (class_Rings_Oidom(T_b)-> (hAPP(c_Polynomial_Opoly(T_b,V_pa_2),V_ca_2)=c_Groups_Ozero__class_Ozero(T_b)<->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_ca_2),c_Polynomial_OpCons(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))),V_pa_2))).
% 15.31/15.18  all V_pa_2 V_ca_2 T_b (class_Rings_Oidom(T_b)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_ca_2,c_Polynomial_OpCons(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))),V_pa_2)<->hAPP(c_Polynomial_Opoly(T_b,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_b,V_ca_2))=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.18  all V_l_2 V_P_2 T_b (class_Rings_Odvd(T_b)&class_Rings_Osemiring__0(T_b)-> ((exists B_x hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x))))<-> (exists B_x (c_Rings_Odvd__class_Odvd(T_b,V_l_2,c_Groups_Oplus__class_Oplus(T_b,B_x,c_Groups_Ozero__class_Ozero(T_b)))&hBOOL(hAPP(V_P_2,B_x)))))).
% 15.31/15.18  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))))).
% 15.31/15.18  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)).
% 15.31/15.18  c_HOL_Obool_Obool__size(c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.18  c_HOL_Obool_Obool__size(c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.18  all V_y V_x T_a (class_Rings_Ocomm__ring__1(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))).
% 15.31/15.18  all V_k c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k).
% 15.31/15.18  all V_t_2 V_m_2 V_k_2 (V_k_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)-> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m_2,V_t_2)<->c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2)))).
% 15.31/15.18  all V_t_2 V_d_2 (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)<->c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2))).
% 15.31/15.18  all V_t_2 V_d_2 (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)<->c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2),V_t_2)).
% 15.31/15.18  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))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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))))).
% 15.31/15.18  all V_d_2 V_ca_2 V_b_2 V_a_2 T_b (class_Groups_Oab__group__add(T_b)-> (c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_b,V_ca_2,V_d_2)-> (V_a_2=V_b_2<->V_ca_2=V_d_2))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  all V_b_2 V_a_2 T_b (class_Rings_Odivision__ring__inverse__zero(T_b)-> (c_Rings_Oinverse__class_Oinverse(T_b,V_a_2)=c_Rings_Oinverse__class_Oinverse(T_b,V_b_2)<->V_a_2=V_b_2)).
% 15.31/15.18  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).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  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)))).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  all V_a_2 T_b (class_Rings_Odivision__ring__inverse__zero(T_b)-> (c_Rings_Oinverse__class_Oinverse(T_b,V_a_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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).
% 15.31/15.18  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)).
% 15.31/15.18  all V_b_2 V_a_2 T_b (class_Groups_Oab__group__add(T_b)-> (V_a_2=V_b_2<->c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.18  all V_b_2 V_a_2 T_b (class_Groups_Ogroup__add(T_b)-> (c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_a_2=V_b_2)).
% 15.31/15.18  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))).
% 15.31/15.18  all V_n V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_n)).
% 15.31/15.18  all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya))).
% 15.31/15.18  all V_b V_a_H V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b))).
% 15.31/15.18  all V_y V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y))).
% 15.31/15.18  all V_b_H V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H))).
% 15.31/15.18  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).
% 15.31/15.18  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).
% 15.31/15.18  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)).
% 15.31/15.18  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))))).
% 15.31/15.18  all V_n V_m V_k (c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n))-> (V_k!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n))).
% 15.31/15.18  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)).
% 15.31/15.18  all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.18  all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  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).
% 15.31/15.18  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).
% 15.31/15.18  all V_w V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))).
% 15.31/15.18  all V_z2 V_z1 V_w (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))).
% 15.31/15.18  all V_k V_n V_m (hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))).
% 15.31/15.18  all V_n V_m V_k (hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))).
% 15.31/15.18  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).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(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))))).
% 15.31/15.18  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)))).
% 15.31/15.18  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (hAPP(hAPP(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)).
% 15.31/15.18  all V_n 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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_n))).
% 15.31/15.18  all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_2 T_b (class_Rings_Oring(T_b)-> (c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2),V_ca_2)=c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2),V_d_2)<->c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)),V_e_2),V_ca_2)=V_d_2)).
% 15.31/15.18  all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_2 T_b (class_Rings_Oring(T_b)-> (c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2),V_ca_2)=c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2),V_d_2)<->V_ca_2=c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_b_2,V_a_2)),V_e_2),V_d_2))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(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,hAPP(hAPP(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)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)))).
% 15.31/15.18  all V_b V_a V_y V_x T_a (class_Rings_Oring(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b))).
% 15.31/15.18  all V_t_2 V_D_2 V_d_2 T_b (class_Rings_Ocomm__ring(T_b)&class_Rings_Odvd(T_b)-> (c_Rings_Odvd__class_Odvd(T_b,V_d_2,V_D_2)-> (all B_x B_k (c_Rings_Odvd__class_Odvd(T_b,V_d_2,c_Groups_Oplus__class_Oplus(T_b,B_x,V_t_2))<->c_Rings_Odvd__class_Odvd(T_b,V_d_2,c_Groups_Oplus__class_Oplus(T_b,c_Groups_Ominus__class_Ominus(T_b,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2)),V_t_2)))))).
% 15.31/15.18  all V_t_2 V_D_2 V_d_2 T_b (class_Rings_Ocomm__ring(T_b)&class_Rings_Odvd(T_b)-> (c_Rings_Odvd__class_Odvd(T_b,V_d_2,V_D_2)-> (all B_x B_k (c_Rings_Odvd__class_Odvd(T_b,V_d_2,c_Groups_Oplus__class_Oplus(T_b,B_x,V_t_2))<->c_Rings_Odvd__class_Odvd(T_b,V_d_2,c_Groups_Oplus__class_Oplus(T_b,c_Groups_Ominus__class_Ominus(T_b,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2)),V_t_2)))))).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_ca_2 V_t_2 V_x_2 V_d_2 V_a_2 (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_d_2)-> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2))<->c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_d_2)),V_t_2)))).
% 15.31/15.18  all V_m_2 V_n_2 V_k_2 (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_n_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)))<->c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,V_n_2)).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  all V_n_2 V_m_2 V_k_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(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)).
% 15.31/15.18  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)).
% 15.31/15.18  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).
% 15.31/15.18  all V_w V_z (c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))).
% 15.31/15.18  all V_w V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w)).
% 15.31/15.18  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)).
% 15.31/15.18  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))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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))))).
% 15.31/15.18  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(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))).
% 15.31/15.18  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(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))).
% 15.31/15.18  all V_x T_a (class_Rings_Oring__1(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a))=hAPP(hAPP(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)))).
% 15.31/15.18  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))).
% 15.31/15.18  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)))).
% 15.31/15.18  all V_n V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(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)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(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)))).
% 15.31/15.18  all V_p V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=c_Groups_Oone__class_Oone(tc_Nat_Onat))& (V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))).
% 15.31/15.18  all V_m V_n T_a (class_Power_Opower(T_a)-> (V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=c_Groups_Oone__class_Oone(T_a))& (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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)))))).
% 15.31/15.18  all V_a T_a (class_Fields_Ofield(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(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))).
% 15.31/15.18  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))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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))))).
% 15.31/15.18  all V_b V_n V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b),V_n))-> (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b))).
% 15.31/15.18  all V_x c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_x).
% 15.31/15.18  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)).
% 15.31/15.18  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).
% 15.31/15.18  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).
% 15.31/15.18  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))).
% 15.31/15.18  all V_y V_x (V_x=V_y->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)).
% 15.31/15.18  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)).
% 15.31/15.18  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).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  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)))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  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).
% 15.31/15.18  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).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_n V_m V_k (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n))-> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_n)->c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_m))).
% 15.31/15.18  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)).
% 15.31/15.18  all V_x c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.18  all V_x c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_x).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  all V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(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))).
% 15.31/15.18  all V_x_2 T_b (class_Fields_Ofield__inverse__zero(T_b)-> (c_Rings_Oinverse__class_Oinverse(T_b,V_x_2)=c_Groups_Oone__class_Oone(T_b)<->V_x_2=c_Groups_Oone__class_Oone(T_b))).
% 15.31/15.18  all V_b V_n V_a (c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b),V_n))-> (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b))).
% 15.31/15.18  all V_b_2 V_a_2 V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2))<->c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_b_2))).
% 15.31/15.18  all V_b_2 V_a_2 V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2))<->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a_2,V_b_2))).
% 15.31/15.18  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))).
% 15.31/15.18  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)))).
% 15.31/15.18  all V_x V_n T_a (class_Groups_Omonoid__mult(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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)))))).
% 15.31/15.18  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)).
% 15.31/15.18  all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)).
% 15.31/15.18  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)).
% 15.31/15.18  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)))).
% 15.31/15.18  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))))).
% 15.31/15.18  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))))).
% 15.31/15.18  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)).
% 15.31/15.18  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))))).
% 15.31/15.18  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))))).
% 15.31/15.18  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))))).
% 15.31/15.18  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))))).
% 15.31/15.18  all V_b_2 V_a_2 T_b (class_Fields_Olinordered__field__inverse__zero(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_b))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2)&c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b))&c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_b_2))).
% 15.31/15.18  all V_b_2 V_a_2 T_b (class_Fields_Olinordered__field__inverse__zero(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2)&c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b))&c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ozero__class_Ozero(T_b)))).
% 15.31/15.18  all V_ca_2 V_b_2 V_a_2 T_b (class_Fields_Olinordered__field__inverse__zero(T_b)-> (c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2))<-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)->c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))->c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)))& (-c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))->c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)))))).
% 15.31/15.18  all V_a_2 V_ca_2 V_b_2 T_b (class_Fields_Olinordered__field__inverse__zero(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2),V_a_2)<-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)->c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)))& (-c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))->c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2))))).
% 15.31/15.18  all V_b_2 V_a_2 V_ca_2 T_b (class_Fields_Olinordered__field(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2))<->c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)))).
% 15.31/15.18  all V_a_2 V_b_2 V_ca_2 T_b (class_Fields_Olinordered__field(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2),V_a_2)<->c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))))).
% 15.31/15.18  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,hAPP(hAPP(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)))).
% 15.31/15.18  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,hAPP(hAPP(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))))).
% 15.31/15.18  all V_b_2 V_a_2 V_ca_2 T_b (class_Fields_Olinordered__field(T_b)-> (c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))-> (c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2))<->c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))))).
% 15.31/15.18  all V_a_2 V_b_2 V_ca_2 T_b (class_Fields_Olinordered__field(T_b)-> (c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))-> (c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2),V_a_2)<->c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)))).
% 15.31/15.18  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),hAPP(hAPP(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)))))).
% 15.31/15.18  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),hAPP(hAPP(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)))))).
% 15.31/15.18  all V_w V_z V_y V_x T_a (class_Fields_Ofield__inverse__zero(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w))).
% 15.31/15.18  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))).
% 15.31/15.18  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)))))).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  all V_n V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n)=c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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))))).
% 15.31/15.18  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)))).
% 15.31/15.18  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)))).
% 15.31/15.18  all V_b_2 V_a_2 V_ca_2 T_b (class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,V_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_b,V_ca_2,V_b_2))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2))).
% 15.31/15.18  all V_b_2 V_ca_2 V_a_2 T_b (class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_b,V_b_2,V_ca_2))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2))).
% 15.31/15.18  all V_d_2 V_ca_2 V_b_2 V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_b,V_ca_2,V_d_2)-> (c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless(T_b,V_ca_2,V_d_2)))).
% 15.31/15.18  all V_b_2 V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2))<->c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))).
% 15.31/15.18  all V_b_2 V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2),V_b_2)<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2),V_a_2))).
% 15.31/15.18  all V_a_2 V_b_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.31/15.18  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)).
% 15.31/15.18  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  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).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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)))).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  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))))).
% 15.31/15.18  all V_t V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)->V_s!=V_t).
% 15.31/15.18  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)->V_m!=V_n).
% 15.31/15.18  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 15.31/15.18  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)).
% 15.31/15.18  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)))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_c V_b V_a T_a (class_Rings_Odivision__ring(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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)))).
% 15.31/15.18  all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))))).
% 15.31/15.18  all V_n V_m V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))).
% 15.31/15.18  all V_y_2 V_x_2 V_b_2 T_b (class_Rings_Olinordered__semidom(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),V_b_2)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2)))).
% 15.31/15.18  all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)-> (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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))).
% 15.31/15.18  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 15.31/15.18  all V_b V_a V_c T_a (class_Rings_Odivision__ring(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)-> (hAPP(hAPP(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)))).
% 15.31/15.18  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=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)->c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)=V_a))).
% 15.31/15.18  all V_a_2 V_b_2 V_ca_2 T_b (class_Rings_Odivision__ring(T_b)-> (V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)-> (c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)=V_a_2<->V_b_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)))).
% 15.31/15.18  all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Odivision__ring(T_b)-> (V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)-> (V_a_2=c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)<->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)=V_b_2))).
% 15.31/15.18  all V_w_2 V_x_2 V_z_2 V_y_2 T_b (class_Fields_Ofield(T_b)-> (V_y_2!=c_Groups_Ozero__class_Ozero(T_b)-> (V_z_2!=c_Groups_Ozero__class_Ozero(T_b)-> (c_Rings_Oinverse__class_Odivide(T_b,V_x_2,V_y_2)=c_Rings_Oinverse__class_Odivide(T_b,V_w_2,V_z_2)<->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2))))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))).
% 15.31/15.18  all V_a_2 V_ca_2 V_b_2 T_b (class_Fields_Ofield__inverse__zero(T_b)-> (c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)=V_a_2<-> (V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)->V_b_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))& (V_ca_2=c_Groups_Ozero__class_Ozero(T_b)->V_a_2=c_Groups_Ozero__class_Ozero(T_b)))).
% 15.31/15.18  all V_ca_2 V_b_2 V_a_2 T_b (class_Fields_Ofield__inverse__zero(T_b)-> (V_a_2=c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)<-> (V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)=V_b_2)& (V_ca_2=c_Groups_Ozero__class_Ozero(T_b)->V_a_2=c_Groups_Ozero__class_Ozero(T_b)))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_a_2 V_b_2 T_b (class_Rings_Odivision__ring(T_b)-> (V_b_2!=c_Groups_Ozero__class_Ozero(T_b)-> (c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2)=c_Groups_Oone__class_Oone(T_b)<->V_a_2=V_b_2))).
% 15.31/15.18  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)))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_n V_a V_b T_a (class_Fields_Ofield(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n)=c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))).
% 15.31/15.18  all V_n V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a)),V_n)).
% 15.31/15.18  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))).
% 15.31/15.18  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))).
% 15.31/15.18  all V_b V_a T_a (class_Fields_Ofield(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))).
% 15.31/15.18  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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.31/15.18  all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2)))).
% 15.31/15.18  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),hAPP(hAPP(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)))).
% 15.31/15.18  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),hAPP(hAPP(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)))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.31/15.18  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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))).
% 15.31/15.18  all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)))).
% 15.31/15.18  all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)&c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))&c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2))).
% 15.31/15.18  all V_b_2 V_ca_2 V_a_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)&c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))&c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2))).
% 15.31/15.18  all V_a T_a (class_Rings_Olinordered__ring(T_a)-> -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a))).
% 15.31/15.18  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))))).
% 15.31/15.18  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))))).
% 15.31/15.18  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))))).
% 15.31/15.18  all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_b))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)))).
% 15.31/15.18  all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_b))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)))).
% 15.31/15.18  all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_a_2))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2))).
% 15.31/15.18  all V_b_2 V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_b)))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)))).
% 15.31/15.18  all V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2))).
% 15.31/15.18  all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2),V_a_2)<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2))).
% 15.31/15.18  all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)))).
% 15.31/15.18  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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))))).
% 15.31/15.18  all V_n 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,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))).
% 15.31/15.18  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)))).
% 15.31/15.18  all V_n_2 V_m_2 V_a_2 T_b (class_Rings_Olinordered__semidom(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),V_a_2)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2)=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)<->V_m_2=V_n_2))).
% 15.31/15.18  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)))).
% 15.31/15.18  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)))).
% 15.31/15.18  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))))).
% 15.31/15.18  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))))).
% 15.31/15.18  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))))).
% 15.31/15.18  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)))).
% 15.31/15.18  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)))).
% 15.31/15.18  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)))).
% 15.31/15.18  all V_a_2 T_b (class_Fields_Olinordered__field__inverse__zero(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Oinverse(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)))).
% 15.31/15.18  all V_a_2 T_b (class_Fields_Olinordered__field__inverse__zero(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Rings_Oinverse__class_Oinverse(T_b,V_a_2))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2))).
% 15.31/15.18  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)))).
% 15.31/15.18  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)).
% 15.31/15.18  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)))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m))).
% 15.31/15.18  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)).
% 15.31/15.18  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))))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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)))).
% 15.31/15.18  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)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)<->V_m_2=V_n_2)).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(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))).
% 15.31/15.18  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(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)).
% 15.31/15.18  all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(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)).
% 15.31/15.18  all V_n_2 V_k_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(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)).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))).
% 15.31/15.18  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))).
% 15.31/15.18  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)).
% 15.31/15.18  all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(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)).
% 15.31/15.18  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)).
% 15.31/15.18  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)).
% 15.31/15.18  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).
% 15.31/15.18  all V_n V_m V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 15.31/15.18  all V_n_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.18  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)))).
% 15.31/15.18  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))).
% 15.31/15.18  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))).
% 15.31/15.18  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)))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z))))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_z))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_y))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x),V_y),V_z))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_y))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z))))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_z))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x),V_y),V_z))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)),V_h)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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)),hAPP(hAPP(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))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_y_2 V_x_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)))<->V_x_2!=c_Groups_Ozero__class_Ozero(T_b)|V_y_2!=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a))).
% 15.31/15.18  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)))).
% 15.31/15.18  all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_2 T_b (class_Rings_Oordered__ring(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2),V_d_2))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2))).
% 15.31/15.18  all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_2 T_b (class_Rings_Oordered__ring(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2),V_d_2))<->c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_b_2,V_a_2)),V_e_2),V_d_2)))).
% 15.31/15.18  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 15.31/15.18  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 15.31/15.18  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))))).
% 15.31/15.18  all V_x_2 T_b (class_Fields_Olinordered__field__inverse__zero(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),c_Rings_Oinverse__class_Oinverse(T_b,V_x_2))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_x_2)&c_Orderings_Oord__class_Oless(T_b,V_x_2,c_Groups_Oone__class_Oone(T_b)))).
% 15.31/15.18  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))))).
% 15.31/15.18  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)))).
% 15.31/15.18  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)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)))).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))).
% 15.31/15.18  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)).
% 15.31/15.18  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).
% 15.31/15.18  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(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))).
% 15.31/15.18  all V_n V_m V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(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))).
% 15.31/15.18  all V_b_2 V_a_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))<-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)->hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))& (all B_d (V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)->hBOOL(hAPP(V_P_2,B_d))))).
% 15.31/15.18  all V_b_2 V_a_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))<-> -(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)& -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| (exists B_d (V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)& -hBOOL(hAPP(V_P_2,B_d)))))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_n 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_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 15.31/15.18  all V_n 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_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a))))).
% 15.31/15.18  all V_x V_n T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|V_x=c_Groups_Oone__class_Oone(T_a)->c_Rings_Odvd__class_Odvd(T_a,V_x,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)))).
% 15.31/15.18  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).
% 15.31/15.18  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)))).
% 15.31/15.18  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,hAPP(hAPP(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))).
% 15.31/15.18  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,hAPP(hAPP(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))).
% 15.31/15.18  all V_n_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),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_x_2)).
% 15.31/15.18  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))).
% 15.31/15.18  all V_b_2 V_a_2 T_b (class_Divides_Osemiring__div(T_b)-> (c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2)<->c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2)=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_n V_m V_k (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))-> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_n)->c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_m))).
% 15.31/15.18  all V_n V_m V_f (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_f,V_m)-> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_f,V_n)->c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_f,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)))).
% 15.31/15.18  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))).
% 15.31/15.18  all V_m V_y V_x (c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m)=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y),V_m)).
% 15.31/15.18  all V_y V_m V_x (c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m),V_y),V_m)=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y),V_m)).
% 15.31/15.18  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)).
% 15.31/15.18  all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k))).
% 15.31/15.18  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)).
% 15.31/15.18  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)))).
% 15.31/15.18  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=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q)))).
% 15.31/15.18  all V_d_2 V_m_2 (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<-> (exists B_q (V_m_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q)))).
% 15.31/15.18  all V_m V_n V_k (c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(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)).
% 15.31/15.18  all V_b V_a (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b))).
% 15.31/15.18  all V_b V_a (c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))).
% 15.31/15.18  all V_m V_x (c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m)=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_x),V_m)).
% 15.31/15.18  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).
% 15.31/15.18  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)).
% 15.31/15.18  all V_y V_m V_x (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m)).
% 15.31/15.18  all V_k V_n V_m (hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))).
% 15.31/15.18  all V_n V_m V_k (hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))).
% 15.31/15.18  all V_c V_b V_a (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c)).
% 15.31/15.18  all V_c V_b V_a (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)).
% 15.31/15.18  all V_b (c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.31/15.18  all V_a (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.31/15.18  all V_a V_b (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b)).
% 15.31/15.18  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)).
% 15.31/15.18  all V_a V_b (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))).
% 15.31/15.18  all V_l V_k (c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k),V_l)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.31/15.18  all V_l V_k (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_l))!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.31/15.18  all V_y_2 V_n_2 V_x_2 (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_n_2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_n_2)<->c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x_2,V_y_2))).
% 15.31/15.19  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,hAPP(hAPP(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)).
% 15.31/15.19  all V_b V_a ((c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))& (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b))).
% 15.31/15.19  all V_b V_a ((c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))& (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))).
% 15.31/15.19  c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 15.31/15.19  all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)->c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)))).
