%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SWW249+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n023.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 13:22:16 EDT 2022

% Result   : Unknown 15.82s 15.72s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SWW249+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n023.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 03:20:33 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 15.82/15.65  ----- Otter 3.3f, August 2004 -----
% 15.82/15.65  The process was started by sandbox2 on n023.cluster.edu,
% 15.82/15.65  Wed Jul 27 03:20:33 2022
% 15.82/15.65  The command was "./otter".  The process ID is 14801.
% 15.82/15.65  
% 15.82/15.65  set(prolog_style_variables).
% 15.82/15.65  set(auto).
% 15.82/15.65     dependent: set(auto1).
% 15.82/15.65     dependent: set(process_input).
% 15.82/15.65     dependent: clear(print_kept).
% 15.82/15.65     dependent: clear(print_new_demod).
% 15.82/15.65     dependent: clear(print_back_demod).
% 15.82/15.65     dependent: clear(print_back_sub).
% 15.82/15.65     dependent: set(control_memory).
% 15.82/15.65     dependent: assign(max_mem, 12000).
% 15.82/15.65     dependent: assign(pick_given_ratio, 4).
% 15.82/15.65     dependent: assign(stats_level, 1).
% 15.82/15.65     dependent: assign(max_seconds, 10800).
% 15.82/15.65  clear(print_given).
% 15.82/15.65  
% 15.82/15.65  formula_list(usable).
% 15.82/15.65  all A (A=A).
% 15.82/15.65  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).
% 15.82/15.65  class_Rings_Oidom(t_a)-> -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_p)).
% 15.82/15.65  all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))).
% 15.82/15.65  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))).
% 15.82/15.65  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))).
% 15.82/15.65  all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_OSuc,V_n))).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))).
% 15.82/15.65  all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 15.82/15.65  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))->hBOOL(hAPP(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))))))).
% 15.82/15.65  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a)))))).
% 15.82/15.65  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_x V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),V_x)=hAPP(hAPP(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)))).
% 15.82/15.65  all V_y_2 V_x_2 V_b_2 T_b (class_Rings_Olinordered__semidom(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b)),V_b_2))-> (hBOOL(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2),V_y_2))))).
% 15.82/15.65  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)).
% 15.82/15.65  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)).
% 15.82/15.65  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)).
% 15.82/15.65  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)).
% 15.82/15.65  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)).
% 15.82/15.65  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)).
% 15.82/15.65  all V_n_2 V_m_2 V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)<->V_m_2=V_n_2).
% 15.82/15.65  all V_k V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(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))).
% 15.82/15.65  all V_n V_m V_k (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(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))).
% 15.82/15.65  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)).
% 15.82/15.65  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).
% 15.82/15.65  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)).
% 15.82/15.65  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).
% 15.82/15.65  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)))).
% 15.82/15.65  all V_f_2 T_c T_b (c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)<-> (all B_x B_y (hAPP(V_f_2,B_x)=hAPP(V_f_2,B_y)))).
% 15.82/15.65  all V_m_2 V_x_2 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2)=hAPP(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=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.82/15.65  all V_n (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.82/15.65  all V_n V_m V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))-> (hBOOL(hAPP(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)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)))).
% 15.82/15.65  all V_n_2 V_x_2 (hBOOL(hAPP(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)))<->hBOOL(hAPP(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)).
% 15.82/15.65  all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.82/15.65  all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))->hBOOL(hAPP(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))))).
% 15.82/15.65  all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))->hBOOL(hAPP(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))))).
% 15.82/15.65  all