% 15.31/15.19  all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)|V_w_2=V_z_2).
% 15.31/15.19  all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.31/15.19  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m,V_n)-> -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m))).
% 15.31/15.19  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c)),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)))).
% 15.31/15.19  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i),B_j)->hBOOL(hAPP(V_P_2,B_j))))))).
% 15.31/15.19  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(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k)=c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 15.31/15.19  all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.31/15.19  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint)<->V_m_2=c_Groups_Oone__class_Oone(tc_Int_Oint)&V_n_2=c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 15.31/15.19  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)).
% 15.31/15.19  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)).
% 15.31/15.19  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).
% 15.31/15.19  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)).
% 15.31/15.19  all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)).
% 15.31/15.19  all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c)).
% 15.31/15.19  all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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)).
% 15.31/15.19  all V_b V_a V_c T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))).
% 15.31/15.19  all V_b V_c V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c)).
% 15.31/15.19  all V_b V_c V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)).
% 15.31/15.19  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c)))).
% 15.31/15.19  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)).
% 15.31/15.19  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)).
% 15.31/15.19  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)).
% 15.31/15.19  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)).
% 15.31/15.19  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)).
% 15.31/15.19  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)).
% 15.31/15.19  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)).
% 15.31/15.19  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)))).
% 15.31/15.19  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)))).
% 15.31/15.19  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)).
% 15.31/15.19  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)).
% 15.31/15.19  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)).
% 15.31/15.19  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))).
% 15.31/15.19  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)).
% 15.31/15.19  all V_m_2 V_n_2 V_k_2 T_b (class_Divides_Osemiring__div(T_b)-> (c_Rings_Odvd__class_Odvd(T_b,V_k_2,V_n_2)-> (c_Rings_Odvd__class_Odvd(T_b,V_k_2,c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2))<->c_Rings_Odvd__class_Odvd(T_b,V_k_2,V_m_2)))).
% 15.31/15.19  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))).
% 15.31/15.19  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))))).
% 15.31/15.19  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)))).
% 15.31/15.19  all V_a V_b T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.19  all V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.19  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)).
% 15.31/15.19  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b)).
% 15.31/15.19  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b)).
% 15.31/15.19  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))))))).
% 15.31/15.19  all V_r_2 V_q_2 V_y_2 V_x_2 T_b (class_Fields_Ofield(T_b)-> (c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)<->V_x_2=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2),V_y_2),V_r_2)& (V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))->V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))& (V_y_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))->V_r_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_b,V_r_2),c_Polynomial_Odegree(T_b,V_y_2))))).
% 15.31/15.19  all V_y V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x)).
% 15.31/15.19  all V_r_2 V_q_2 V_y_2 T_b (class_Fields_Ofield(T_b)-> (c_Polynomial_Opdivmod__rel(T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),V_y_2,V_q_2,V_r_2)<->V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))&V_r_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))).
% 15.31/15.19  all V_r_2 V_q_2 V_x_2 T_b (class_Fields_Ofield(T_b)-> (c_Polynomial_Opdivmod__rel(T_b,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),V_q_2,V_r_2)<->V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))&V_r_2=V_x_2)).
% 15.31/15.19  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)))).
% 15.31/15.19  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)).
% 15.31/15.19  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)))).
% 15.31/15.19  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)).
% 15.31/15.19  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))).
% 15.31/15.19  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))).
% 15.31/15.19  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))).
% 15.31/15.19  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,hAPP(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_r_H),V_r))))).
% 15.31/15.19  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)))).
% 15.31/15.19  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))).
% 15.31/15.19  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))).
% 15.31/15.19  all V_pa_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Polynomial_Opos__poly(T_b,V_pa_2)<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),c_Polynomial_Odegree(T_b,V_pa_2))))).
% 15.31/15.19  all V_pa_2 V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Polynomial_Opos__poly(T_b,c_Polynomial_OpCons(T_b,V_a_2,V_pa_2))<->c_Polynomial_Opos__poly(T_b,V_pa_2)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))&c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2))).
% 15.31/15.19  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)))).
% 15.31/15.19  all V_y_2 V_x_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_b),V_x_2,V_y_2)<->c_Polynomial_Opos__poly(T_b,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_b),V_y_2,V_x_2)))).
% 15.31/15.19  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))))).
% 15.31/15.19  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))))).
% 15.31/15.19  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))).
% 15.31/15.19  all V_k 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_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))).
% 15.31/15.19  all V_z V_x V_d (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)),V_z)).
% 15.31/15.19  all V_c V_b V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_c),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c))).
% 15.31/15.19  all V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)&c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_a).
% 15.31/15.19  all V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.19  all V_b V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.31/15.19  all V_a_2 V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))).
% 15.31/15.19  all V_a_2 V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2))).
% 15.31/15.19  all V_b V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))).
% 15.31/15.19  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))).
% 15.31/15.19  all V_a_2 T_b (class_Groups_Oordered__ab__group__add__abs(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Oabs__class_Oabs(T_b,V_a_2))<->V_a_2!=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.19  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a)).
% 15.31/15.19  all V_d V_b V_c V_a T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))))).
% 15.31/15.19  all V_b_2 V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Oabs__class_Oabs(T_b,V_a_2),V_b_2)<->c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)&c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2),V_b_2))).
% 15.31/15.19  all V_x V_y T_a (class_Divides_Oring__div(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)->c_Divides_Odiv__class_Odiv(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y))=c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)))).
% 15.31/15.19  all V_x V_y T_a (class_Divides_Oring__div(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y)=c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)))).
% 15.31/15.19  all V_n V_x V_y T_a (class_Divides_Osemiring__div(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),V_n)=c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)))).
% 15.31/15.19  all V_b V_a T_a (class_Fields_Olinordered__field__inverse__zero(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))).
% 15.31/15.19  all T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.19  all V_a_2 T_b (class_Groups_Oordered__ab__group__add__abs(T_b)-> (c_Groups_Oabs__class_Oabs(T_b,V_a_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.19  all V_a T_a (class_Rings_Olinordered__idom(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)).
% 15.31/15.19  all V_b V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))).
% 15.31/15.19  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))).
% 15.31/15.19  all T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a)).
% 15.31/15.19  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Oabs__class_Oabs(T_a,V_a)).
% 15.31/15.19  all V_n V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n)).
% 15.31/15.19  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a))=c_Groups_Oabs__class_Oabs(T_a,V_a)).
% 15.31/15.19  all V_k_2 V_m_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Rings_Odvd__class_Odvd(T_b,V_m_2,c_Groups_Oabs__class_Oabs(T_b,V_k_2))<->c_Rings_Odvd__class_Odvd(T_b,V_m_2,V_k_2))).
% 15.31/15.19  all V_k_2 V_m_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Rings_Odvd__class_Odvd(T_b,c_Groups_Oabs__class_Oabs(T_b,V_m_2),V_k_2)<->c_Rings_Odvd__class_Odvd(T_b,V_m_2,V_k_2))).
% 15.31/15.19  all V_k V_l T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Oabs__class_Oabs(T_a,V_l)=c_Groups_Oabs__class_Oabs(T_a,V_k)->c_Rings_Odvd__class_Odvd(T_a,V_l,V_k))).
% 15.31/15.19  all V_a T_a (class_Fields_Olinordered__field__inverse__zero(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a))).
% 15.31/15.19  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))).
% 15.31/15.19  all V_b V_a (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b)-> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_b,V_a)->c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_a)=c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_b))).
% 15.31/15.19  all V_x_2 (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_x_2,c_Groups_Oone__class_Oone(tc_Int_Oint))<->c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)=c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 15.31/15.19  all V_n V_m (c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n))=c_Groups_Oone__class_Oone(tc_Int_Oint)->c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m)=c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 15.31/15.19  all V_n V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n))=c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 15.31/15.19  all V_a T_a (class_Fields_Olinordered__field(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)))).
% 15.31/15.19  all V_a V_b T_a (class_Fields_Olinordered__field(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))).
% 15.31/15.19  all V_ca_2 V_b_2 V_a_2 T_b (class_Divides_Osemiring__div(T_b)-> (c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2)-> (c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_ca_2)-> (c_Rings_Odvd__class_Odvd(T_b,c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2),c_Divides_Odiv__class_Odiv(T_b,V_ca_2,V_a_2))<->c_Rings_Odvd__class_Odvd(T_b,V_b_2,V_ca_2))))).
% 15.31/15.19  all V_x V_y (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_y,V_x)->c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_y))).
% 15.31/15.19  all V_a (V_a!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a)=c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 15.31/15.19  all V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a).
% 15.31/15.19  all V_b V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b)).
% 15.31/15.19  all V_b V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)).
% 15.31/15.19  all V_b (c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.31/15.19  all V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.19  all V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.19  all V_y V_x V_z T_a (class_Divides_Osemiring__div(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_z,V_x)-> (c_Rings_Odvd__class_Odvd(T_a,V_z,V_y)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_z)=c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_z),c_Divides_Odiv__class_Odiv(T_a,V_y,V_z))))).
% 15.31/15.19  all V_b V_a T_a (class_Divides_Osemiring__div(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a))=V_b)).
% 15.31/15.19  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)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_c))=c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c))).
% 15.31/15.19  all V_b V_a T_a (class_Divides_Osemiring__div(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_a)=V_b)).
% 15.31/15.19  all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_c)=c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c),V_a))).
% 15.31/15.19  all V_w V_z V_x V_y T_a (class_Divides_Osemiring__div(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)-> (c_Rings_Odvd__class_Odvd(T_a,V_z,V_w)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),c_Divides_Odiv__class_Odiv(T_a,V_w,V_z))=c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z))))).
% 15.31/15.19  all V_a T_a (class_Divides_Osemiring__div(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,V_a,V_a)=c_Groups_Oone__class_Oone(T_a))).
% 15.31/15.19  all V_m V_n (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n))=V_m).
% 15.31/15.19  all V_b V_a V_c T_a (class_Divides_Osemiring__div(T_a)-> (V_c=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=c_Groups_Ozero__class_Ozero(T_a))& (V_c!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))).
% 15.31/15.19  all V_a V_b T_a (class_Divides_Osemiring__div(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b)=V_a)).
% 15.31/15.19  all V_a V_b T_a (class_Divides_Osemiring__div(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b)=V_a)).
% 15.31/15.19  all V_b V_a V_c T_a (class_Divides_Osemiring__div(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))).
% 15.31/15.19  all V_b V_a V_c T_a (class_Divides_Osemiring__div(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))).
% 15.31/15.19  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Oabs__class_Oabs(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a))).
% 15.31/15.19  all V_a T_a (class_Groups_Oabs__if(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Oabs__class_Oabs(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a))& (-c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a)).
% 15.31/15.19  all V_x V_y T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_x),V_y)=c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)))).
% 15.31/15.19  all V_k V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x))).
% 15.31/15.19  all V_b V_a V_c (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c)).
% 15.31/15.19  all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))<->V_z_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.31/15.19  all V_i ((c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))->c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_i))& (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))->c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)=V_i)).
% 15.31/15.19  all V_k V_b V_a (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_k)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_k)).
% 15.31/15.19  all V_k V_a V_b (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_k)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_k)).
% 15.31/15.19  all V_c V_b V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c))).
% 15.31/15.19  all V_b V_a (V_a=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))).
% 15.31/15.19  all V_n V_m (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n)),V_n))).
% 15.31/15.19  all V_m V_n (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))).
% 15.31/15.19  all V_c V_a V_b T_a (class_Divides_Osemiring__div(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b)=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))).
% 15.31/15.19  all V_c V_a V_b T_a (class_Divides_Osemiring__div(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b)=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))).
% 15.31/15.19  all V_a V_b T_a (class_Divides_Osemiring__div(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a)))).
% 15.31/15.19  all V_a V_b T_a (class_Divides_Osemiring__div(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b)=c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a)))).
% 15.31/15.19  all V_ca_2 V_b_2 V_a_2 T_b (class_Divides_Osemiring__div(T_b)-> (V_a_2!=c_Groups_Ozero__class_Ozero(T_b)-> (c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2)-> (c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2)=V_ca_2<->V_b_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2))))).
% 15.31/15.19  all V_d_2 V_b_2 V_ca_2 V_a_2 T_b (class_Divides_Osemiring__div(T_b)-> (V_a_2!=c_Groups_Ozero__class_Ozero(T_b)-> (V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)-> (c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2)-> (c_Rings_Odvd__class_Odvd(T_b,V_ca_2,V_d_2)-> (c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2)=c_Divides_Odiv__class_Odiv(T_b,V_d_2,V_ca_2)<->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2))))))).
% 15.31/15.19  all V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b))=V_a).
% 15.31/15.19  all V_a V_b T_a (class_Divides_Osemiring__div(T_a)->c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))=V_a).
% 15.31/15.19  all V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))=V_a).
% 15.31/15.19  all V_c V_a V_b T_a (class_Divides_Osemiring__div(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 15.31/15.19  all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 15.31/15.19  all V_n_2 V_m_2 (V_m_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)-> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2),V_m_2)<->c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 15.31/15.19  all V_n_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))<->V_x_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.19  all V_b V_a V_c (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)->c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))).
% 15.31/15.19  all V_a V_b (V_b!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)-> (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)))& (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Oone__class_Oone(tc_Int_Oint)))).
% 15.31/15.19  all V_a V_b (V_b!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)-> (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)))& (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Oone__class_Oone(tc_Int_Oint)))).
% 15.31/15.19  all V_x V_z V_d (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))).
% 15.31/15.19  all V_r_2 V_a_2 V_x_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Oabs__class_Oabs(T_b,c_Groups_Ominus__class_Ominus(T_b,V_x_2,V_a_2)),V_r_2)<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_r_2),V_x_2)&c_Orderings_Oord__class_Oless(T_b,V_x_2,c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_r_2)))).
% 15.31/15.19  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)))))).
% 15.31/15.19  all V_c V_b V_a (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_c),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c)),V_c))).
% 15.31/15.19  all V_y V_x T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))).
% 15.31/15.19  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.19  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_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)=V_q)).
% 15.31/15.19  all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Osgn__class_Osgn(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)))).
% 15.31/15.19  all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2))).
% 15.31/15.19  all V_z V_y V_x T_a (class_Fields_Ofield(T_a)->c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z))=c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z)).
% 15.31/15.19  all V_y V_x T_a (class_Fields_Ofield(T_a)->c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y))=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y))).
% 15.31/15.19  all V_y V_x T_a (class_Fields_Ofield(T_a)->c_Divides_Odiv__class_Odiv(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_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y))).
% 15.31/15.19  all V_x T_a (class_Rings_Olinordered__idom(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x))=V_x).
% 15.31/15.19  all V_k T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,V_k)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k))).
% 15.31/15.19  all V_y V_x V_a T_a (class_Fields_Ofield(T_a)->c_Divides_Odiv__class_Odiv(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_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y))).
% 15.31/15.19  all V_n V_m V_k ((V_k=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (V_k!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n))).
% 15.31/15.19  all V_m (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=V_m).
% 15.31/15.19  all V_c V_b V_a (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c)).
% 15.31/15.19  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)).
% 15.31/15.19  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))).
% 15.31/15.19  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)).
% 15.31/15.19  all V_b V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(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))).
% 15.31/15.19  all V_y V_x T_a (class_RealVector_Oreal__normed__div__algebra(T_a)->c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))=hAPP(hAPP(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))).
% 15.31/15.19  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)).
% 15.31/15.19  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)).
% 15.31/15.19  all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Groups_Osgn__class_Osgn(T_b,V_a_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.19  all V_x_2 T_b (class_RealVector_Oreal__normed__vector(T_b)-> (c_Groups_Osgn__class_Osgn(T_b,V_x_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_x_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.19  all V_n V_m V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)).
% 15.31/15.19  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n)=V_m).
% 15.31/15.19  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n)=V_m).
% 15.31/15.19  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(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_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m))).
% 15.31/15.19  all V_c V_b V_a (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c)),V_c))).
% 15.31/15.19  all V_c V_b V_a (c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b))).
% 15.31/15.19  all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_n)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))).
% 15.31/15.19  all V_m V_n (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))).
% 15.31/15.19  all V_n V_m (c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_n))).
% 15.31/15.19  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_Odiv(tc_Polynomial_Opoly(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),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)))).
% 15.31/15.19  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_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.31/15.19  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))).
% 15.31/15.19  all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Groups_Osgn__class_Osgn(T_b,V_a_2)=c_Groups_Oone__class_Oone(T_b)<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2))).
% 15.31/15.19  all V_z V_y V_x T_a (class_Fields_Ofield(T_a)->c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z))=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))).
% 15.31/15.19  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,V_m,V_n)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)))).
% 15.31/15.19  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,V_m,V_n)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)))).
% 15.31/15.19  all V_k_2 V_n_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))& (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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i),B_j)->hBOOL(hAPP(V_P_2,B_i))))))).
% 15.31/15.19  all V_x T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))->c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x))& (-c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))->c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x)=V_x)).
% 15.31/15.19  all V_c V_a (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(V_a),V_c)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_c),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c),c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)),V_c))).
% 15.31/15.19  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)))).
% 15.31/15.19  all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Groups_Osgn__class_Osgn(T_b,V_a_2)=c_Groups_Ouminus__class_Ouminus(T_b,c_Groups_Oone__class_Oone(T_b))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)))).
% 15.31/15.19  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))))).
% 15.31/15.19  all V_n_2 V_P_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)-> (hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))<-> (all B_i B_j (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j)&c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)&V_n_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)->hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)))))).
% 15.31/15.19  all V_n_2 V_P_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))<-> (all B_i B_j (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j)&c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))&V_n_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)->hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)))))).
% 15.31/15.19  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a))).
% 15.31/15.19  all V_a_2 T_b (class_Groups_Oordered__ab__group__add__abs(T_b)-> (c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Oabs__class_Oabs(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.19  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a)).
% 15.31/15.19  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a))).
% 15.31/15.19  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b))).
% 15.31/15.19  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))).
% 15.31/15.19  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a))).
% 15.31/15.19  all V_b_2 V_a_2 T_b (class_Groups_Oordered__ab__group__add__abs(T_b)-> (c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Oabs__class_Oabs(T_b,V_a_2),V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2,V_b_2)&c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2),V_b_2))).
% 15.31/15.19  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(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_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)))).
% 15.31/15.19  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b))).
% 15.31/15.19  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))).
% 15.31/15.19  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))).
% 15.31/15.19  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)))).
% 15.31/15.19  all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y)))).
% 15.31/15.19  all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)-> (c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2,V_b_2)))).
% 15.31/15.19  all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))-> (c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2,V_a_2)))).
% 15.31/15.19  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))).
% 15.31/15.19  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))).
% 15.31/15.19  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))).
% 15.31/15.19  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))).
% 15.31/15.19  all V_b V_c V_a T_a (class_Rings_Olinordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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)))).
% 15.31/15.19  all V_b V_c V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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)))).
% 15.31/15.19  all V_b V_a V_c T_a (class_Rings_Olinordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(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)))).
% 15.31/15.19  all V_b V_a V_c T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(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)))).
% 15.31/15.19  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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)))).
% 15.31/15.19  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(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)))).
% 15.31/15.19  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))))).
% 15.31/15.19  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))))).
% 15.31/15.19  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))))).
% 15.31/15.19  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))))).
% 15.31/15.19  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))))).
% 15.31/15.19  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))))).
% 15.31/15.19  all V_y_2 V_x_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_b))<->V_x_2=c_Groups_Ozero__class_Ozero(T_b)&V_y_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.19  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))).
% 15.31/15.19  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x))))).
% 15.31/15.19  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x))))).
% 15.31/15.19  all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))-> (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,V_a,V_b)))).
% 15.31/15.19  all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_2 T_b (class_Rings_Oordered__ring(T_b)-> (c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2),V_d_2))<->c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2))).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Groups_Ocancel__ab__semigroup__add(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Rings_Oring__1__no__zero__divisors(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Rings_Oring__no__zero__divisors(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Groups_Ocancel__semigroup__add(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Groups_Oab__semigroup__mult(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Groups_Ocomm__monoid__mult(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Groups_Oab__semigroup__add(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Rings_Ono__zero__divisors(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Groups_Ocomm__monoid__add(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Rings_Ocomm__semiring__1(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Rings_Ocomm__semiring__0(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Rings_Ocomm__semiring(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Groups_Oab__group__add(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Rings_Ozero__ne_q__one(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Groups_Omonoid__mult(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Rings_Ocomm__ring__1(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Groups_Omonoid__add(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Rings_Osemiring__0(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Groups_Ogroup__add(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Rings_Omult__zero(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Rings_Ocomm__ring(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Rings_Osemiring(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Rings_Oring__1(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Power_Opower(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Groups_Ozero(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Rings_Oring(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Groups_Oone(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Rings_Odvd(T)).
% 15.31/15.19  all T (class_Rings_Oidom(T)->class_Groups_Ocancel__comm__monoid__add(T)).
% 15.31/15.19  all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat).
% 15.31/15.19  class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint).
% 15.31/15.19  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 15.31/15.19  class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 15.31/15.19  class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 15.31/15.19  class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 15.31/15.19  class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 15.31/15.19  class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint).
% 15.31/15.19  class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 15.31/15.19  class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 15.31/15.19  class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 15.31/15.19  class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 15.31/15.19  class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 15.31/15.19  class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 15.31/15.19  class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 15.31/15.19  class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 15.31/15.19  class_Rings_Olinordered__semiring(tc_Int_Oint).
% 15.31/15.19  class_Rings_Olinordered__semidom(tc_Int_Oint).
% 15.31/15.19  class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 15.31/15.19  class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 15.31/15.19  class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 15.31/15.19  class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 15.31/15.19  class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 15.31/15.19  class_Rings_Olinordered__ring(tc_Int_Oint).
% 15.31/15.19  class_Rings_Olinordered__idom(tc_Int_Oint).
% 15.31/15.19  class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 15.31/15.19  class_Rings_Ocomm__semiring__0(tc_Int_Oint).
% 15.31/15.19  class_Divides_Osemiring__div(tc_Int_Oint).
% 15.31/15.19  class_Rings_Ocomm__semiring(tc_Int_Oint).
% 15.31/15.19  class_Groups_Oab__group__add(tc_Int_Oint).
% 15.31/15.19  class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 15.31/15.19  class_Rings_Oordered__ring(tc_Int_Oint).
% 15.31/15.19  class_Groups_Omonoid__mult(tc_Int_Oint).
% 15.31/15.19  class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 15.31/15.19  class_Groups_Omonoid__add(tc_Int_Oint).
% 15.31/15.19  class_Rings_Osemiring__0(tc_Int_Oint).
% 15.31/15.19  class_Groups_Ogroup__add(tc_Int_Oint).
% 15.31/15.19  class_Divides_Oring__div(tc_Int_Oint).
% 15.31/15.19  class_Rings_Omult__zero(tc_Int_Oint).
% 15.31/15.19  class_Rings_Ocomm__ring(tc_Int_Oint).
% 15.31/15.19  class_Int_Oring__char__0(tc_Int_Oint).
% 15.31/15.19  class_Rings_Osemiring(tc_Int_Oint).
% 15.31/15.19  class_Groups_Osgn__if(tc_Int_Oint).
% 15.31/15.19  class_Groups_Oabs__if(tc_Int_Oint).
% 15.31/15.19  class_Rings_Oring__1(tc_Int_Oint).
% 15.31/15.19  class_Power_Opower(tc_Int_Oint).
% 15.31/15.19  class_Groups_Ozero(tc_Int_Oint).
% 15.31/15.19  class_Rings_Oring(tc_Int_Oint).
% 15.31/15.19  class_Rings_Oidom(tc_Int_Oint).
% 15.31/15.19  class_Groups_Oone(tc_Int_Oint).
% 15.31/15.19  class_Rings_Odvd(tc_Int_Oint).
% 15.31/15.19  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 15.31/15.19  class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 15.31/15.19  class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 15.31/15.19  class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 15.31/15.19  class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 15.31/15.19  class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 15.31/15.19  class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 15.31/15.19  class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 15.31/15.19  class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 15.31/15.19  class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 15.31/15.19  class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 15.31/15.19  class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 15.31/15.19  class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 15.31/15.19  class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 15.31/15.19  class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 15.31/15.19  class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 15.31/15.19  class_Rings_Ocomm__semiring__0(tc_Nat_Onat).
% 15.31/15.19  class_Divides_Osemiring__div(tc_Nat_Onat).
% 15.31/15.19  class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 15.31/15.19  class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 15.31/15.19  class_Groups_Omonoid__mult(tc_Nat_Onat).
% 15.31/15.19  class_Groups_Omonoid__add(tc_Nat_Onat).
% 15.31/15.19  class_Rings_Osemiring__0(tc_Nat_Onat).
% 15.31/15.19  class_Rings_Omult__zero(tc_Nat_Onat).
% 15.31/15.19  class_Rings_Osemiring(tc_Nat_Onat).
% 15.31/15.19  class_Power_Opower(tc_Nat_Onat).
% 15.31/15.19  class_Groups_Ozero(tc_Nat_Onat).
% 15.31/15.19  class_Groups_Oone(tc_Nat_Onat).
% 15.31/15.19  class_Rings_Odvd(tc_Nat_Onat).
% 15.31/15.19  all T_1 (class_Rings_Oidom(T_1)->class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Fields_Ofield(T_1)->class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Fields_Ofield(T_1)->class_Divides_Oring__div(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Osemiring(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Oring__1(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Power_Opower(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Groups_Ozero(T_1)->class_Groups_Ozero(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Oring(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oidom(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Oone(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Odvd(tc_Polynomial_Opoly(T_1))).
% 15.31/15.19  all V_y_2 V_x_2 (-hBOOL(c_fe_qual(V_x_2,V_y_2))|V_x_2=V_y_2).
% 15.31/15.19  all V_y_2 V_x_2 (V_x_2!=V_y_2|hBOOL(c_fe_qual(V_x_2,V_y_2))).
% 15.31/15.19  -hBOOL(c_fFalse).
% 15.31/15.19  hBOOL(c_fTrue).
% 15.31/15.19  -(exists B_k B_a (B_a!=c_Groups_Ozero__class_Ozero(t_a)& (exists B_q ((c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))->c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fe_qual(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (c_Polynomial_OpCons(t_a,v_c____,v_cs____)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))->c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fe_qual(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))))& (all B_z (hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),B_z)))))))).
% 15.31/15.19  class_Rings_Oidom(t_a).
% 15.31/15.19  end_of_list.
% 15.31/15.19  
% 15.31/15.19  -------> usable clausifies to:
% 15.31/15.19  
% 15.31/15.19  list(usable).
% 15.31/15.19  0 [] A=A.
% 15.31/15.19  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.
% 15.31/15.19  0 [] -class_Rings_Oidom(t_a)|v_c____!=c_Groups_Ozero__class_Ozero(t_a).
% 15.31/15.19  0 [] -class_Rings_Oidom(t_a)|$c1!=c_Groups_Ozero__class_Ozero(t_a).
% 15.31/15.19  0 [] -class_Rings_Oidom(t_a)|hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),$c1)!=c_Groups_Ozero__class_Ozero(t_a).
% 15.31/15.19  0 [] -class_Rings_Oidom(t_a)|$c2!=c_Groups_Ozero__class_Ozero(t_a).
% 15.31/15.19  0 [] -class_Rings_Oidom(t_a)|hAPP(c_Polynomial_Opoly(t_a,v_p),$c2)!=c_Groups_Ozero__class_Ozero(t_a).
% 15.31/15.19  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).
% 15.31/15.19  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)).
% 15.31/15.19  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)).
% 15.31/15.19  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).
% 15.31/15.19  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))).
% 15.31/15.19  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).
% 15.31/15.19  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)).
% 15.31/15.19  0 [] -class_Rings_Oidom(t_a)|B_z=c_Groups_Ozero__class_Ozero(t_a)|hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z)=c_Groups_Ozero__class_Ozero(t_a)|$c4!=c_Groups_Ozero__class_Ozero(t_a).
% 15.31/15.19  0 [] -class_Rings_Oidom(t_a)|B_z=c_Groups_Ozero__class_Ozero(t_a)|hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z)=c_Groups_Ozero__class_Ozero(t_a)|v_cs____!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fe_qual($c3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,$c3))),$c5))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.19  0 [] -class_Rings_Oidom(t_a)|B_z=c_Groups_Ozero__class_Ozero(t_a)|hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z)=c_Groups_Ozero__class_Ozero(t_a)|v_cs____=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fe_qual($c3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,$c3))),$c5))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,v_cs____)).
% 15.31/15.19  0 [] -class_Rings_Oidom(t_a)|B_z=c_Groups_Ozero__class_Ozero(t_a)|hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z)=c_Groups_Ozero__class_Ozero(t_a)|hAPP(c_Polynomial_Opoly(t_a,v_cs____),X1)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X1),$c5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,$c4,$c3)),X1)).
% 15.31/15.19  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).
% 15.31/15.19  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).
% 15.31/15.19  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)).
% 15.31/15.19  0 [] -class_Groups_Ozero(T_b)|c_Polynomial_OpCons(T_b,V_a_2,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.19  0 [] -class_Groups_Ozero(T_b)|c_Polynomial_OpCons(T_b,V_a_2,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.19  0 [] -class_Groups_Ozero(T_b)|c_Polynomial_OpCons(T_b,V_a_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_a_2!=c_Groups_Ozero__class_Ozero(T_b)|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.19  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).
% 15.31/15.19  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)).
% 15.31/15.19  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).
% 15.31/15.19  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)).
% 15.31/15.19  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).
% 15.31/15.19  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)).
% 15.31/15.19  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).
% 15.31/15.19  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)).
% 15.31/15.19  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).
% 15.31/15.19  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)).
% 15.31/15.19  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).
% 15.31/15.19  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)).
% 15.31/15.19  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)!=hAPP(hAPP(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).
% 15.31/15.19  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)|V_m_2!=V_n_2.
% 15.31/15.19  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(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).
% 15.31/15.19  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)!=hAPP(hAPP(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).
% 15.31/15.19  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2!=V_n_2.
% 15.31/15.19  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(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).
% 15.31/15.19  0 [] hAPP(hAPP(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).
% 15.31/15.19  0 [] hAPP(hAPP(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).
% 15.31/15.19  0 [] hAPP(hAPP(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).
% 15.31/15.19  0 [] hAPP(hAPP(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).
% 15.31/15.19  0 [] hAPP(hAPP(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).
% 15.31/15.19  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)|V_m_2=V_n_2.
% 15.31/15.19  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)|V_m_2!=V_n_2.
% 15.31/15.19  0 [] hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)).
% 15.31/15.19  0 [] hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)).
% 15.31/15.19  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.
% 15.31/15.19  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.
% 15.31/15.19  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(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)).
% 15.31/15.19  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(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)).
% 15.31/15.19  0 [] hAPP(hAPP(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)).
% 15.31/15.19  0 [] hAPP(hAPP(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)).
% 15.31/15.19  0 [] hAPP(hAPP(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)).
% 15.31/15.19  0 [] hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 15.31/15.19  0 [] hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 15.31/15.19  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,hAPP(hAPP(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)).
% 15.31/15.19  0 [] c_Nat_OSuc(V_x)!=c_Nat_OSuc(V_y)|V_x=V_y.
% 15.31/15.19  0 [] c_Nat_OSuc(V_nat_2)!=c_Nat_OSuc(V_nat_H_2)|V_nat_2=V_nat_H_2.
% 15.31/15.19  0 [] c_Nat_OSuc(V_nat_2)=c_Nat_OSuc(V_nat_H_2)|V_nat_2!=V_nat_H_2.
% 15.31/15.20  0 [] c_Nat_OSuc(V_n)!=V_n.
% 15.31/15.20  0 [] V_n!=c_Nat_OSuc(V_n).
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Groups_Ozero(T_b)|c_Polynomial_OpCons(T_b,V_a_2,V_pa_2)!=c_Polynomial_OpCons(T_b,V_b_2,V_q_2)|V_a_2=V_b_2.
% 15.31/15.20  0 [] -class_Groups_Ozero(T_b)|c_Polynomial_OpCons(T_b,V_a_2,V_pa_2)!=c_Polynomial_OpCons(T_b,V_b_2,V_q_2)|V_pa_2=V_q_2.
% 15.31/15.20  0 [] -class_Groups_Ozero(T_b)|c_Polynomial_OpCons(T_b,V_a_2,V_pa_2)=c_Polynomial_OpCons(T_b,V_b_2,V_q_2)|V_a_2!=V_b_2|V_pa_2!=V_q_2.
% 15.31/15.20  0 [] -class_Int_Oring__char__0(T_b)| -class_Rings_Oidom(T_b)|c_Polynomial_Opoly(T_b,V_pa_2)!=c_Polynomial_Opoly(T_b,V_q_2)|V_pa_2=V_q_2.
% 15.31/15.20  0 [] -class_Int_Oring__char__0(T_b)| -class_Rings_Oidom(T_b)|c_Polynomial_Opoly(T_b,V_pa_2)=c_Polynomial_Opoly(T_b,V_q_2)|V_pa_2!=V_q_2.
% 15.31/15.20  0 [] c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m).
% 15.31/15.20  0 [] c_Nat_OSuc(V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_nat_H).
% 15.31/15.20  0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 15.31/15.20  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n.
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Groups_Ozero(T_b)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_b,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.20  0 [] -class_Groups_Ozero(T_b)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_b,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x)=hAPP(hAPP(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)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n).
% 15.31/15.20  0 [] -class_Int_Oring__char__0(T_b)| -class_Rings_Oidom(T_b)|c_Polynomial_Opoly(T_b,V_pa_2)!=c_Polynomial_Opoly(T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.20  0 [] -class_Int_Oring__char__0(T_b)| -class_Rings_Oidom(T_b)|c_Polynomial_Opoly(T_b,V_pa_2)=c_Polynomial_Opoly(T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)).
% 15.31/15.20  0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)).
% 15.31/15.20  0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)).
% 15.31/15.20  0 [] -class_Power_Opower(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 15.31/15.20  0 [] -class_Rings_Oidom(t_a)|v_c____!=c_Groups_Ozero__class_Ozero(t_a)|$c7!=c_Groups_Ozero__class_Ozero(t_a).
% 15.31/15.20  0 [] -class_Rings_Oidom(t_a)|v_c____!=c_Groups_Ozero__class_Ozero(t_a)|c_Polynomial_OpCons(t_a,v_c____,v_cs____)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fe_qual($c6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,$c6))),$c8))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] -class_Rings_Oidom(t_a)|v_c____!=c_Groups_Ozero__class_Ozero(t_a)|c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fe_qual($c6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,$c6))),$c8))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))).
% 15.31/15.20  0 [] -class_Rings_Oidom(t_a)|v_c____!=c_Groups_Ozero__class_Ozero(t_a)|hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),B_z)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),$c8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,$c7,$c6)),B_z)).
% 15.31/15.20  0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_OSuc(V_n))=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.20  0 [] -class_Power_Opower(T_b)| -class_Rings_Omult__zero(T_b)| -class_Rings_Ono__zero__divisors(T_b)| -class_Rings_Ozero__ne_q__one(T_b)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Power_Opower(T_b)| -class_Rings_Omult__zero(T_b)| -class_Rings_Ono__zero__divisors(T_b)| -class_Rings_Ozero__ne_q__one(T_b)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] -class_Power_Opower(T_b)| -class_Rings_Omult__zero(T_b)| -class_Rings_Ono__zero__divisors(T_b)| -class_Rings_Ozero__ne_q__one(T_b)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c))!=c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)|c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(T_b)|V_x_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)|c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(T_b)|V_y_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)|c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(T_b)|V_x_2!=c_Groups_Ozero__class_Ozero(T_b)|V_y_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m).
% 15.31/15.20  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r)).
% 15.31/15.20  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.20  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_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)|V_x_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.20  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_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).
% 15.31/15.20  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_x_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|V_b_2!=c_Groups_Oplus__class_Oplus(T_b,V_b_2,V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|V_b_2=c_Groups_Oplus__class_Oplus(T_b,V_b_2,V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)).
% 15.31/15.20  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|V_a_2=V_b_2|V_ca_2=V_d_2|c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2))!=c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)).
% 15.31/15.20  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|V_a_2!=V_b_2|c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2))=c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)).
% 15.31/15.20  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|V_ca_2!=V_d_2|c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2))=c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m).
% 15.31/15.20  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2))!=c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))|V_w_2=V_x_2|V_y_2=V_z_2.
% 15.31/15.20  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2))=c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))|V_w_2!=V_x_2.
% 15.31/15.20  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2))=c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))|V_y_2!=V_z_2.
% 15.31/15.20  0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)!=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.20  0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 15.31/15.20  0 [] -class_Groups_Ocomm__monoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)).
% 15.31/15.20  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))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q))).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|hAPP(c_Polynomial_Opoly(T_b,V_pa_2),V_a_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|c_Polynomial_Oorder(T_b,V_a_2,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|hAPP(c_Polynomial_Opoly(T_b,V_pa_2),V_a_2)=c_Groups_Ozero__class_Ozero(T_b)|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|hAPP(c_Polynomial_Opoly(T_b,V_pa_2),V_a_2)=c_Groups_Ozero__class_Ozero(T_b)|c_Polynomial_Oorder(T_b,V_a_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k).
% 15.31/15.20  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)!=hAPP(hAPP(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.
% 15.31/15.20  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(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).
% 15.31/15.20  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2!=V_n_2.
% 15.31/15.20  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)).
% 15.31/15.20  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 15.31/15.20  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)).
% 15.31/15.20  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)).
% 15.31/15.20  0 [] -class_Rings_Osemiring(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Rings_Ono__zero__divisors(T_a)|hAPP(hAPP(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).
% 15.31/15.20  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)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.20  0 [] -class_Rings_Oring__no__zero__divisors(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)|V_b_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Rings_Oring__no__zero__divisors(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Rings_Oring__no__zero__divisors(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_b)|V_b_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.20  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.20  0 [] -class_Rings_Omult__zero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.20  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.20  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.20  0 [] -class_Rings_Omult__zero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.20  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_a_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_a_2)=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|c_Groups_Ozero__class_Ozero(T_b)!=c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|c_Groups_Ozero__class_Ozero(T_b)=c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  0 [] -class_Groups_Ozero(T_c)|hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_c)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c))),V_z_2)!=V_z_2|c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,c_Polynomial_OpCons(T_c,V_a_2,V_pa_2))=hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,V_pa_2)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__0(T_b)|c_Polynomial_Osynthetic__div(T_b,V_pa_2,V_ca_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|c_Polynomial_Odegree(T_b,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__0(T_b)|c_Polynomial_Osynthetic__div(T_b,V_pa_2,V_ca_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|c_Polynomial_Odegree(T_b,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(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))))),V_n))=V_n.
% 15.31/15.20  0 [] -class_Groups_Ocomm__monoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a.
% 15.31/15.20  0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a.
% 15.31/15.20  0 [] -class_Groups_Ocomm__monoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a.
% 15.31/15.20  0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a.
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Groups_Oone(T_b)|c_Groups_Oone__class_Oone(T_b)!=V_x_2|V_x_2=c_Groups_Oone__class_Oone(T_b).
% 15.31/15.20  0 [] -class_Groups_Oone(T_b)|c_Groups_Oone__class_Oone(T_b)=V_x_2|V_x_2!=c_Groups_Oone__class_Oone(T_b).
% 15.31/15.20  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))).
% 15.31/15.20  0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.20  0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a.
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a.
% 15.31/15.20  0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a).
% 15.31/15.20  0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_a.
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_x.
% 15.31/15.20  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)=V_n.
% 15.31/15.20  0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(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).
% 15.31/15.20  0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(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).
% 15.31/15.20  0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(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).
% 15.31/15.20  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 15.31/15.20  0 [] hAPP(hAPP(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).
% 15.31/15.20  0 [] hAPP(hAPP(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).
% 15.31/15.20  0 [] hAPP(hAPP(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).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_m,V_m)=hAPP(hAPP(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).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m))=hAPP(hAPP(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).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m)=hAPP(hAPP(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).
% 15.31/15.20  0 [] -class_Power_Opower(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a).
% 15.31/15.20  0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.20  0 [] c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n).
% 15.31/15.20  0 [] c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 15.31/15.20  0 [] V_m!=hAPP(hAPP(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).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a).
% 15.31/15.20  0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.20  0 [] -class_Groups_Ozero(T_b)|c_Groups_Ozero__class_Ozero(T_b)!=V_x_2|V_x_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Groups_Ozero(T_b)|c_Groups_Ozero__class_Ozero(T_b)=V_x_2|V_x_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Groups_Oab__semigroup__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Groups_Ocancel__semigroup__add(T_b)|c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_b_2)!=c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_ca_2)|V_b_2=V_ca_2.
% 15.31/15.20  0 [] -class_Groups_Ocancel__semigroup__add(T_b)|c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_b_2)=c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_ca_2)|V_b_2!=V_ca_2.
% 15.31/15.20  0 [] -class_Groups_Ocancel__semigroup__add(T_b)|c_Groups_Oplus__class_Oplus(T_b,V_b_2,V_a_2)!=c_Groups_Oplus__class_Oplus(T_b,V_ca_2,V_a_2)|V_b_2=V_ca_2.
% 15.31/15.20  0 [] -class_Groups_Ocancel__semigroup__add(T_b)|c_Groups_Oplus__class_Oplus(T_b,V_b_2,V_a_2)=c_Groups_Oplus__class_Oplus(T_b,V_ca_2,V_a_2)|V_b_2!=V_ca_2.
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)).
% 15.31/15.20  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Groups_Ozero(T_c)|hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_c)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c))),V_z_2)!=V_z_2|c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c)))=V_z_2.
% 15.31/15.20  0 [] -class_Groups_Ozero(T_c)|c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,c_Polynomial_OpCons(T_c,V_a_2,V_pa_2))=hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_If(T_b,c_fe_qual(V_pa_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c))),V_z_2,c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,V_pa_2))).
% 15.31/15.20  0 [] -class_Power_Opower(T_b)|c_Power_Opower__class_Opower(T_b)=c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(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.
% 15.31/15.20  0 [] -class_Rings_Ocomm__ring__1(T_a)|hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,c_Groups_Oone__class_Oone(T_a),V_n)),V_p)),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)).
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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))).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(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))))),V_n)),V_n)=c_Groups_Oone__class_Oone(T_a).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))).
% 15.31/15.20  0 [] -class_Groups_Ogroup__add(T_b)|c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)!=c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)|V_a_2=V_b_2.
% 15.31/15.20  0 [] -class_Groups_Ogroup__add(T_b)|c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)=c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)|V_a_2!=V_b_2.
% 15.31/15.20  0 [] -class_Groups_Ogroup__add(T_b)|c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)!=V_b_2|c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)=V_a_2.
% 15.31/15.20  0 [] -class_Groups_Ogroup__add(T_b)|c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)=V_b_2|c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)!=V_a_2.
% 15.31/15.20  0 [] -class_Groups_Ogroup__add(T_b)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)|V_b_2=c_Groups_Ouminus__class_Ouminus(T_b,V_a_2).
% 15.31/15.20  0 [] -class_Groups_Ogroup__add(T_b)|V_a_2=c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)|V_b_2!=c_Groups_Ouminus__class_Ouminus(T_b,V_a_2).
% 15.31/15.20  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.
% 15.31/15.20  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)).
% 15.31/15.20  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)).
% 15.31/15.20  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)).
% 15.31/15.20  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)).
% 15.31/15.20  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z).
% 15.31/15.20  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z.
% 15.31/15.20  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)=V_z.
% 15.31/15.20  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)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)).
% 15.31/15.20  0 [] -class_Groups_Ozero(T_b)|c_Polynomial_Omonom(T_b,V_a_2,V_n_2)!=c_Polynomial_Omonom(T_b,V_b_2,V_n_2)|V_a_2=V_b_2.
% 15.31/15.20  0 [] -class_Groups_Ozero(T_b)|c_Polynomial_Omonom(T_b,V_a_2,V_n_2)=c_Polynomial_Omonom(T_b,V_b_2,V_n_2)|V_a_2!=V_b_2.
% 15.31/15.20  0 [] -class_Groups_Ozero(T_b)|c_Polynomial_Ocoeff(T_b,V_x_2)!=c_Polynomial_Ocoeff(T_b,V_y_2)|V_x_2=V_y_2.
% 15.31/15.20  0 [] -class_Groups_Ozero(T_b)|c_Polynomial_Ocoeff(T_b,V_x_2)=c_Polynomial_Ocoeff(T_b,V_y_2)|V_x_2!=V_y_2.
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Groups_Ozero(T_b)|V_pa_2!=V_q_2|hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),B_n)=hAPP(c_Polynomial_Ocoeff(T_b,V_q_2),B_n).
% 15.31/15.20  0 [] -class_Groups_Ozero(T_b)|V_pa_2=V_q_2|hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),$f2(V_q_2,V_pa_2,T_b))!=hAPP(c_Polynomial_Ocoeff(T_b,V_q_2),$f2(V_q_2,V_pa_2,T_b)).
% 15.31/15.20  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).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_n).
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Groups_Ogroup__add(T_b)|c_Groups_Ozero__class_Ozero(T_b)!=c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)|c_Groups_Ozero__class_Ozero(T_b)=V_a_2.
% 15.31/15.20  0 [] -class_Groups_Ogroup__add(T_b)|c_Groups_Ozero__class_Ozero(T_b)=c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)|c_Groups_Ozero__class_Ozero(T_b)!=V_a_2.
% 15.31/15.20  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|V_a_2=c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Groups_Ogroup__add(T_b)|c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Groups_Ogroup__add(T_b)|c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)!=V_a_2|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)=V_a_2|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)|V_a_2=V_b_2|V_a_2=c_Groups_Ouminus__class_Ouminus(T_b,V_b_2).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)|V_a_2!=V_b_2.
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_b,V_b_2).
% 15.31/15.20  0 [] -class_Rings_Oring(T_a)|hAPP(hAPP(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))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b).
% 15.31/15.20  0 [] -class_Rings_Oring(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 15.31/15.20  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)).
% 15.31/15.20  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 15.31/15.20  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)).
% 15.31/15.20  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 15.31/15.20  0 [] -class_Rings_Oring(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b).
% 15.31/15.20  0 [] -class_Rings_Oring(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_p).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Polynomial_Osmult(T_a,c_Groups_Oone__class_Oone(T_a),V_p)=V_p.
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 15.31/15.20  0 [] c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Groups_Ogroup__add(T_b)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)|c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Groups_Ogroup__add(T_b)|V_a_2=c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)|c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x).
% 15.31/15.20  0 [] -class_Rings_Oring__1__no__zero__divisors(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)!=c_Groups_Oone__class_Oone(T_b)|V_x_2=c_Groups_Oone__class_Oone(T_b)|V_x_2=c_Groups_Ouminus__class_Ouminus(T_b,c_Groups_Oone__class_Oone(T_b)).
% 15.31/15.20  0 [] -class_Rings_Oring__1__no__zero__divisors(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)=c_Groups_Oone__class_Oone(T_b)|V_x_2!=c_Groups_Oone__class_Oone(T_b).
% 15.31/15.20  0 [] -class_Rings_Oring__1__no__zero__divisors(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)=c_Groups_Oone__class_Oone(T_b)|V_x_2!=c_Groups_Ouminus__class_Ouminus(T_b,c_Groups_Oone__class_Oone(T_b)).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|c_Polynomial_Osmult(T_b,V_a_2,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_a_2=c_Groups_Ozero__class_Ozero(T_b)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|c_Polynomial_Osmult(T_b,V_a_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|c_Polynomial_Osmult(T_b,V_a_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Polynomial_Osmult(T_a,V_a,V_p)).
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  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)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Groups_Ozero(T_b)|c_Polynomial_Omonom(T_b,V_a_2,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Groups_Ozero(T_b)|c_Polynomial_Omonom(T_b,V_a_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  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)).
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Rings_Oring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  0 [] hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_one_2.
% 15.31/15.20  0 [] hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2))=hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),V_n_2)).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Groups_Ozero(T_b)|hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),c_Polynomial_Odegree(T_b,V_pa_2))!=c_Groups_Ozero__class_Ozero(T_b)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.20  0 [] -class_Groups_Ozero(T_b)|hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),c_Polynomial_Odegree(T_b,V_pa_2))=c_Groups_Ozero__class_Ozero(T_b)|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)).
% 15.31/15.20  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))).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(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)))=hAPP(hAPP(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))).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))!=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x_2=V_y_2|V_x_2=c_Groups_Ouminus__class_Ouminus(T_b,V_y_2).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x_2!=V_y_2.
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x_2!=c_Groups_Ouminus__class_Ouminus(T_b,V_y_2).
% 15.31/15.20  0 [] -class_Groups_Ogroup__add(T_b)|c_Groups_Oplus__class_Oplus(T_b,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_y_2=c_Groups_Ouminus__class_Ouminus(T_b,V_x_2).
% 15.31/15.20  0 [] -class_Groups_Ogroup__add(T_b)|c_Groups_Oplus__class_Oplus(T_b,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_b)|V_y_2!=c_Groups_Ouminus__class_Ouminus(T_b,V_x_2).
% 15.31/15.20  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))).
% 15.31/15.20  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),hAPP(hAPP(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).
% 15.31/15.20  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),hAPP(hAPP(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).
% 15.31/15.20  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),hAPP(hAPP(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).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(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).
% 15.31/15.20  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))).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  0 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.31/15.20  0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.31/15.20  0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z))=V_z.
% 15.31/15.20  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.31/15.20  0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)).
% 15.31/15.20  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.31/15.20  0 [] c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n)=V_n.
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a,V_a).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_b)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_k_2,c_Polynomial_Opoly__gcd(T_b,V_x_2,V_y_2))|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_k_2,V_x_2).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_b)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_k_2,c_Polynomial_Opoly__gcd(T_b,V_x_2,V_y_2))|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_k_2,V_y_2).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_b)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_k_2,c_Polynomial_Opoly__gcd(T_b,V_x_2,V_y_2))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_k_2,V_x_2)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_k_2,V_y_2).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)=V_z.
% 15.31/15.20  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z.
% 15.31/15.20  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z).
% 15.31/15.20  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)).
% 15.31/15.20  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 15.31/15.20  0 [] -class_Rings_Odvd(T_a)|V_a!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)|c_Rings_Odvd__class_Odvd(T_a,V_b,V_a).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)|c_Rings_Odvd__class_Odvd(T_a,V_a,V_c).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)|c_Rings_Odvd__class_Odvd(T_a,V_b,V_c).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oone__class_Oone(T_a),V_a).
% 15.31/15.20  0 [] -class_Rings_Ocomm__ring__1(T_b)| -c_Rings_Odvd__class_Odvd(T_b,V_x_2,c_Groups_Ouminus__class_Ouminus(T_b,V_y_2))|c_Rings_Odvd__class_Odvd(T_b,V_x_2,V_y_2).
% 15.31/15.20  0 [] -class_Rings_Ocomm__ring__1(T_b)|c_Rings_Odvd__class_Odvd(T_b,V_x_2,c_Groups_Ouminus__class_Ouminus(T_b,V_y_2))| -c_Rings_Odvd__class_Odvd(T_b,V_x_2,V_y_2).
% 15.31/15.20  0 [] -class_Rings_Ocomm__ring__1(T_b)| -c_Rings_Odvd__class_Odvd(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_x_2),V_y_2)|c_Rings_Odvd__class_Odvd(T_b,V_x_2,V_y_2).
% 15.31/15.20  0 [] -class_Rings_Ocomm__ring__1(T_b)|c_Rings_Odvd__class_Odvd(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_x_2),V_y_2)| -c_Rings_Odvd__class_Odvd(T_b,V_x_2,V_y_2).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)|c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)).
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opoly__gcd(T_b,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_x_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opoly__gcd(T_b,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opoly__gcd(T_b,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_x_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_y_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)| -c_Rings_Odvd__class_Odvd(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|c_Rings_Odvd__class_Odvd(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))|V_ca_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|c_Rings_Odvd__class_Odvd(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))| -c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)| -c_Rings_Odvd__class_Odvd(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|c_Rings_Odvd__class_Odvd(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))|V_ca_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|c_Rings_Odvd__class_Odvd(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))| -c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_pa_2,c_Polynomial_Osmult(T_b,V_a_2,V_q_2))|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_pa_2,V_q_2).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_pa_2,c_Polynomial_Osmult(T_b,V_a_2,V_q_2))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_pa_2,V_q_2).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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.
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__0(T_b)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_b,V_pa_2,V_h_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__0(T_b)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_b,V_pa_2,V_h_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_b)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),c_Polynomial_Osmult(T_b,V_a_2,V_pa_2),V_q_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b)|V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_b)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),c_Polynomial_Osmult(T_b,V_a_2,V_pa_2),V_q_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_pa_2,V_q_2).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_b)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),c_Polynomial_Osmult(T_b,V_a_2,V_pa_2),V_q_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_pa_2,V_q_2).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_b)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),c_Polynomial_Osmult(T_b,V_a_2,V_pa_2),V_q_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_b)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),c_Polynomial_Osmult(T_b,V_a_2,V_pa_2),V_q_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),V_pa_2,V_q_2).
% 15.31/15.20  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)).
% 15.31/15.20  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))).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|hAPP(c_Polynomial_Opoly(T_b,V_pa_2),V_ca_2)!=c_Groups_Ozero__class_Ozero(T_b)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_ca_2),c_Polynomial_OpCons(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))),V_pa_2).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|hAPP(c_Polynomial_Opoly(T_b,V_pa_2),V_ca_2)=c_Groups_Ozero__class_Ozero(T_b)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_ca_2),c_Polynomial_OpCons(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))),V_pa_2).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_ca_2,c_Polynomial_OpCons(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))),V_pa_2)|hAPP(c_Polynomial_Opoly(T_b,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_b,V_ca_2))=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Rings_Oidom(T_b)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_ca_2,c_Polynomial_OpCons(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))),V_pa_2)|hAPP(c_Polynomial_Opoly(T_b,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_b,V_ca_2))!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Rings_Odvd(T_b)| -class_Rings_Osemiring__0(T_b)| -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))|c_Rings_Odvd__class_Odvd(T_b,V_l_2,c_Groups_Oplus__class_Oplus(T_b,$f3(V_l_2,V_P_2,T_b),c_Groups_Ozero__class_Ozero(T_b))).
% 15.31/15.20  0 [] -class_Rings_Odvd(T_b)| -class_Rings_Osemiring__0(T_b)| -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))|hBOOL(hAPP(V_P_2,$f3(V_l_2,V_P_2,T_b))).
% 15.31/15.20  0 [] -class_Rings_Odvd(T_b)| -class_Rings_Osemiring__0(T_b)|hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),$f4(V_l_2,V_P_2,T_b))))| -c_Rings_Odvd__class_Odvd(T_b,V_l_2,c_Groups_Oplus__class_Oplus(T_b,X2,c_Groups_Ozero__class_Ozero(T_b)))| -hBOOL(hAPP(V_P_2,X2)).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f5(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.
% 15.31/15.20  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),$f5(V_y,V_x,V_d,T_a),V_x)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.31/15.20  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f5(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.
% 15.31/15.20  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),$f5(V_y,V_x,V_d,T_a),V_x)|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.31/15.20  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f5(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.
% 15.31/15.20  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),$f5(V_y,V_x,V_d,T_a),V_y)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.31/15.20  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f5(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.
% 15.31/15.20  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),$f5(V_y,V_x,V_d,T_a),V_y)|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.31/15.20  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f5(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.
% 15.31/15.20  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),$f5(V_y,V_x,V_d,T_a),V_d)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.31/15.20  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f5(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.
% 15.31/15.20  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),$f5(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.
% 15.31/15.20  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).
% 15.31/15.20  0 [] c_HOL_Obool_Obool__size(c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] c_HOL_Obool_Obool__size(c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)).
% 15.31/15.20  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k).
% 15.31/15.20  0 [] V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m_2,V_t_2)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2)).
% 15.31/15.20  0 [] V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m_2,V_t_2)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2)).
% 15.31/15.20  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2)).
% 15.31/15.20  0 [] c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2)).
% 15.31/15.20  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2),V_t_2).
% 15.31/15.20  0 [] c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2),V_t_2).
% 15.31/15.20  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))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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)).
% 15.31/15.20  0 [] -class_Groups_Oab__group__add(T_b)|c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_b,V_ca_2,V_d_2)|V_a_2!=V_b_2|V_ca_2=V_d_2.
% 15.31/15.20  0 [] -class_Groups_Oab__group__add(T_b)|c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_b,V_ca_2,V_d_2)|V_a_2=V_b_2|V_ca_2!=V_d_2.
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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.
% 15.31/15.20  0 [] -class_Rings_Odivision__ring__inverse__zero(T_b)|c_Rings_Oinverse__class_Oinverse(T_b,V_a_2)!=c_Rings_Oinverse__class_Oinverse(T_b,V_b_2)|V_a_2=V_b_2.
% 15.31/15.20  0 [] -class_Rings_Odivision__ring__inverse__zero(T_b)|c_Rings_Oinverse__class_Oinverse(T_b,V_a_2)=c_Rings_Oinverse__class_Oinverse(T_b,V_b_2)|V_a_2!=V_b_2.
% 15.31/15.20  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.
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Rings_Odivision__ring__inverse__zero(T_b)|c_Rings_Oinverse__class_Oinverse(T_b,V_a_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Rings_Odivision__ring__inverse__zero(T_b)|c_Rings_Oinverse__class_Oinverse(T_b,V_a_2)=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Groups_Oab__group__add(T_b)|V_a_2!=V_b_2|c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Groups_Oab__group__add(T_b)|V_a_2=V_b_2|c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Groups_Ogroup__add(T_b)|c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=V_b_2.
% 15.31/15.20  0 [] -class_Groups_Ogroup__add(T_b)|c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=V_b_2.
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_n).
% 15.31/15.20  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)).
% 15.31/15.20  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)).
% 15.31/15.20  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)).
% 15.31/15.20  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)).
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n))|V_k=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n).
% 15.31/15.20  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.
% 15.31/15.20  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)).
% 15.31/15.20  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)).
% 15.31/15.20  0 [] hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)).
% 15.31/15.20  0 [] hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)).
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(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)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Rings_Odivision__ring(T_a)|hAPP(hAPP(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.
% 15.31/15.20  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_n).
% 15.31/15.20  0 [] -class_Rings_Oring(T_b)|c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2),V_ca_2)!=c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2),V_d_2)|c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)),V_e_2),V_ca_2)=V_d_2.
% 15.31/15.20  0 [] -class_Rings_Oring(T_b)|c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2),V_ca_2)=c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2),V_d_2)|c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)),V_e_2),V_ca_2)!=V_d_2.
% 15.31/15.20  0 [] -class_Rings_Oring(T_b)|c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2),V_ca_2)!=c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2),V_d_2)|V_ca_2=c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_b_2,V_a_2)),V_e_2),V_d_2).
% 15.31/15.20  0 [] -class_Rings_Oring(T_b)|c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2),V_ca_2)=c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2),V_d_2)|V_ca_2!=c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_b_2,V_a_2)),V_e_2),V_d_2).
% 15.31/15.20  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(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,hAPP(hAPP(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)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))).
% 15.31/15.20  0 [] -class_Rings_Oring(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__ring(T_b)| -class_Rings_Odvd(T_b)| -c_Rings_Odvd__class_Odvd(T_b,V_d_2,V_D_2)| -c_Rings_Odvd__class_Odvd(T_b,V_d_2,c_Groups_Oplus__class_Oplus(T_b,B_x,V_t_2))|c_Rings_Odvd__class_Odvd(T_b,V_d_2,c_Groups_Oplus__class_Oplus(T_b,c_Groups_Ominus__class_Ominus(T_b,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2)),V_t_2)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__ring(T_b)| -class_Rings_Odvd(T_b)| -c_Rings_Odvd__class_Odvd(T_b,V_d_2,V_D_2)|c_Rings_Odvd__class_Odvd(T_b,V_d_2,c_Groups_Oplus__class_Oplus(T_b,B_x,V_t_2))| -c_Rings_Odvd__class_Odvd(T_b,V_d_2,c_Groups_Oplus__class_Oplus(T_b,c_Groups_Ominus__class_Ominus(T_b,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2)),V_t_2)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__ring(T_b)| -class_Rings_Odvd(T_b)| -c_Rings_Odvd__class_Odvd(T_b,V_d_2,V_D_2)| -c_Rings_Odvd__class_Odvd(T_b,V_d_2,c_Groups_Oplus__class_Oplus(T_b,B_x,V_t_2))|c_Rings_Odvd__class_Odvd(T_b,V_d_2,c_Groups_Oplus__class_Oplus(T_b,c_Groups_Ominus__class_Ominus(T_b,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2)),V_t_2)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__ring(T_b)| -class_Rings_Odvd(T_b)| -c_Rings_Odvd__class_Odvd(T_b,V_d_2,V_D_2)|c_Rings_Odvd__class_Odvd(T_b,V_d_2,c_Groups_Oplus__class_Oplus(T_b,B_x,V_t_2))| -c_Rings_Odvd__class_Odvd(T_b,V_d_2,c_Groups_Oplus__class_Oplus(T_b,c_Groups_Ominus__class_Ominus(T_b,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2)),V_t_2)).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_d_2)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2))|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_d_2)),V_t_2)).
% 15.31/15.20  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_d_2)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2))| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_d_2)),V_t_2)).
% 15.31/15.20  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_n_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)))|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,V_n_2).
% 15.31/15.20  0 [] c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_n_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)))| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,V_n_2).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(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).
% 15.31/15.20  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(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).
% 15.31/15.20  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(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).
% 15.31/15.20  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).
% 15.31/15.20  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 15.31/15.20  0 [] c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)).
% 15.31/15.20  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w).
% 15.31/15.20  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).
% 15.31/15.20  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))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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)).
% 15.31/15.20  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(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).
% 15.31/15.20  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(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).
% 15.31/15.20  0 [] -class_Rings_Oring__1(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a))=hAPP(hAPP(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))).
% 15.31/15.20  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)).
% 15.31/15.20  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.
% 15.31/15.20  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)).
% 15.31/15.20  0 [] V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(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)).
% 15.31/15.20  0 [] V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.31/15.20  0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 15.31/15.20  0 [] -class_Power_Opower(T_a)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=c_Groups_Oone__class_Oone(T_a).
% 15.31/15.20  0 [] -class_Power_Opower(T_a)|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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))).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(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).
% 15.31/15.20  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))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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)).
% 15.31/15.20  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b),V_n))|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b).
% 15.31/15.20  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_x).
% 15.31/15.20  0 [] V_x_2!=V_y_2|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2).
% 15.31/15.20  0 [] V_x_2!=V_y_2|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2).
% 15.31/15.20  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).
% 15.31/15.20  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.
% 15.31/15.20  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  0 [] V_x!=V_y|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y).
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n))| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_n)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_m).
% 15.31/15.20  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).
% 15.31/15.20  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.20  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_x).
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(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)).
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_b)|c_Rings_Oinverse__class_Oinverse(T_b,V_x_2)!=c_Groups_Oone__class_Oone(T_b)|V_x_2=c_Groups_Oone__class_Oone(T_b).
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_b)|c_Rings_Oinverse__class_Oinverse(T_b,V_x_2)=c_Groups_Oone__class_Oone(T_b)|V_x_2!=c_Groups_Oone__class_Oone(T_b).
% 15.31/15.20  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b),V_n))|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b).
% 15.31/15.20  0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2))|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_b_2).
% 15.31/15.20  0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2))| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_b_2).
% 15.31/15.20  0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2))|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a_2,V_b_2).
% 15.31/15.20  0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2))| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a_2,V_b_2).
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Groups_Omonoid__mult(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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))).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)).
% 15.31/15.20  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_b_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_b_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_b_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2)|c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_b_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)).
% 15.31/15.20  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,hAPP(hAPP(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).
% 15.31/15.20  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,hAPP(hAPP(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)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2).
% 15.31/15.20  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),hAPP(hAPP(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)).
% 15.31/15.20  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),hAPP(hAPP(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)).
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)).
% 15.31/15.20  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).
% 15.31/15.20  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)))).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n)=c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,V_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_b,V_ca_2,V_b_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,V_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_b,V_ca_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_b,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_b,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__group__add(T_b)|c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_b,V_ca_2,V_d_2)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,V_d_2).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__group__add(T_b)|c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_b,V_ca_2,V_d_2)|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,V_d_2).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2))|c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2))| -c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2),V_b_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2),V_a_2).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2),V_a_2).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2!=V_n_2.
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  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.
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)|V_s!=V_t.
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)|V_m!=V_n.
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.31/15.20  0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Rings_Odivision__ring(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)).
% 15.31/15.20  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 15.31/15.20  0 [] -class_Rings_Olinordered__semidom(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2).
% 15.31/15.20  0 [] -class_Rings_Olinordered__semidom(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),V_b_2)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2).
% 15.31/15.20  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)| -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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 15.31/15.20  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 15.31/15.20  0 [] -class_Rings_Odivision__ring(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(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).
% 15.31/15.20  0 [] -class_Rings_Odivision__ring(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|V_b!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)|c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)=V_a.
% 15.31/15.20  0 [] -class_Rings_Odivision__ring(T_b)|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)!=V_a_2|V_b_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2).
% 15.31/15.20  0 [] -class_Rings_Odivision__ring(T_b)|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)=V_a_2|V_b_2!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2).
% 15.31/15.20  0 [] -class_Rings_Odivision__ring(T_b)|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)=V_b_2.
% 15.31/15.20  0 [] -class_Rings_Odivision__ring(T_b)|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)!=V_b_2.
% 15.31/15.20  0 [] -class_Fields_Ofield(T_b)|V_y_2=c_Groups_Ozero__class_Ozero(T_b)|V_z_2=c_Groups_Ozero__class_Ozero(T_b)|c_Rings_Oinverse__class_Odivide(T_b,V_x_2,V_y_2)!=c_Rings_Oinverse__class_Odivide(T_b,V_w_2,V_z_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_b)|V_y_2=c_Groups_Ozero__class_Ozero(T_b)|V_z_2=c_Groups_Ozero__class_Ozero(T_b)|c_Rings_Oinverse__class_Odivide(T_b,V_x_2,V_y_2)=c_Rings_Oinverse__class_Odivide(T_b,V_w_2,V_z_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2).
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b).
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b).
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_b)|c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)!=V_a_2|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|V_b_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2).
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_b)|c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)!=V_a_2|V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_b)|c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)=V_a_2|V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_b)|c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)=V_a_2|V_b_2!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)|V_ca_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_b)|c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)=V_a_2|V_b_2!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_b)|V_a_2!=c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)=V_b_2.
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_b)|V_a_2!=c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)|V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_b)|V_a_2=c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)|V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_b)|V_a_2=c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)!=V_b_2|V_ca_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_b)|V_a_2=c_Rings_Oinverse__class_Odivide(T_b,V_b_2,V_ca_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)!=V_b_2|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Rings_Odivision__ring(T_b)|V_b_2=c_Groups_Ozero__class_Ozero(T_b)|c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2)!=c_Groups_Oone__class_Oone(T_b)|V_a_2=V_b_2.
% 15.31/15.20  0 [] -class_Rings_Odivision__ring(T_b)|V_b_2=c_Groups_Ozero__class_Ozero(T_b)|c_Rings_Oinverse__class_Odivide(T_b,V_a_2,V_b_2)=c_Groups_Oone__class_Oone(T_b)|V_a_2!=V_b_2.
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n)=c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)).
% 15.31/15.20  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a)),V_n).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)).
% 15.31/15.20  0 [] -class_Fields_Ofield(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 15.31/15.20  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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2).
% 15.31/15.20  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(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).
% 15.31/15.20  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(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).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.20  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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Groups_Olinordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Rings_Olinordered__idom(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Rings_Olinordered__idom(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Groups_Olinordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_a_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.20  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_a_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.20  0 [] -class_Groups_Oordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.20  0 [] -class_Groups_Olinordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2),V_a_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.20  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.20  0 [] -class_Rings_Olinordered__idom(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Rings_Olinordered__idom(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)).
% 15.31/15.20  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,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 15.31/15.20  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))).
% 15.31/15.20  0 [] -class_Rings_Olinordered__semidom(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),V_a_2)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2)!=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)|V_m_2=V_n_2.
% 15.31/15.20  0 [] -class_Rings_Olinordered__semidom(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),V_a_2)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2)=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)|V_m_2!=V_n_2.
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Oinverse(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Rings_Oinverse__class_Oinverse(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Rings_Oinverse__class_Oinverse(T_b,V_a_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Rings_Oinverse__class_Oinverse(T_b,V_a_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.20  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($f6(V_n_2,V_m_2)).
% 15.31/15.20  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,$f6(V_n_2,V_m_2),V_n_2).
% 15.31/15.20  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2!=c_Nat_OSuc(B_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)|V_n_2=c_Nat_OSuc($f7(V_n_2)).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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))).
% 15.31/15.20  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)).
% 15.31/15.20  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))).
% 15.31/15.20  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))).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2=V_n_2.
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2!=V_n_2.
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(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).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(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).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(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).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(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).
% 15.31/15.20  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(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).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(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).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(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).
% 15.31/15.20  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(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).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(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).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(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).
% 15.31/15.20  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(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).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(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).
% 15.31/15.20  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(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).
% 15.31/15.20  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)).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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.
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2).
% 15.31/15.20  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_z).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_y).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x),V_y),V_z).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_y).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_z).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x),V_y),V_z).
% 15.31/15.20  0 [] -class_RealVector_Oreal__field(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)),V_h)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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)),hAPP(hAPP(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)).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)))|V_x_2!=c_Groups_Ozero__class_Ozero(T_b)|V_y_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)))|V_x_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring__strict(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)))|V_y_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.20  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))).
% 15.31/15.20  0 [] -class_Rings_Oordered__ring(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2),V_d_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2).
% 15.31/15.20  0 [] -class_Rings_Oordered__ring(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2),V_d_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2).
% 15.31/15.20  0 [] -class_Rings_Oordered__ring(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2),V_d_2))|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_b_2,V_a_2)),V_e_2),V_d_2)).
% 15.31/15.20  0 [] -class_Rings_Oordered__ring(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2),V_d_2))| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_b_2,V_a_2)),V_e_2),V_d_2)).
% 15.31/15.20  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 15.31/15.20  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),c_Rings_Oinverse__class_Oinverse(T_b,V_x_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_x_2).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),c_Rings_Oinverse__class_Oinverse(T_b,V_x_2))|c_Orderings_Oord__class_Oless(T_b,V_x_2,c_Groups_Oone__class_Oone(T_b)).
% 15.31/15.20  0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),c_Rings_Oinverse__class_Oinverse(T_b,V_x_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_x_2)| -c_Orderings_Oord__class_Oless(T_b,V_x_2,c_Groups_Oone__class_Oone(T_b)).
% 15.31/15.20  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))).
% 15.31/15.20  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)).
% 15.31/15.20  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)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 15.31/15.20  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).
% 15.31/15.20  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.
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(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).
% 15.31/15.20  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(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).
% 15.31/15.20  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(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).
% 15.31/15.20  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.31/15.20  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|V_a_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 15.31/15.20  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f9(V_b_2,V_a_2,V_P_2)).
% 15.31/15.20  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)| -hBOOL(hAPP(V_P_2,$f9(V_b_2,V_a_2,V_P_2))).
% 15.31/15.20  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f9(V_b_2,V_a_2,V_P_2)).
% 15.31/15.20  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f9(V_b_2,V_a_2,V_P_2))).
% 15.31/15.20  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.31/15.20  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|V_a_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 15.31/15.20  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f10(V_b_2,V_a_2,V_P_2)).
% 15.31/15.20  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)| -hBOOL(hAPP(V_P_2,$f10(V_b_2,V_a_2,V_P_2))).
% 15.31/15.20  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f10(V_b_2,V_a_2,V_P_2)).
% 15.31/15.20  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f10(V_b_2,V_a_2,V_P_2))).
% 15.31/15.20  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).
% 15.31/15.20  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_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 15.31/15.20  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_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Rings_Odvd__class_Odvd(T_a,V_x,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)).
% 15.31/15.20  0 [] -class_Rings_Ocomm__semiring__1(T_a)|V_x!=c_Groups_Oone__class_Oone(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_x,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)).
% 15.31/15.20  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.
% 15.31/15.20  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))).
% 15.31/15.20  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,hAPP(hAPP(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).
% 15.31/15.20  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,hAPP(hAPP(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).
% 15.31/15.20  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,hAPP(hAPP(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).
% 15.31/15.20  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,hAPP(hAPP(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).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),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_x_2).
% 15.31/15.20  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.20  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2).
% 15.31/15.20  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)).
% 15.31/15.20  0 [] -class_Divides_Osemiring__div(T_b)| -c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2)|c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2)=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  0 [] -class_Divides_Osemiring__div(T_b)|c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2)|c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2)!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_n)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_m).
% 15.31/15.20  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_f,V_m)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_f,V_n)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_f,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)).
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m)=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y),V_m).
% 15.31/15.20  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m),V_y),V_m)=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y),V_m).
% 15.31/15.20  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).
% 15.31/15.20  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)).
% 15.31/15.20  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).
% 15.31/15.20  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).
% 15.31/15.20  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)).
% 15.31/15.20  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=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),$f11(V_d_2,V_m_2)).
% 15.31/15.20  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!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q).
% 15.31/15.20  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_m_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),$f12(V_d_2,V_m_2)).
% 15.31/15.20  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_m_2!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q).
% 15.31/15.20  0 [] c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(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).
% 15.31/15.20  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b)).
% 15.31/15.20  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)).
% 15.31/15.20  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m)=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_x),V_m).
% 15.31/15.20  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.
% 15.31/15.20  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).
% 15.31/15.20  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m).
% 15.31/15.20  0 [] hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)).
% 15.31/15.20  0 [] hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)).
% 15.31/15.20  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c).
% 15.31/15.20  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c).
% 15.31/15.20  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b).
% 15.31/15.21  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).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k),V_l)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_l))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_n_2)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_n_2)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x_2,V_y_2)).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_n_2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_n_2)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x_2,V_y_2)).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(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).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)).
% 15.31/15.21  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)|V_w_2=V_z_2.
% 15.31/15.21  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 15.31/15.21  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|V_w_2!=V_z_2.
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.31/15.21  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m,V_n)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m).
% 15.31/15.21  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c)),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)).
% 15.31/15.21  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)).
% 15.31/15.21  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i),B_j)|hBOOL(hAPP(V_P_2,B_j)).
% 15.31/15.21  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,$f13(V_k_2,V_n_2,V_P_2),V_k_2).
% 15.31/15.21  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),$f14(V_k_2,V_n_2,V_P_2)),$f13(V_k_2,V_n_2,V_P_2)).
% 15.31/15.21  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,$f13(V_k_2,V_n_2,V_P_2))).
% 15.31/15.21  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,V_n_2))|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f13(V_k_2,V_n_2,V_P_2),V_k_2).
% 15.31/15.21  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),$f14(V_k_2,V_n_2,V_P_2)),$f13(V_k_2,V_n_2,V_P_2)).
% 15.31/15.21  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,$f13(V_k_2,V_n_2,V_P_2))).
% 15.31/15.21  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(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k)=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.31/15.21  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_m_2=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_n_2=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_m_2!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_n_2!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.31/15.21  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).
% 15.31/15.21  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).
% 15.31/15.21  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.
% 15.31/15.21  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).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c).
% 15.31/15.21  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c).
% 15.31/15.21  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).
% 15.31/15.21  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).
% 15.31/15.21  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).
% 15.31/15.21  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).
% 15.31/15.21  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).
% 15.31/15.21  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).
% 15.31/15.21  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).
% 15.31/15.21  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).
% 15.31/15.21  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).
% 15.31/15.21  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).
% 15.31/15.21  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).
% 15.31/15.21  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).
% 15.31/15.21  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).
% 15.31/15.21  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).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_b)| -c_Rings_Odvd__class_Odvd(T_b,V_k_2,V_n_2)| -c_Rings_Odvd__class_Odvd(T_b,V_k_2,c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2))|c_Rings_Odvd__class_Odvd(T_b,V_k_2,V_m_2).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_b)| -c_Rings_Odvd__class_Odvd(T_b,V_k_2,V_n_2)|c_Rings_Odvd__class_Odvd(T_b,V_k_2,c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2))| -c_Rings_Odvd__class_Odvd(T_b,V_k_2,V_m_2).
% 15.31/15.21  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).
% 15.31/15.21  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)).
% 15.31/15.21  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).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b)=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b)=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.21  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).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b).
% 15.31/15.21  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))).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_b)| -c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2),V_y_2),V_r_2).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_b)| -c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)|V_y_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_b)| -c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)|V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_r_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_b,V_r_2),c_Polynomial_Odegree(T_b,V_y_2)).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2!=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2),V_y_2),V_r_2)|V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_r_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2!=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2),V_y_2),V_r_2)|V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_b,V_r_2),c_Polynomial_Odegree(T_b,V_y_2)).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2!=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2),V_y_2),V_r_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_y_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2!=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2),V_y_2),V_r_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_r_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2!=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2),V_y_2),V_r_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_b,V_r_2),c_Polynomial_Odegree(T_b,V_y_2)).
% 15.31/15.21  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_b)| -c_Polynomial_Opdivmod__rel(T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),V_y_2,V_q_2,V_r_2)|V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_b)| -c_Polynomial_Opdivmod__rel(T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),V_y_2,V_q_2,V_r_2)|V_r_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opdivmod__rel(T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),V_y_2,V_q_2,V_r_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_r_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_b)| -c_Polynomial_Opdivmod__rel(T_b,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),V_q_2,V_r_2)|V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_b)| -c_Polynomial_Opdivmod__rel(T_b,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),V_q_2,V_r_2)|V_r_2=V_x_2.
% 15.31/15.21  0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opdivmod__rel(T_b,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),V_q_2,V_r_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_r_2!=V_x_2.
% 15.31/15.21  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))).
% 15.31/15.21  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).
% 15.31/15.21  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)).
% 15.31/15.21  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.
% 15.31/15.21  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.
% 15.31/15.21  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.
% 15.31/15.21  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.
% 15.31/15.21  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.
% 15.31/15.21  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,hAPP(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_r_H),V_r)).
% 15.31/15.21  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).
% 15.31/15.21  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)).
% 15.31/15.21  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)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)| -c_Polynomial_Opos__poly(T_b,V_pa_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),c_Polynomial_Odegree(T_b,V_pa_2))).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)|c_Polynomial_Opos__poly(T_b,V_pa_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),c_Polynomial_Odegree(T_b,V_pa_2))).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)| -c_Polynomial_Opos__poly(T_b,c_Polynomial_OpCons(T_b,V_a_2,V_pa_2))|c_Polynomial_Opos__poly(T_b,V_pa_2)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)| -c_Polynomial_Opos__poly(T_b,c_Polynomial_OpCons(T_b,V_a_2,V_pa_2))|c_Polynomial_Opos__poly(T_b,V_pa_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)|c_Polynomial_Opos__poly(T_b,c_Polynomial_OpCons(T_b,V_a_2,V_pa_2))| -c_Polynomial_Opos__poly(T_b,V_pa_2).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)|c_Polynomial_Opos__poly(T_b,c_Polynomial_OpCons(T_b,V_a_2,V_pa_2))|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)| -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_b),V_x_2,V_y_2)|c_Polynomial_Opos__poly(T_b,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_b),V_y_2,V_x_2)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)|c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_b),V_x_2,V_y_2)| -c_Polynomial_Opos__poly(T_b,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_b),V_y_2,V_x_2)).
% 15.31/15.21  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 15.31/15.21  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)).
% 15.31/15.21  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)).
% 15.31/15.21  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_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)),V_z).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_c),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_a.
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b)=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Oabs__class_Oabs(T_b,V_a_2))|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Oabs__class_Oabs(T_b,V_a_2))|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a.
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oabs__class_Oabs(T_b,V_a_2),V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oabs__class_Oabs(T_b,V_a_2),V_b_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2),V_b_2).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Oabs__class_Oabs(T_b,V_a_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2),V_b_2).
% 15.31/15.21  0 [] -class_Divides_Oring__div(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)|c_Divides_Odiv__class_Odiv(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y))=c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)).
% 15.31/15.21  0 [] -class_Divides_Oring__div(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y)=c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),V_n)=c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)).
% 15.31/15.21  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_b)|c_Groups_Oabs__class_Oabs(T_b,V_a_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_b)|c_Groups_Oabs__class_Oabs(T_b,V_a_2)=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Oabs__class_Oabs(T_a,V_a).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a))=c_Groups_Oabs__class_Oabs(T_a,V_a).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)| -c_Rings_Odvd__class_Odvd(T_b,V_m_2,c_Groups_Oabs__class_Oabs(T_b,V_k_2))|c_Rings_Odvd__class_Odvd(T_b,V_m_2,V_k_2).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)|c_Rings_Odvd__class_Odvd(T_b,V_m_2,c_Groups_Oabs__class_Oabs(T_b,V_k_2))| -c_Rings_Odvd__class_Odvd(T_b,V_m_2,V_k_2).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)| -c_Rings_Odvd__class_Odvd(T_b,c_Groups_Oabs__class_Oabs(T_b,V_m_2),V_k_2)|c_Rings_Odvd__class_Odvd(T_b,V_m_2,V_k_2).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)|c_Rings_Odvd__class_Odvd(T_b,c_Groups_Oabs__class_Oabs(T_b,V_m_2),V_k_2)| -c_Rings_Odvd__class_Odvd(T_b,V_m_2,V_k_2).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,V_l)!=c_Groups_Oabs__class_Oabs(T_a,V_k)|c_Rings_Odvd__class_Odvd(T_a,V_l,V_k).
% 15.31/15.21  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)).
% 15.31/15.21  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_b,V_a)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_a)=c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_b).
% 15.31/15.21  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_x_2,c_Groups_Oone__class_Oone(tc_Int_Oint))|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.31/15.21  0 [] c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_x_2,c_Groups_Oone__class_Oone(tc_Int_Oint))|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.31/15.21  0 [] c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n))!=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m)=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n))=c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 15.31/15.21  0 [] -class_Fields_Olinordered__field(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)).
% 15.31/15.21  0 [] -class_Fields_Olinordered__field(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_b)| -c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2)| -c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_ca_2)| -c_Rings_Odvd__class_Odvd(T_b,c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2),c_Divides_Odiv__class_Odiv(T_b,V_ca_2,V_a_2))|c_Rings_Odvd__class_Odvd(T_b,V_b_2,V_ca_2).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_b)| -c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2)| -c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_ca_2)|c_Rings_Odvd__class_Odvd(T_b,c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2),c_Divides_Odiv__class_Odiv(T_b,V_ca_2,V_a_2))| -c_Rings_Odvd__class_Odvd(T_b,V_b_2,V_ca_2).
% 15.31/15.21  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_y,V_x)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_y)).
% 15.31/15.21  0 [] V_a=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a)=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a.
% 15.31/15.21  0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_z,V_x)| -c_Rings_Odvd__class_Odvd(T_a,V_z,V_y)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_z)=c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_z),c_Divides_Odiv__class_Odiv(T_a,V_y,V_z)).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a))=V_b.
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_c,V_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_c))=c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_a)=V_b.
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_c)=c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c),V_a).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)| -c_Rings_Odvd__class_Odvd(T_a,V_z,V_w)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),c_Divides_Odiv__class_Odiv(T_a,V_w,V_z))=c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,V_a,V_a)=c_Groups_Oone__class_Oone(T_a).
% 15.31/15.21  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n))=V_m.
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|V_c!=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=c_Groups_Ozero__class_Ozero(T_a).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b)=V_a.
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b)=V_a.
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a).
% 15.31/15.21  0 [] -class_Groups_Oabs__if(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a).
% 15.31/15.21  0 [] -class_Groups_Oabs__if(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a.
% 15.31/15.21  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_x),V_y)=c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))|V_z_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.31/15.21  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))|V_z_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_i).
% 15.31/15.21  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)=V_i.
% 15.31/15.21  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_k)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_k).
% 15.31/15.21  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_k)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_k).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)).
% 15.31/15.21  0 [] V_a=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n)),V_n)).
% 15.31/15.21  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b)=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b)=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a)).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b)=c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a)).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)| -c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2)|c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2)!=V_ca_2|V_b_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)| -c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2)|c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2)=V_ca_2|V_b_2!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)| -c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2)| -c_Rings_Odvd__class_Odvd(T_b,V_ca_2,V_d_2)|c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2)!=c_Divides_Odiv__class_Odiv(T_b,V_d_2,V_ca_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)| -c_Rings_Odvd__class_Odvd(T_b,V_a_2,V_b_2)| -c_Rings_Odvd__class_Odvd(T_b,V_ca_2,V_d_2)|c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2)=c_Divides_Odiv__class_Odiv(T_b,V_d_2,V_ca_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b))=V_a.
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))=V_a.
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))=V_a.
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c).
% 15.31/15.21  0 [] -class_Divides_Osemiring__div(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c).
% 15.31/15.21  0 [] V_m_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2),V_m_2)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.31/15.21  0 [] V_m_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2),V_m_2)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_n_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))|V_x_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))|V_x_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.31/15.21  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)).
% 15.31/15.21  0 [] V_b=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)).
% 15.31/15.21  0 [] V_b=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 15.31/15.21  0 [] V_b=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)).
% 15.31/15.21  0 [] V_b=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oabs__class_Oabs(T_b,c_Groups_Ominus__class_Ominus(T_b,V_x_2,V_a_2)),V_r_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_r_2),V_x_2).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oabs__class_Oabs(T_b,c_Groups_Ominus__class_Ominus(T_b,V_x_2,V_a_2)),V_r_2)|c_Orderings_Oord__class_Oless(T_b,V_x_2,c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_r_2)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Oabs__class_Oabs(T_b,c_Groups_Ominus__class_Ominus(T_b,V_x_2,V_a_2)),V_r_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_r_2),V_x_2)| -c_Orderings_Oord__class_Oless(T_b,V_x_2,c_Groups_Oplus__class_Oplus(T_b,V_a_2,V_r_2)).
% 15.31/15.21  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)).
% 15.31/15.21  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)).
% 15.31/15.21  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))).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_c),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c)),V_c)).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)|c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)=V_q.
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Osgn__class_Osgn(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Osgn__class_Osgn(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_a)|c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z))=c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_a)|c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y))=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_a)|c_Divides_Odiv__class_Odiv(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_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x))=V_x.
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,V_k)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_a)|c_Divides_Odiv__class_Odiv(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_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.31/15.21  0 [] V_k!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21  0 [] V_k=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=V_m.
% 15.31/15.21  0 [] c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c).
% 15.31/15.21  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).
% 15.31/15.21  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)).
% 15.31/15.21  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).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(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)).
% 15.31/15.21  0 [] -class_RealVector_Oreal__normed__div__algebra(T_a)|c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))=hAPP(hAPP(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)).
% 15.31/15.21  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).
% 15.31/15.21  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).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_a_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_a_2)=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.21  0 [] -class_RealVector_Oreal__normed__vector(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_x_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_x_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.21  0 [] -class_RealVector_Oreal__normed__vector(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_x_2)=c_Groups_Ozero__class_Ozero(T_b)|V_x_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n)=V_m.
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n)=V_m.
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(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_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c)),V_c)).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)).
% 15.31/15.21  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_n)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)).
% 15.31/15.21  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)).
% 15.31/15.21  0 [] c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_n)).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(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),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.31/15.21  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_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.31/15.21  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).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_a_2)!=c_Groups_Oone__class_Oone(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_a_2)=c_Groups_Oone__class_Oone(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_a)|c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z))=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.31/15.21  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,V_m,V_n)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21  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,V_m,V_n)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)).
% 15.31/15.21  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,V_m,V_n)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)).
% 15.31/15.21  0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.31/15.21  0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i),B_j)|hBOOL(hAPP(V_P_2,B_i)).
% 15.31/15.21  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(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).
% 15.31/15.21  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(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,hAPP(hAPP(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)).
% 15.31/15.21  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(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,$f16(V_k_2,V_n_2,V_P_2))).
% 15.31/15.21  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f15(V_k_2,V_n_2,V_P_2),V_k_2).
% 15.31/15.21  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(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)).
% 15.31/15.21  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f16(V_k_2,V_n_2,V_P_2))).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))|c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))|c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x)=V_x.
% 15.31/15.21  0 [] c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(V_a),V_c)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_c),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c),c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)),V_c)).
% 15.31/15.21  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)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_a_2)!=c_Groups_Ouminus__class_Ouminus(T_b,c_Groups_Oone__class_Oone(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_a_2)=c_Groups_Ouminus__class_Ouminus(T_b,c_Groups_Oone__class_Oone(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.31/15.21  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).
% 15.31/15.21  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).
% 15.31/15.21  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)).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)| -hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)|V_n_2!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)|hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),$f17(V_n_2,V_P_2,V_k_2)).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,$f17(V_n_2,V_P_2,V_k_2),V_k_2).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))|V_n_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f18(V_n_2,V_P_2,V_k_2)),$f17(V_n_2,V_P_2,V_k_2)).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(hAPP(V_P_2,$f18(V_n_2,V_P_2,V_k_2)),$f17(V_n_2,V_P_2,V_k_2))).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|V_n_2!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)|hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,$f19(V_n_2,V_P_2,V_k_2)).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f19(V_n_2,V_P_2,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))|V_n_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f20(V_n_2,V_P_2,V_k_2)),$f19(V_n_2,V_P_2,V_k_2)).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(hAPP(V_P_2,$f20(V_n_2,V_P_2,V_k_2)),$f19(V_n_2,V_P_2,V_k_2))).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_b)| -c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Oabs__class_Oabs(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_b)|c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Oabs__class_Oabs(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a.
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a)).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_b)| -c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Oabs__class_Oabs(T_b,V_a_2),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2,V_b_2).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_b)| -c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Oabs__class_Oabs(T_b,V_a_2),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2),V_b_2).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_b)|c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Oabs__class_Oabs(T_b,V_a_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2),V_b_2).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(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_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))).
% 15.31/15.21  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))).
% 15.31/15.21  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2,V_b_2).
% 15.31/15.21  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2,V_b_2).
% 15.31/15.21  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2,V_a_2).
% 15.31/15.21  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2,V_a_2).
% 15.31/15.21  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 15.31/15.21  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 15.31/15.21  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 15.31/15.21  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__semiring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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).
% 15.31/15.21  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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).
% 15.31/15.21  0 [] -class_Rings_Olinordered__semiring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(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).
% 15.31/15.21  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(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).
% 15.31/15.21  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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).
% 15.31/15.21  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(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).
% 15.31/15.21  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)).
% 15.31/15.21  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)).
% 15.31/15.21  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)).
% 15.31/15.21  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)).
% 15.31/15.21  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)).
% 15.31/15.21  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)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_b))|V_x_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.21  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_b))|V_y_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.21  0 [] -class_Rings_Olinordered__ring__strict(T_b)|c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_b))|V_x_2!=c_Groups_Ozero__class_Ozero(T_b)|V_y_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.31/15.21  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))).
% 15.31/15.21  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x).
% 15.31/15.21  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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x).
% 15.31/15.21  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))| -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,V_a,V_b).
% 15.31/15.21  0 [] -class_Rings_Oordered__ring(T_b)| -c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2),V_d_2))|c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2).
% 15.31/15.21  0 [] -class_Rings_Oordered__ring(T_b)|c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2),V_d_2))| -c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Oplus__class_Oplus(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Groups_Ocancel__ab__semigroup__add(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Rings_Oring__1__no__zero__divisors(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Rings_Oring__no__zero__divisors(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Groups_Ocancel__semigroup__add(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Groups_Oab__semigroup__mult(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Groups_Ocomm__monoid__mult(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Groups_Oab__semigroup__add(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Rings_Ono__zero__divisors(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Groups_Ocomm__monoid__add(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Rings_Ocomm__semiring__1(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Rings_Ocomm__semiring__0(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Rings_Ocomm__semiring(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Groups_Oab__group__add(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Rings_Ozero__ne_q__one(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Groups_Omonoid__mult(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Rings_Ocomm__ring__1(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Groups_Omonoid__add(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Rings_Osemiring__0(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Groups_Ogroup__add(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Rings_Omult__zero(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Rings_Ocomm__ring(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Rings_Osemiring(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Rings_Oring__1(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Power_Opower(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Groups_Ozero(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Rings_Oring(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Groups_Oone(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Rings_Odvd(T).
% 15.31/15.21  0 [] -class_Rings_Oidom(T)|class_Groups_Ocancel__comm__monoid__add(T).
% 15.31/15.21  0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint).
% 15.31/15.21  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Olinordered__semiring(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Olinordered__semidom(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Olinordered__ring(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Olinordered__idom(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Ocomm__semiring__0(tc_Int_Oint).
% 15.31/15.21  0 [] class_Divides_Osemiring__div(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Ocomm__semiring(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Oab__group__add(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Oordered__ring(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Omonoid__mult(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Omonoid__add(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Osemiring__0(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Ogroup__add(tc_Int_Oint).
% 15.31/15.21  0 [] class_Divides_Oring__div(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Omult__zero(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Ocomm__ring(tc_Int_Oint).
% 15.31/15.21  0 [] class_Int_Oring__char__0(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Osemiring(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Osgn__if(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Oabs__if(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Oring__1(tc_Int_Oint).
% 15.31/15.21  0 [] class_Power_Opower(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Ozero(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Oring(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Oidom(tc_Int_Oint).
% 15.31/15.21  0 [] class_Groups_Oone(tc_Int_Oint).
% 15.31/15.21  0 [] class_Rings_Odvd(tc_Int_Oint).
% 15.31/15.21  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Rings_Ocomm__semiring__0(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Divides_Osemiring__div(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Groups_Omonoid__mult(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Groups_Omonoid__add(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Rings_Osemiring__0(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Rings_Omult__zero(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Rings_Osemiring(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Power_Opower(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Groups_Ozero(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Groups_Oone(tc_Nat_Onat).
% 15.31/15.21  0 [] class_Rings_Odvd(tc_Nat_Onat).
% 15.31/15.21  0 [] -class_Rings_Oidom(T_1)|class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Oidom(T_1)|class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Oidom(T_1)|class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Oidom(T_1)|class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_1)|class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Fields_Ofield(T_1)|class_Divides_Oring__div(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_1)|class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Power_Opower(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Groups_Ozero(T_1)|class_Groups_Ozero(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Oring(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Oidom(T_1)|class_Rings_Oidom(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Oone(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Odvd(tc_Polynomial_Opoly(T_1)).
% 15.31/15.21  0 [] -hBOOL(c_fe_qual(V_x_2,V_y_2))|V_x_2=V_y_2.
% 15.31/15.21  0 [] V_x_2!=V_y_2|hBOOL(c_fe_qual(V_x_2,V_y_2)).
% 15.31/15.21  0 [] -hBOOL(c_fFalse).
% 15.31/15.21  0 [] hBOOL(c_fTrue).
% 15.31/15.21  0 [] B_a=c_Groups_Ozero__class_Ozero(t_a)|c_Polynomial_OpCons(t_a,v_c____,v_cs____)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fe_qual(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))!=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))|hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),$f21(B_k,B_a,B_q))!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),$f21(B_k,B_a,B_q)),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),$f21(B_k,B_a,B_q))).
% 15.31/15.21  0 [] B_a=c_Groups_Ozero__class_Ozero(t_a)|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fe_qual(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Polynomial_OpCons(t_a,v_c____,v_cs____)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))|hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),$f21(B_k,B_a,B_q))!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),$f21(B_k,B_a,B_q)),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),$f21(B_k,B_a,B_q))).
% 15.31/15.21  0 [] B_a=c_Groups_Ozero__class_Ozero(t_a)|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fe_qual(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fe_qual(B_q,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,B_q))),B_k))!=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))|hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),$f21(B_k,B_a,B_q))!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),$f21(B_k,B_a,B_q)),B_k)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,B_a,B_q)),$f21(B_k,B_a,B_q))).
% 15.31/15.21  0 [] class_Rings_Oidom(t_a).
% 15.31/15.21  end_of_list.
% 15.31/15.21  
% 15.31/15.21  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 15.31/15.21  
% 15.31/15.21  This ia a non-Horn set with equality.  The strategy will be
% 15.31/15.21  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 15.31/15.21  deletion, with positive clauses in sos and nonpositive
% 15.31/15.21  clauses in usable.
% 15.31/15.21  
% 15.31/15.21     dependent: set(knuth_bendix).
% 15.31/15.21     dependent: set(anl_eq).
% 15.31/15.21     dependent: set(para_from).
% 15.31/15.21     dependent: set(para_into).
% 15.31/15.21     dependent: clear(para_from_right).
% 15.31/15.21     dependent: clear(para_into_right).
% 15.31/15.21     dependent: set(para_from_vars).
% 15.31/15.21     dependent: set(eq_units_both_ways).
% 15.31/15.21     dependent: set(dynamic_demod_all).
% 15.31/15.21     dependent: set(dynamic_demod).
% 15.31/15.21     dependent: set(order_eq).
% 15.31/15.21     dependent: set(back_demod).
% 15.31/15.21     dependent: set(lrpo).
% 15.31/15.21     dependent: set(hyper_res).
% 15.31/15.21     dependent: set(unit_deletion).
% 15.31/15.21     dependent: set(factor).
% 15.31/15.21  
% 15.31/15.21  ------------> process usable:
% 15.31/15.21  ** KEPT (pick-wt=14): 1 [] hAPP(A,$f1(B,A))!=hAPP(B,$f1(B,A))|A=B.
% 15.31/15.21  ** KEPT (pick-wt=6): 3 [copy,2,flip.2] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=v_c____.
% 15.31/15.21  ** KEPT (pick-wt=6): 5 [copy,4,flip.2] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=$c1.
% 15.31/15.21  ** KEPT (pick-wt=13): 7 [copy,6,flip.2] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),$c1).
% 15.31/15.21  ** KEPT (pick-wt=6): 9 [copy,8,flip.2] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=$c2.
% 15.31/15.21  ** KEPT (pick-wt=10): 11 [copy,10,flip.2] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=hAPP(c_Polynomial_Opoly(t_a,v_p),$c2).
% 15.31/15.21  ** KEPT (pick-wt=16): 12 [] -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).
% 15.31/15.21  ** KEPT (pick-wt=18): 13 [] -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)).
% 15.31/15.21    Following clause subsumed by 13 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)).
% 15.31/15.21  ** KEPT (pick-wt=13): 14 [] -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).
% 15.31/15.21  ** KEPT (pick-wt=24): 15 [] -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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),hAPP(c_Polynomial_Opoly(A,C),D))).
% 15.31/15.21  ** KEPT (pick-wt=13): 16 [] -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).
% 15.31/15.21  ** KEPT (pick-wt=15): 18 [copy,17,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).
% 15.31/15.21  ** KEPT (pick-wt=18): 20 [copy,19,flip.4] -class_Rings_Oidom(t_a)|A=c_Groups_Ozero__class_Ozero(t_a)|hAPP(c_Polynomial_Opoly(t_a,v_cs____),A)=c_Groups_Ozero__class_Ozero(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=$c4.
% 15.31/15.21  ** KEPT (pick-wt=39): 22 [copy,21,flip.4] -class_Rings_Oidom(t_a)|A=c_Groups_Ozero__class_Ozero(t_a)|hAPP(c_Polynomial_Opoly(t_a,v_cs____),A)=c_Groups_Ozero__class_Ozero(t_a)|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))!=v_cs____|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fe_qual($c3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,$c3))),$c5))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21  ** KEPT (pick-wt=41): 24 [copy,23,flip.4] -class_Rings_Oidom(t_a)|A=c_Groups_Ozero__class_Ozero(t_a)|hAPP(c_Polynomial_Opoly(t_a,v_cs____),A)=c_Groups_Ozero__class_Ozero(t_a)|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))=v_cs____|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fe_qual($c3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,$c3))),$c5))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,v_cs____)).
% 15.31/15.21  ** KEPT (pick-wt=38): 26 [copy,25,flip.4] -class_Rings_Oidom(t_a)|A=c_Groups_Ozero__class_Ozero(t_a)|hAPP(c_Polynomial_Opoly(t_a,v_cs____),A)=c_Groups_Ozero__class_Ozero(t_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B),$c5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,$c4,$c3)),B))=hAPP(c_Polynomial_Opoly(t_a,v_cs____),B).
% 15.31/15.21  ** KEPT (pick-wt=12): 27 [] -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).
% 15.31/15.21  ** KEPT (pick-wt=10): 28 [] -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).
% 15.31/15.21  ** KEPT (pick-wt=13): 29 [] -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)).
% 15.31/15.21  ** KEPT (pick-wt=14): 30 [] -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).
% 15.31/15.21  ** KEPT (pick-wt=15): 31 [] -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)).
% 15.31/15.21  ** KEPT (pick-wt=19): 32 [] -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)).
% 15.31/15.21  ** KEPT (pick-wt=17): 33 [] 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).
% 15.31/15.21  ** KEPT (pick-wt=18): 34 [] 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)).
% 15.31/15.21  ** KEPT (pick-wt=16): 35 [] 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).
% 15.31/15.21  ** KEPT (pick-wt=17): 36 [] 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)).
% 15.31/15.21  ** KEPT (pick-wt=17): 37 [] 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).
% 15.31/15.21  ** KEPT (pick-wt=17): 38 [] 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)).
% 15.31/15.21  ** KEPT (pick-wt=17): 39 [] 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).
% 15.31/15.21  ** KEPT (pick-wt=18): 40 [] 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)).
% 15.31/15.21  ** KEPT (pick-wt=16): 41 [] 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).
% 15.31/15.21  ** KEPT (pick-wt=17): 42 [] 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)).
% 15.31/15.21  ** KEPT (pick-wt=17): 43 [] 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).
% 15.31/15.21  ** KEPT (pick-wt=17): 44 [] 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)).
% 15.31/15.21  ** KEPT (pick-wt=20): 45 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)|A=C|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21  ** KEPT (pick-wt=16): 46 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)|A!=C.
% 15.31/15.21  ** KEPT (pick-wt=17): 47 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21  ** KEPT (pick-wt=20): 48 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B=C|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21  ** KEPT (pick-wt=16): 49 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B!=C.
% 15.31/15.21  ** KEPT (pick-wt=17): 50 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21  ** KEPT (pick-wt=17): 51 [] hAPP(hAPP(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).
% 15.31/15.21  ** KEPT (pick-wt=13): 52 [] hAPP(hAPP(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).
% 15.31/15.21  ** KEPT (pick-wt=13): 53 [] hAPP(hAPP(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).
% 15.31/15.21  ** KEPT (pick-wt=18): 54 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),C)|B=C.
% 15.31/15.21    Following clause subsumed by 49 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),C)|B!=C.
% 15.31/15.21  ** KEPT (pick-wt=11): 55 [] -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.
% 15.31/15.21  ** KEPT (pick-wt=11): 56 [] -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.
% 15.31/15.21  ** KEPT (pick-wt=15): 57 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(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)).
% 15.31/15.21  ** KEPT (pick-wt=15): 58 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(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)).
% 15.31/15.21  ** KEPT (pick-wt=15): 59 [] hAPP(hAPP(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)).
% 15.31/15.21  ** KEPT (pick-wt=15): 60 [] hAPP(hAPP(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)).
% 15.31/15.21  ** KEPT (pick-wt=20): 61 [] hAPP(hAPP(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)).
% 15.31/15.21  ** KEPT (pick-wt=30): 62 [] -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,hAPP(hAPP(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)).
% 15.31/15.21  ** KEPT (pick-wt=8): 63 [] c_Nat_OSuc(A)!=c_Nat_OSuc(B)|A=B.
% 15.31/15.21    Following clause subsumed by 63 during input processing: 0 [] c_Nat_OSuc(A)!=c_Nat_OSuc(B)|A=B.
% 15.31/15.21  ** KEPT (pick-wt=8): 64 [] c_Nat_OSuc(A)=c_Nat_OSuc(B)|A!=B.
% 15.31/15.21  ** KEPT (pick-wt=4): 65 [] c_Nat_OSuc(A)!=A.
% 15.31/15.21    Following clause subsumed by 65 during input processing: 0 [flip.1] c_Nat_OSuc(A)!=A.
% 15.31/15.21  ** KEPT (pick-wt=12): 66 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)|A=C.
% 15.31/15.21  ** KEPT (pick-wt=12): 67 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)|A!=C.
% 15.31/15.21  ** KEPT (pick-wt=12): 68 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)|B=C.
% 15.31/15.21  ** KEPT (pick-wt=12): 69 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)|B!=C.
% 15.31/15.21  ** KEPT (pick-wt=14): 70 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)!=c_Polynomial_OpCons(A,D,E)|B=D.
% 15.31/15.21  ** KEPT (pick-wt=14): 71 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)!=c_Polynomial_OpCons(A,D,E)|C=E.
% 15.31/15.21  ** KEPT (pick-wt=17): 72 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)=c_Polynomial_OpCons(A,D,E)|B!=D|C!=E.
% 15.31/15.21  ** KEPT (pick-wt=14): 73 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)!=c_Polynomial_Opoly(A,C)|B=C.
% 15.31/15.21  ** KEPT (pick-wt=14): 74 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)=c_Polynomial_Opoly(A,C)|B!=C.
% 15.31/15.21  ** KEPT (pick-wt=5): 75 [] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21    Following clause subsumed by 75 during input processing: 0 [flip.1] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21    Following clause subsumed by 75 during input processing: 0 [] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21    Following clause subsumed by 75 during input processing: 0 [] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21    Following clause subsumed by 75 during input processing: 0 [flip.1] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21    Following clause subsumed by 75 during input processing: 0 [flip.1] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21  ** KEPT (pick-wt=10): 76 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=A|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21  ** KEPT (pick-wt=11): 77 [] 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).
% 15.31/15.21  ** KEPT (pick-wt=11): 78 [] 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).
% 15.31/15.21  ** KEPT (pick-wt=15): 79 [] 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).
% 15.31/15.21  ** KEPT (pick-wt=13): 80 [] -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)).
% 15.31/15.21    Following clause subsumed by 16 during input processing: 0 [] -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)).
% 15.31/15.21  ** KEPT (pick-wt=25): 82 [copy,81,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)).
% 15.31/15.21  ** KEPT (pick-wt=28): 83 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Polynomial_Opoly(A,B),D)),hAPP(c_Polynomial_Opoly(A,C),D)).
% 15.31/15.21  ** KEPT (pick-wt=24): 84 [] -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)).
% 15.31/15.21  ** KEPT (pick-wt=24): 85 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Polynomial_Opoly(A,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),D)=hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Polynomial_Opoly(A,B),D)),C).
% 15.31/15.21    Following clause subsumed by 73 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)).
% 15.31/15.21    Following clause subsumed by 74 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)).
% 15.31/15.21  ** KEPT (pick-wt=28): 86 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)).
% 15.31/15.21  ** KEPT (pick-wt=28): 88 [copy,87,flip.2] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)).
% 15.31/15.21  ** KEPT (pick-wt=21): 89 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C)).
% 15.31/15.21  ** KEPT (pick-wt=21): 91 [copy,90,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 15.31/15.21  ** KEPT (pick-wt=21): 92 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B).
% 15.31/15.21    Following clause subsumed by 91 during input processing: 0 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 15.31/15.21  ** KEPT (pick-wt=21): 93 [] -class_Power_Opower(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 15.31/15.21    Following clause subsumed by 3 during input processing: 0 [flip.2,flip.3] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=v_c____|c_Groups_Ozero__class_Ozero(t_a)!=$c7.
% 15.31/15.21    Following clause subsumed by 3 during input processing: 0 [unit_del,75,flip.2,flip.3] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=v_c____|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))!=c_Polynomial_OpCons(t_a,v_c____,v_cs____).
% 15.31/15.21    Following clause subsumed by 3 during input processing: 0 [flip.2,flip.3] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=v_c____|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))=c_Polynomial_OpCons(t_a,v_c____,v_cs____)|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fe_qual($c6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,$c6))),$c8))=c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))).
% 15.31/15.21    Following clause subsumed by 3 during input processing: 0 [flip.2,flip.3] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=v_c____|hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),A),$c8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,$c7,$c6)),A))=hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),A).
% 15.31/15.21  ** KEPT (pick-wt=15): 94 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),c_Nat_OSuc(B))=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.21  ** KEPT (pick-wt=21): 95 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.21  ** KEPT (pick-wt=21): 96 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21  ** KEPT (pick-wt=25): 97 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.21  ** KEPT (pick-wt=31): 98 [] -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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E))!=c_Groups_Oplus__class_Oplus(A,D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),F)).
% 15.31/15.21  ** KEPT (pick-wt=23): 99 [] -class_Rings_Olinordered__ring__strict(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.21  ** KEPT (pick-wt=23): 100 [] -class_Rings_Olinordered__ring__strict(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.21  ** KEPT (pick-wt=27): 101 [] -class_Rings_Olinordered__ring__strict(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(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).
% 15.31/15.21  ** KEPT (pick-wt=31): 102 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)).
% 15.31/15.21  ** KEPT (pick-wt=19): 103 [] hAPP(hAPP(c_Power_Opower__class_Opower(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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.31/15.21  ** KEPT (pick-wt=14): 104 [] hAPP(hAPP(c_Power_Opower__class_Opower(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).
% 15.31/15.21  ** KEPT (pick-wt=15): 105 [] hAPP(hAPP(c_Power_Opower__class_Opower(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)).
% 15.31/15.21  ** KEPT (pick-wt=15): 106 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B).
% 15.31/15.21  ** KEPT (pick-wt=25): 107 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 15.31/15.21  ** KEPT (pick-wt=25): 109 [copy,108,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.31/15.21    Following clause subsumed by 109 during input processing: 0 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.31/15.21  ** KEPT (pick-wt=25): 110 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),C).
% 15.31/15.21    Following clause subsumed by 109 during input processing: 0 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))).
% 15.31/15.21    Following clause subsumed by 107 during input processing: 0 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),E)).
% 15.31/15.21  ** KEPT (pick-wt=35): 111 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 15.31/15.21  ** KEPT (pick-wt=11): 112 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,C,B).
% 15.31/15.21  ** KEPT (pick-wt=17): 113 [] -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)).
% 15.31/15.21  ** KEPT (pick-wt=17): 115 [copy,114,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)).
% 15.31/15.21    Following clause subsumed by 115 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)).
% 15.31/15.21  ** KEPT (pick-wt=17): 116 [] -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).
% 15.31/15.21  ** KEPT (pick-wt=23): 117 [] -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)).
% 15.31/15.21  ** KEPT (pick-wt=25): 119 [copy,118,flip.2] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)).
% 15.31/15.21  ** KEPT (pick-wt=25): 120 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)).
% 15.31/15.21  ** KEPT (pick-wt=12): 121 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.21  ** KEPT (pick-wt=12): 122 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.21  ** KEPT (pick-wt=9): 123 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 15.31/15.21  ** KEPT (pick-wt=9): 124 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 15.31/15.21  ** KEPT (pick-wt=12): 126 [copy,125,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).
% 15.31/15.21  ** KEPT (pick-wt=12): 128 [copy,127,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).
% 15.31/15.21  ** KEPT (pick-wt=26): 129 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 15.31/15.21  ** KEPT (pick-wt=37): 130 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B=C|D=E|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))!=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.31/15.21  ** KEPT (pick-wt=34): 131 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B!=C|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.31/15.21  ** KEPT (pick-wt=34): 132 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B!=C|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)).
% 15.31/15.21  ** KEPT (pick-wt=26): 133 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.31/15.21    Following clause subsumed by 133 during input processing: 0 [flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,D)),C)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)).
% 15.31/15.21    Following clause subsumed by 130 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))!=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|B=D|C=E.
% 15.31/15.22    Following clause subsumed by 131 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|B!=D.
% 15.31/15.22    Following clause subsumed by 132 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|C!=E.
% 15.31/15.22  ** KEPT (pick-wt=15): 134 [] -class_Rings_Oring__1__no__zero__divisors(A)|B=c_Groups_Ozero__class_Ozero(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=25): 135 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 15.31/15.22  ** KEPT (pick-wt=30): 136 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)).
% 15.31/15.22  ** KEPT (pick-wt=30): 137 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)).
% 15.31/15.22  ** KEPT (pick-wt=29): 138 [] -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))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),c_Polynomial_Opcompose(A,C,D))).
% 15.31/15.22  ** KEPT (pick-wt=22): 139 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=15): 140 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=17): 141 [] -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).
% 15.31/15.22    Following clause subsumed by 48 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=C.
% 15.31/15.22    Following clause subsumed by 50 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.31/15.22    Following clause subsumed by 49 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B!=C.
% 15.31/15.22  ** KEPT (pick-wt=26): 142 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 15.31/15.22    Following clause subsumed by 142 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 15.31/15.22  ** KEPT (pick-wt=26): 143 [] -class_Rings_Ocomm__semiring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.31/15.22  ** KEPT (pick-wt=26): 144 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.31/15.22    Following clause subsumed by 144 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.31/15.22  ** KEPT (pick-wt=32): 146 [copy,145,flip.2] -class_Rings_Osemiring(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D),E)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),E)).
% 15.31/15.22  ** KEPT (pick-wt=12): 147 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=20): 148 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=19): 149 [] -class_Rings_Ono__zero__divisors(A)|hAPP(hAPP(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).
% 15.31/15.22    Following clause subsumed by 149 during input processing: 0 [] -class_Rings_Ono__zero__divisors(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)!=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=19): 150 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(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).
% 15.31/15.22  ** KEPT (pick-wt=15): 151 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=15): 152 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=12): 153 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22    Following clause subsumed by 153 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=12): 154 [] -class_Rings_Omult__zero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=12): 155 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22    Following clause subsumed by 155 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=12): 156 [] -class_Rings_Omult__zero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=13): 157 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=13): 158 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=9): 159 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 15.31/15.22  ** KEPT (pick-wt=9): 160 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 15.31/15.22  ** KEPT (pick-wt=13): 161 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=13): 162 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=9): 163 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 15.31/15.22  ** KEPT (pick-wt=9): 164 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 15.31/15.22  ** KEPT (pick-wt=36): 166 [copy,165,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)).
% 15.31/15.22  ** KEPT (pick-wt=16): 167 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=16): 168 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=22): 169 [] -class_Rings_Ocomm__semiring__1(A)|c_Polynomial_Odegree(A,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Polynomial_OpCons(A,B,c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),C))=C.
% 15.31/15.22  ** KEPT (pick-wt=11): 170 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 15.31/15.22  ** KEPT (pick-wt=11): 171 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 15.31/15.22  ** KEPT (pick-wt=11): 172 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 15.31/15.22  ** KEPT (pick-wt=11): 173 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 15.31/15.22  ** KEPT (pick-wt=12): 174 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=10): 175 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)!=B|B=c_Groups_Oone__class_Oone(A).
% 15.31/15.22  ** KEPT (pick-wt=10): 176 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)=B|B!=c_Groups_Oone__class_Oone(A).
% 15.31/15.22  ** KEPT (pick-wt=13): 178 [copy,177,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)).
% 15.31/15.22  ** KEPT (pick-wt=7): 180 [copy,179,flip.2] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 15.31/15.22    Following clause subsumed by 180 during input processing: 0 [] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 15.31/15.22  ** KEPT (pick-wt=11): 181 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 15.31/15.22  ** KEPT (pick-wt=11): 182 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 15.31/15.22  ** KEPT (pick-wt=12): 183 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Oone__class_Oone(A)),B)=c_Groups_Oone__class_Oone(A).
% 15.31/15.22  ** KEPT (pick-wt=11): 184 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat))=B.
% 15.31/15.22  ** KEPT (pick-wt=11): 185 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat))=B.
% 15.31/15.22  ** KEPT (pick-wt=13): 187 [copy,186,flip.1] hAPP(hAPP(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).
% 15.31/15.22  ** KEPT (pick-wt=13): 189 [copy,188,flip.1] hAPP(hAPP(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).
% 15.31/15.22  ** KEPT (pick-wt=17): 191 [copy,190,flip.1] hAPP(hAPP(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).
% 15.31/15.22    Following clause subsumed by 187 during input processing: 0 [] hAPP(hAPP(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).
% 15.31/15.22    Following clause subsumed by 189 during input processing: 0 [] hAPP(hAPP(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).
% 15.31/15.22    Following clause subsumed by 191 during input processing: 0 [] hAPP(hAPP(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).
% 15.31/15.22  ** KEPT (pick-wt=18): 193 [copy,192,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(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).
% 15.31/15.22  ** KEPT (pick-wt=22): 195 [copy,194,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 15.31/15.22  ** KEPT (pick-wt=22): 197 [copy,196,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),C).
% 15.31/15.22  ** KEPT (pick-wt=12): 198 [] -class_Power_Opower(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(A).
% 15.31/15.22  ** KEPT (pick-wt=12): 199 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(A).
% 15.31/15.22  ** KEPT (pick-wt=16): 201 [copy,200,flip.1] hAPP(hAPP(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).
% 15.31/15.22  ** KEPT (pick-wt=10): 202 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=12): 203 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=18): 204 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Oone__class_Oone(A).
% 15.31/15.22  ** KEPT (pick-wt=18): 205 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=10): 206 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=10): 207 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=25): 208 [] -class_Groups_Oab__semigroup__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.31/15.22  ** KEPT (pick-wt=17): 209 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=14): 210 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 15.31/15.22  ** KEPT (pick-wt=14): 211 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,B,D)|C!=D.
% 15.31/15.22  ** KEPT (pick-wt=14): 212 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,D,C)|B=D.
% 15.31/15.22  ** KEPT (pick-wt=14): 213 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,D,C)|B!=D.
% 15.31/15.22    Following clause subsumed by 210 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.
% 15.31/15.22  ** KEPT (pick-wt=14): 214 [] -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.
% 15.31/15.22    Following clause subsumed by 212 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.
% 15.31/15.22  ** KEPT (pick-wt=21): 215 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=24): 216 [] -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.
% 15.31/15.22  ** KEPT (pick-wt=32): 218 [copy,217,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)).
% 15.31/15.22  ** KEPT (pick-wt=11): 219 [] -class_Power_Opower(A)|c_Power_Opower__class_Opower(A)=c_Power_Opower_Opower(A,c_Groups_Oone__class_Oone(A),c_Groups_Otimes__class_Otimes(A)).
% 15.31/15.22  ** KEPT (pick-wt=38): 220 [] -class_Rings_Ocomm__ring__1(A)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),c_Polynomial_Osynthetic__div(A,C,B)),c_Polynomial_OpCons(A,hAPP(c_Polynomial_Opoly(A,C),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))=C.
% 15.31/15.22  ** KEPT (pick-wt=33): 221 [] -class_Rings_Ocomm__ring__1(A)|hAPP(c_Polynomial_Opoly(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Polynomial_Omonom(A,c_Groups_Oone__class_Oone(A),B)),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)),hAPP(c_Polynomial_Opoly(A,C),D)).
% 15.31/15.22  ** KEPT (pick-wt=25): 222 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=22): 223 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=21): 224 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=25): 225 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Polynomial_Ocoeff(A,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Polynomial_OpCons(A,B,c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),C)),C)=c_Groups_Oone__class_Oone(A).
% 15.31/15.22  ** KEPT (pick-wt=31): 226 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D))).
% 15.31/15.22  ** KEPT (pick-wt=31): 227 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D))).
% 15.31/15.22  ** KEPT (pick-wt=12): 228 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=c_Groups_Ouminus__class_Ouminus(A,C)|B=C.
% 15.31/15.22  ** KEPT (pick-wt=12): 229 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=c_Groups_Ouminus__class_Ouminus(A,C)|B!=C.
% 15.31/15.22  ** KEPT (pick-wt=12): 230 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=C|c_Groups_Ouminus__class_Ouminus(A,C)=B.
% 15.31/15.22    Following clause subsumed by 230 during input processing: 0 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=C|c_Groups_Ouminus__class_Ouminus(A,C)!=B.
% 15.31/15.22  ** KEPT (pick-wt=12): 231 [] -class_Groups_Ogroup__add(A)|B!=c_Groups_Ouminus__class_Ouminus(A,C)|C=c_Groups_Ouminus__class_Ouminus(A,B).
% 15.31/15.22    Following clause subsumed by 231 during input processing: 0 [] -class_Groups_Ogroup__add(A)|B=c_Groups_Ouminus__class_Ouminus(A,C)|C!=c_Groups_Ouminus__class_Ouminus(A,B).
% 15.31/15.22  ** KEPT (pick-wt=9): 232 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ouminus__class_Ouminus(A,B))=B.
% 15.31/15.22  ** KEPT (pick-wt=21): 233 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_Osmult(A,B,C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Polynomial_Ocoeff(A,C),D)).
% 15.31/15.22  ** KEPT (pick-wt=14): 234 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,B,C)!=c_Polynomial_Omonom(A,D,C)|B=D.
% 15.31/15.22  ** KEPT (pick-wt=14): 235 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,B,C)=c_Polynomial_Omonom(A,D,C)|B!=D.
% 15.31/15.22  ** KEPT (pick-wt=12): 236 [] -class_Groups_Ozero(A)|c_Polynomial_Ocoeff(A,B)!=c_Polynomial_Ocoeff(A,C)|B=C.
% 15.31/15.22  ** KEPT (pick-wt=12): 237 [] -class_Groups_Ozero(A)|c_Polynomial_Ocoeff(A,B)=c_Polynomial_Ocoeff(A,C)|B!=C.
% 15.31/15.22  ** KEPT (pick-wt=16): 239 [copy,238,flip.2] -class_Rings_Ocomm__ring(A)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C))=c_Polynomial_Osmult(A,c_Groups_Ouminus__class_Ouminus(A,B),C).
% 15.31/15.22  ** KEPT (pick-wt=18): 240 [] -class_Groups_Oab__group__add(A)|hAPP(c_Polynomial_Ocoeff(A,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)),C)=c_Groups_Ouminus__class_Ouminus(A,hAPP(c_Polynomial_Ocoeff(A,B),C)).
% 15.31/15.22  ** KEPT (pick-wt=17): 242 [copy,241,flip.2] -class_Rings_Ocomm__ring(A)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C))=c_Polynomial_Osmult(A,B,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)).
% 15.31/15.22  ** KEPT (pick-wt=16): 243 [] -class_Groups_Ozero(A)|B!=C|hAPP(c_Polynomial_Ocoeff(A,B),D)=hAPP(c_Polynomial_Ocoeff(A,C),D).
% 15.31/15.22  ** KEPT (pick-wt=22): 244 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=16): 245 [] -class_Groups_Oab__group__add(A)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Polynomial_Omonom(A,B,C))=c_Polynomial_Omonom(A,c_Groups_Ouminus__class_Ouminus(A,B),C).
% 15.31/15.22  ** KEPT (pick-wt=19): 246 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osmult(A,B,c_Polynomial_Omonom(A,C,D))=c_Polynomial_Omonom(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D).
% 15.31/15.22  ** KEPT (pick-wt=15): 247 [] -class_Groups_Ozero(A)|B!=C|hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_Omonom(A,D,B)),C)=D.
% 15.31/15.22  ** KEPT (pick-wt=16): 248 [] -class_Groups_Ozero(A)|B=C|hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_Omonom(A,D,B)),C)=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=18): 249 [] -class_Rings_Ocomm__ring(A)|hAPP(c_Polynomial_Opoly(A,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)),C)=c_Groups_Ouminus__class_Ouminus(A,hAPP(c_Polynomial_Opoly(A,B),C)).
% 15.31/15.22  ** KEPT (pick-wt=19): 250 [] -class_Groups_Oab__group__add(A)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,B,C))=c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)).
% 15.31/15.22    Following clause subsumed by 250 during input processing: 0 [] -class_Groups_Oab__group__add(A)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,B,C))=c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)).
% 15.31/15.22  ** KEPT (pick-wt=9): 251 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=12): 252 [] -class_Groups_Ogroup__add(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Ouminus__class_Ouminus(A,B)|c_Groups_Ozero__class_Ozero(A)=B.
% 15.31/15.22  ** KEPT (pick-wt=12): 253 [] -class_Groups_Ogroup__add(A)|c_Groups_Ozero__class_Ozero(A)=c_Groups_Ouminus__class_Ouminus(A,B)|c_Groups_Ozero__class_Ozero(A)!=B.
% 15.31/15.22  ** KEPT (pick-wt=11): 255 [copy,254,flip.2] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=11): 257 [copy,256,flip.2] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=12): 258 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=12): 259 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22    Following clause subsumed by 255 during input processing: 0 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22    Following clause subsumed by 257 during input processing: 0 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=23): 260 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)|B=C|B=c_Groups_Ouminus__class_Ouminus(A,C).
% 15.31/15.22  ** KEPT (pick-wt=18): 261 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)|B!=C.
% 15.31/15.22  ** KEPT (pick-wt=20): 262 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)|B!=c_Groups_Ouminus__class_Ouminus(A,C).
% 15.31/15.22  ** KEPT (pick-wt=19): 263 [] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C).
% 15.31/15.22  ** KEPT (pick-wt=19): 264 [] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,B)),C)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ouminus__class_Ouminus(A,C)).
% 15.31/15.22  ** KEPT (pick-wt=19): 265 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,B)),C)=c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 15.31/15.22    Following clause subsumed by 265 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,B)),C)=c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 15.31/15.22  ** KEPT (pick-wt=19): 266 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ouminus__class_Ouminus(A,C))=c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 15.31/15.22    Following clause subsumed by 266 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ouminus__class_Ouminus(A,C))=c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 15.31/15.22  ** KEPT (pick-wt=19): 268 [copy,267,flip.2] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,B)),C)=c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 15.31/15.22  ** KEPT (pick-wt=19): 270 [copy,269,flip.2] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ouminus__class_Ouminus(A,C))=c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 15.31/15.22  ** KEPT (pick-wt=17): 271 [] -class_Groups_Oab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oplus__class_Oplus(A,B,C))=c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)).
% 15.31/15.22  ** KEPT (pick-wt=17): 272 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oplus__class_Oplus(A,B,C))=c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Groups_Ouminus__class_Ouminus(A,B)).
% 15.31/15.22  ** KEPT (pick-wt=13): 273 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),C))=C.
% 15.31/15.22  ** KEPT (pick-wt=13): 274 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Oplus__class_Oplus(A,B,C))=C.
% 15.31/15.22  ** KEPT (pick-wt=19): 276 [copy,275,flip.2] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osmult(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D)=c_Polynomial_Osmult(A,B,c_Polynomial_Osmult(A,C,D)).
% 15.31/15.22  ** KEPT (pick-wt=9): 277 [] -class_Rings_Ocomm__semiring__1(A)|c_Polynomial_Osmult(A,c_Groups_Oone__class_Oone(A),B)=B.
% 15.31/15.22  ** KEPT (pick-wt=12): 278 [] -class_Groups_Oab__group__add(A)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.31/15.22  ** KEPT (pick-wt=12): 279 [] -class_Groups_Oab__group__add(A)|c_Polynomial_Odegree(A,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B))=c_Polynomial_Odegree(A,B).
% 15.31/15.22  ** KEPT (pick-wt=12): 280 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=22): 281 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=23): 282 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Polynomial_Osmult(A,B,C)),D)=c_Polynomial_Osmult(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)).
% 15.31/15.22  ** KEPT (pick-wt=23): 283 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),c_Polynomial_Osmult(A,C,D))=c_Polynomial_Osmult(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)).
% 15.31/15.22  ** KEPT (pick-wt=14): 284 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|c_Groups_Ouminus__class_Ouminus(A,B)=C.
% 15.31/15.22  ** KEPT (pick-wt=11): 285 [] -class_Groups_Oab__group__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),B)=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=11): 286 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),B)=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=14): 287 [] -class_Groups_Ogroup__add(A)|B!=c_Groups_Ouminus__class_Ouminus(A,C)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=14): 288 [] -class_Groups_Ogroup__add(A)|B=c_Groups_Ouminus__class_Ouminus(A,C)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=11): 289 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ouminus__class_Ouminus(A,B))=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=15): 291 [copy,290,flip.2] -class_Rings_Ocomm__ring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A))),B)=c_Groups_Ouminus__class_Ouminus(A,B).
% 15.31/15.22  ** KEPT (pick-wt=21): 292 [] -class_Rings_Oring__1__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)!=c_Groups_Oone__class_Oone(A)|B=c_Groups_Oone__class_Oone(A)|B=c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)).
% 15.31/15.22  ** KEPT (pick-wt=15): 293 [] -class_Rings_Oring__1__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=c_Groups_Oone__class_Oone(A)|B!=c_Groups_Oone__class_Oone(A).
% 15.31/15.22  ** KEPT (pick-wt=17): 294 [] -class_Rings_Oring__1__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=c_Groups_Oone__class_Oone(A)|B!=c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)).
% 15.31/15.22  ** KEPT (pick-wt=19): 295 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=14): 296 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=15): 297 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=11): 298 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=12): 299 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=22): 300 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osmult(A,B,c_Polynomial_OpCons(A,C,D))=c_Polynomial_OpCons(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Polynomial_Osmult(A,B,D)).
% 15.31/15.22  ** KEPT (pick-wt=13): 301 [] -class_Groups_Ozero(A)|hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_OpCons(A,B,C)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=B.
% 15.31/15.22  ** KEPT (pick-wt=17): 302 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=21): 303 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,c_Polynomial_Osmult(A,B,C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Polynomial_Opoly(A,C),D)).
% 15.31/15.22  ** KEPT (pick-wt=16): 304 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=21): 305 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=24): 306 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=14): 307 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=14): 308 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=11): 309 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.31/15.22  ** KEPT (pick-wt=14): 310 [] -class_Groups_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Polynomial_Odegree(A,c_Polynomial_Omonom(A,B,C))=C.
% 15.31/15.22  ** KEPT (pick-wt=21): 311 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=30): 312 [] -class_Rings_Oring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ouminus__class_Ouminus(A,B)),C)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A))),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 15.31/15.22  ** KEPT (pick-wt=16): 313 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=16): 314 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=15): 315 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=16): 316 [] -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).
% 15.31/15.22  ** KEPT (pick-wt=17): 317 [] -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).
% 15.31/15.22    Following clause subsumed by 317 during input processing: 0 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=17): 318 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=22): 319 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=16): 320 [] -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)).
% 15.31/15.22  ** KEPT (pick-wt=22): 321 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Polynomial_Opoly(A,c_Polynomial_Omonom(A,B,C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)).
% 15.31/15.22  ** KEPT (pick-wt=14): 323 [copy,322,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)).
% 15.31/15.22  ** KEPT (pick-wt=28): 324 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,E)).
% 15.31/15.22  ** KEPT (pick-wt=39): 325 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Ocoeff(A,hAPP(hAPP(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)))=hAPP(hAPP(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))).
% 15.31/15.22  ** KEPT (pick-wt=29): 326 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))!=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|B=C|B=c_Groups_Ouminus__class_Ouminus(A,C).
% 15.31/15.22  ** KEPT (pick-wt=24): 327 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|B!=C.
% 15.31/15.22  ** KEPT (pick-wt=26): 328 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|B!=c_Groups_Ouminus__class_Ouminus(A,C).
% 15.31/15.22  ** KEPT (pick-wt=14): 329 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ouminus__class_Ouminus(A,B).
% 15.31/15.22  ** KEPT (pick-wt=14): 330 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ouminus__class_Ouminus(A,B).
% 15.31/15.22  ** KEPT (pick-wt=32): 331 [] -class_Rings_Oidom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),c_Polynomial_Oorder(A,C,B)),B).
% 15.31/15.22  ** KEPT (pick-wt=33): 332 [] -class_Rings_Oidom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),c_Nat_OSuc(c_Polynomial_Oorder(A,C,B))),B).
% 15.31/15.22    Following clause subsumed by 332 during input processing: 0 [] -class_Rings_Oidom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),c_Nat_OSuc(c_Polynomial_Oorder(A,C,B))),B).
% 15.31/15.22  ** KEPT (pick-wt=27): 333 [] -class_Rings_Oidom(A)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),c_Polynomial_Oorder(A,B,C)),C).
% 15.31/15.22  ** KEPT (pick-wt=27): 335 [copy,334,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).
% 15.31/15.22  ** KEPT (pick-wt=28): 336 [] -class_Fields_Ofield(A)|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|C!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_Opoly__gcd(A,B,C)),c_Polynomial_Odegree(A,c_Polynomial_Opoly__gcd(A,B,C)))=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=23): 337 [] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_Opoly__gcd(A,B,C)),c_Polynomial_Odegree(A,c_Polynomial_Opoly__gcd(A,B,C)))=c_Groups_Oone__class_Oone(A).
% 15.31/15.22  ** KEPT (pick-wt=23): 338 [] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_Opoly__gcd(A,C,B)),c_Polynomial_Odegree(A,c_Polynomial_Opoly__gcd(A,C,B)))=c_Groups_Oone__class_Oone(A).
% 15.31/15.22  ** KEPT (pick-wt=7): 339 [] -class_Rings_Ocomm__semiring__1(A)|c_Rings_Odvd__class_Odvd(A,B,c_Groups_Ozero__class_Ozero(A)).
% 15.31/15.22  ** KEPT (pick-wt=10): 340 [] -class_Fields_Ofield(A)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_Opoly__gcd(A,B,C),B).
% 15.31/15.22  ** KEPT (pick-wt=10): 341 [] -class_Fields_Ofield(A)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_Opoly__gcd(A,B,C),C).
% 15.31/15.22  ** KEPT (pick-wt=5): 342 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.31/15.22  ** KEPT (pick-wt=11): 343 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A),A)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.31/15.22  ** KEPT (pick-wt=14): 344 [] -class_Fields_Ofield(A)|c_Polynomial_Opoly__gcd(A,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B),C)=c_Polynomial_Opoly__gcd(A,B,C).
% 15.31/15.22  ** KEPT (pick-wt=14): 345 [] -class_Fields_Ofield(A)|c_Polynomial_Opoly__gcd(A,B,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C))=c_Polynomial_Opoly__gcd(A,B,C).
% 15.31/15.22  ** KEPT (pick-wt=6): 346 [] -class_Rings_Ocomm__semiring__1(A)|c_Rings_Odvd__class_Odvd(A,B,B).
% 15.31/15.22  ** KEPT (pick-wt=14): 347 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,B,C)| -c_Rings_Odvd__class_Odvd(A,C,D)|c_Rings_Odvd__class_Odvd(A,B,D).
% 15.31/15.22  ** KEPT (pick-wt=11): 348 [] -class_Fields_Ofield(A)|c_Polynomial_Opoly__gcd(A,B,C)=c_Polynomial_Opoly__gcd(A,C,B).
% 15.31/15.22  ** KEPT (pick-wt=17): 349 [] -class_Fields_Ofield(A)|c_Polynomial_Opoly__gcd(A,B,c_Polynomial_Opoly__gcd(A,C,D))=c_Polynomial_Opoly__gcd(A,C,c_Polynomial_Opoly__gcd(A,B,D)).
% 15.31/15.22  ** KEPT (pick-wt=15): 350 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,c_Polynomial_Opoly__gcd(A,C,D))|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C).
% 15.31/15.22  ** KEPT (pick-wt=15): 351 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,c_Polynomial_Opoly__gcd(A,C,D))|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D).
% 15.31/15.22  ** KEPT (pick-wt=20): 352 [] -class_Fields_Ofield(A)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,c_Polynomial_Opoly__gcd(A,C,D))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D).
% 15.31/15.22  ** KEPT (pick-wt=17): 353 [] -class_Fields_Ofield(A)|c_Polynomial_Opoly__gcd(A,c_Polynomial_Opoly__gcd(A,B,C),D)=c_Polynomial_Opoly__gcd(A,B,c_Polynomial_Opoly__gcd(A,C,D)).
% 15.31/15.22    Following clause subsumed by 352 during input processing: 0 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,c_Polynomial_Opoly__gcd(A,C,D)).
% 15.31/15.22  ** KEPT (pick-wt=11): 354 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,c_Groups_Ozero__class_Ozero(A),B)|B=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.22  ** KEPT (pick-wt=11): 355 [] -class_Rings_Ocomm__semiring__1(A)|c_Rings_Odvd__class_Odvd(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 15.31/15.22  ** KEPT (pick-wt=11): 356 [] -class_Rings_Ocomm__semiring__1(A)|c_Rings_Odvd__class_Odvd(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)).
% 15.31/15.22  ** KEPT (pick-wt=15): 357 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,B,C)|c_Rings_Odvd__class_Odvd(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.31/15.22  ** KEPT (pick-wt=15): 358 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,B,C)|c_Rings_Odvd__class_Odvd(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)).
% 15.31/15.22  ** KEPT (pick-wt=24): 359 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,B,C)| -c_Rings_Odvd__class_Odvd(A,D,E)|c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 15.31/15.22  ** KEPT (pick-wt=14): 360 [] -class_Rings_Odvd(A)|B!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)|c_Rings_Odvd__class_Odvd(A,C,B).
% 15.31/15.22  ** KEPT (pick-wt=15): 361 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D)|c_Rings_Odvd__class_Odvd(A,B,D).
% 15.31/15.22  ** KEPT (pick-wt=15): 362 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D)|c_Rings_Odvd__class_Odvd(A,C,D).
% 15.31/15.22  ** KEPT (pick-wt=17): 363 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,B,C)| -c_Rings_Odvd__class_Odvd(A,B,D)|c_Rings_Odvd__class_Odvd(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 15.31/15.22  ** KEPT (pick-wt=7): 364 [] -class_Rings_Ocomm__semiring__1(A)|c_Rings_Odvd__class_Odvd(A,c_Groups_Oone__class_Oone(A),B).
% 15.31/15.22  ** KEPT (pick-wt=12): 365 [] -class_Rings_Ocomm__ring__1(A)| -c_Rings_Odvd__class_Odvd(A,B,c_Groups_Ouminus__class_Ouminus(A,C))|c_Rings_Odvd__class_Odvd(A,B,C).
% 15.31/15.22  ** KEPT (pick-wt=12): 366 [] -class_Rings_Ocomm__ring__1(A)|c_Rings_Odvd__class_Odvd(A,B,c_Groups_Ouminus__class_Ouminus(A,C))| -c_Rings_Odvd__class_Odvd(A,B,C).
% 15.31/15.22  ** KEPT (pick-wt=12): 367 [] -class_Rings_Ocomm__ring__1(A)| -c_Rings_Odvd__class_Odvd(A,c_Groups_Ouminus__class_Ouminus(A,B),C)|c_Rings_Odvd__class_Odvd(A,B,C).
% 15.31/15.23  ** KEPT (pick-wt=12): 368 [] -class_Rings_Ocomm__ring__1(A)|c_Rings_Odvd__class_Odvd(A,c_Groups_Ouminus__class_Ouminus(A,B),C)| -c_Rings_Odvd__class_Odvd(A,B,C).
% 15.31/15.23  ** KEPT (pick-wt=20): 369 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,B,C)|c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)).
% 15.31/15.23  ** KEPT (pick-wt=15): 370 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,c_Polynomial_Osmult(A,D,C)).
% 15.31/15.23  ** KEPT (pick-wt=15): 371 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C),D)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,D).
% 15.31/15.23  ** KEPT (pick-wt=14): 372 [] -class_Fields_Ofield(A)|c_Polynomial_Opoly__gcd(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.31/15.23  ** KEPT (pick-wt=15): 373 [] -class_Fields_Ofield(A)|c_Polynomial_Opoly__gcd(A,B,C)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.31/15.23  ** KEPT (pick-wt=15): 374 [] -class_Fields_Ofield(A)|c_Polynomial_Opoly__gcd(A,B,C)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.31/15.23  ** KEPT (pick-wt=20): 375 [] -class_Fields_Ofield(A)|c_Polynomial_Opoly__gcd(A,B,C)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|C!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.31/15.23  ** KEPT (pick-wt=24): 376 [] -class_Rings_Oidom(A)| -c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|C=c_Groups_Ozero__class_Ozero(A)|c_Rings_Odvd__class_Odvd(A,B,D).
% 15.31/15.23  ** KEPT (pick-wt=20): 377 [] -class_Rings_Oidom(A)|c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|C!=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.23  ** KEPT (pick-wt=20): 378 [] -class_Rings_Oidom(A)|c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))| -c_Rings_Odvd__class_Odvd(A,B,D).
% 15.31/15.23  ** KEPT (pick-wt=24): 379 [] -class_Rings_Oidom(A)| -c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Odvd__class_Odvd(A,C,D).
% 15.31/15.23  ** KEPT (pick-wt=20): 380 [] -class_Rings_Oidom(A)|c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|B!=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.23  ** KEPT (pick-wt=20): 381 [] -class_Rings_Oidom(A)|c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -c_Rings_Odvd__class_Odvd(A,C,D).
% 15.31/15.23  ** KEPT (pick-wt=12): 382 [] -class_Fields_Ofield(A)|c_Polynomial_Opoly__gcd(A,B,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)).
% 15.31/15.23  ** KEPT (pick-wt=12): 383 [] -class_Fields_Ofield(A)|c_Polynomial_Opoly__gcd(A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)),B)=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)).
% 15.31/15.23  ** KEPT (pick-wt=19): 384 [] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,c_Polynomial_Osmult(A,B,D))|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,D).
% 15.31/15.23  ** KEPT (pick-wt=19): 385 [] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,c_Polynomial_Osmult(A,B,D))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,D).
% 15.31/15.23  ** KEPT (pick-wt=19): 386 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C)|D=c_Groups_Ozero__class_Ozero(A)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,D,B),C).
% 15.31/15.23    Following clause subsumed by 384 during input processing: 0 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,c_Polynomial_Osmult(A,C,D))|C=c_Groups_Ozero__class_Ozero(A)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D).
% 15.31/15.23  ** KEPT (pick-wt=30): 387 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=hAPP(c_Polynomial_Ocoeff(A,C),c_Polynomial_Odegree(A,C))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,B)|B=C.
% 15.31/15.23  ** KEPT (pick-wt=12): 388 [] -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)).
% 15.31/15.23  ** KEPT (pick-wt=15): 389 [] -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)).
% 15.31/15.23  ** KEPT (pick-wt=15): 390 [] -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)).
% 15.31/15.23  ** KEPT (pick-wt=12): 391 [] -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).
% 15.31/15.23  ** KEPT (pick-wt=19): 392 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C),D)|B!=c_Groups_Ozero__class_Ozero(A)|D=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.31/15.23  ** KEPT (pick-wt=19): 393 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C),D)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,D).
% 15.31/15.23    Following clause subsumed by 386 during input processing: 0 [] -class_Fields_Ofield(A)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C),D)|B=c_Groups_Ozero__class_Ozero(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,D).
% 15.31/15.23  ** KEPT (pick-wt=19): 394 [] -class_Fields_Ofield(A)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C),D)|D!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B!=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.23  ** KEPT (pick-wt=20): 395 [] -class_Fields_Ofield(A)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C),D)|D!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),C,D).
% 15.31/15.23  ** KEPT (pick-wt=19): 396 [] -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)).
% 15.31/15.23  ** KEPT (pick-wt=18): 397 [] -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))).
% 15.31/15.23  ** KEPT (pick-wt=26): 398 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Opoly(A,B),C)!=c_Groups_Ozero__class_Ozero(A)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))),B).
% 15.31/15.23  ** KEPT (pick-wt=26): 399 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Opoly(A,B),C)=c_Groups_Ozero__class_Ozero(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))),B).
% 15.31/15.23  ** KEPT (pick-wt=26): 400 [] -class_Rings_Oidom(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,B,c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))),C)|hAPP(c_Polynomial_Opoly(A,C),c_Groups_Ouminus__class_Ouminus(A,B))=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.23  ** KEPT (pick-wt=26): 401 [] -class_Rings_Oidom(A)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,B,c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))),C)|hAPP(c_Polynomial_Opoly(A,C),c_Groups_Ouminus__class_Ouminus(A,B))!=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.23  ** KEPT (pick-wt=24): 402 [] -class_Rings_Odvd(A)| -class_Rings_Osemiring__0(A)| -hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)))|c_Rings_Odvd__class_Odvd(A,C,c_Groups_Oplus__class_Oplus(A,$f3(C,B,A),c_Groups_Ozero__class_Ozero(A))).
% 15.31/15.23  ** KEPT (pick-wt=20): 403 [] -class_Rings_Odvd(A)| -class_Rings_Osemiring__0(A)| -hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)))|hBOOL(hAPP(B,$f3(C,B,A))).
% 15.31/15.23  ** KEPT (pick-wt=28): 404 [] -class_Rings_Odvd(A)| -class_Rings_Osemiring__0(A)|hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),$f4(C,B,A))))| -c_Rings_Odvd__class_Odvd(A,C,c_Groups_Oplus__class_Oplus(A,D,c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(B,D)).
% 15.31/15.23  ** KEPT (pick-wt=42): 405 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),$f5(D,C,B,A),C)|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Oone__class_Oone(A)|c_Polynomial_Opoly__gcd(A,C,D)=B.
% 15.31/15.23  ** KEPT (pick-wt=42): 406 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),$f5(D,C,B,A),C)|D=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Oone__class_Oone(A)|c_Polynomial_Opoly__gcd(A,C,D)=B.
% 15.31/15.23  ** KEPT (pick-wt=47): 407 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),$f5(D,C,B,A),C)|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|D!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Opoly__gcd(A,C,D)=B.
% 15.31/15.23  ** KEPT (pick-wt=47): 408 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),$f5(D,C,B,A),C)|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Ozero__class_Ozero(A)|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Oone__class_Oone(A)|c_Polynomial_Opoly__gcd(A,C,D)=B.
% 15.31/15.23  ** KEPT (pick-wt=42): 409 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),$f5(D,C,B,A),D)|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Oone__class_Oone(A)|c_Polynomial_Opoly__gcd(A,C,D)=B.
% 15.31/15.23  ** KEPT (pick-wt=42): 410 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),$f5(D,C,B,A),D)|D=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Oone__class_Oone(A)|c_Polynomial_Opoly__gcd(A,C,D)=B.
% 15.31/15.23  ** KEPT (pick-wt=47): 411 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),$f5(D,C,B,A),D)|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|D!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Opoly__gcd(A,C,D)=B.
% 15.31/15.23  ** KEPT (pick-wt=47): 412 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),$f5(D,C,B,A),D)|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Ozero__class_Ozero(A)|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Oone__class_Oone(A)|c_Polynomial_Opoly__gcd(A,C,D)=B.
% 15.31/15.23  ** KEPT (pick-wt=42): 413 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),$f5(D,C,B,A),B)|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Oone__class_Oone(A)|c_Polynomial_Opoly__gcd(A,C,D)=B.
% 15.31/15.23  ** KEPT (pick-wt=42): 414 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),$f5(D,C,B,A),B)|D=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Oone__class_Oone(A)|c_Polynomial_Opoly__gcd(A,C,D)=B.
% 15.31/15.23  ** KEPT (pick-wt=47): 415 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),$f5(D,C,B,A),B)|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|D!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Opoly__gcd(A,C,D)=B.
% 15.31/15.23  ** KEPT (pick-wt=47): 416 [] -class_Fields_Ofield(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,C)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),B,D)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),$f5(D,C,B,A),B)|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Ozero__class_Ozero(A)|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Oone__class_Oone(A)|c_Polynomial_Opoly__gcd(A,C,D)=B.
% 15.31/15.23  ** KEPT (pick-wt=21): 417 [] -class_Fields_Ofield(A)|c_Polynomial_Opoly__gcd(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Polynomial_Osmult(A,c_Rings_Oinverse__class_Oinverse(A,hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))),B).
% 15.31/15.23  ** KEPT (pick-wt=35): 418 [] -class_Rings_Ocomm__ring__1(A)|c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,C)),c_Groups_Oplus__class_Oplus(A,B,C)).
% 15.31/15.23  ** KEPT (pick-wt=22): 419 [] A=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,B,C)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)).
% 15.31/15.23  ** KEPT (pick-wt=22): 420 [] A=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,B,C)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)).
% 15.31/15.23  ** KEPT (pick-wt=10): 421 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)).
% 15.31/15.23  ** KEPT (pick-wt=10): 422 [] c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)).
% 15.31/15.23  ** KEPT (pick-wt=10): 423 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),B).
% 15.31/15.23  ** KEPT (pick-wt=10): 424 [] c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A),B).
% 15.31/15.23  ** KEPT (pick-wt=37): 426 [copy,425,flip.4] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_
% 15.31/15.23  Search stopped in tp_alloc by max_mem option.
% 15.31/15.23  Ozero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Ominus__class_Ominus(A,C,B))),c_Rings_Oinverse__class_Oinverse(A,C))=c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)).
% 15.31/15.23  ** KEPT (pick-wt=17): 427 [] -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.
% 15.31/15.23  ** KEPT (pick-wt=17): 428 [] -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.
% 15.31/15.23  ** KEPT (pick-wt=24): 429 [] -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)).
% 15.31/15.23  ** KEPT (pick-wt=25): 431 [copy,430,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)).
% 15.31/15.23  ** KEPT (pick-wt=12): 432 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Rings_Oinverse__class_Oinverse(A,C)|B=C.
% 15.31/15.23    Following clause subsumed by 432 during input processing: 0 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Rings_Oinverse__class_Oinverse(A,C)|B=C.
% 15.31/15.23  ** KEPT (pick-wt=12): 433 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)=c_Rings_Oinverse__class_Oinverse(A,C)|B!=C.
% 15.31/15.23  ** KEPT (pick-wt=9): 434 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Rings_Oinverse__class_Oinverse(A,B))=B.
% 15.31/15.23  ** KEPT (pick-wt=24): 435 [] -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)).
% 15.31/15.23  ** KEPT (pick-wt=21): 436 [] -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)).
% 15.31/15.23  ** KEPT (pick-wt=21): 437 [] -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).
% 15.31/15.23  ** KEPT (pick-wt=20): 438 [] -class_Rings_Odivision__ring(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Rings_Oinverse__class_Oinverse(A,C)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|B=C.
% 15.31/15.23  ** KEPT (pick-wt=12): 439 [] -class_Rings_Odivision__ring(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.23  ** KEPT (pick-wt=13): 440 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Rings_Oinverse__class_Oinverse(A,B))=B.
% 15.31/15.23    Following clause subsumed by 439 during input processing: 0 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.23  ** KEPT (pick-wt=12): 441 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.23  ** KEPT (pick-wt=12): 442 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.23  ** KEPT (pick-wt=9): 443 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 15.31/15.23  ** KEPT (pick-wt=9): 444 [] -class_Rings_Odivision__ring(A)|c_Rings_Oinverse__class_Oinverse(A,c_Groups_Oone__class_Oone(A))=c_Groups_Oone__class_Oone(A).
% 15.31/15.23  
% 15.31/15.23  Search stopped in tp_alloc by max_mem option.
% 15.31/15.23  
% 15.31/15.23  ============ end of search ============
% 15.31/15.23  
% 15.31/15.23  -------------- statistics -------------
% 15.31/15.23  clauses given                  0
% 15.31/15.23  clauses generated              0
% 15.31/15.23  clauses kept                 402
% 15.31/15.23  clauses forward subsumed      53
% 15.31/15.23  clauses back subsumed          0
% 15.31/15.23  Kbytes malloced            11718
% 15.31/15.23  
% 15.31/15.23  ----------- times (seconds) -----------
% 15.31/15.23  user CPU time          0.17          (0 hr, 0 min, 0 sec)
% 15.31/15.23  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 15.31/15.23  wall-clock time       15             (0 hr, 0 min, 15 sec)
% 15.31/15.23  
% 15.31/15.23  Process 22971 finished Wed Jul 27 02:59:00 2022
% 15.31/15.23  Otter interrupted
% 15.31/15.23  PROOF NOT FOUND
%------------------------------------------------------------------------------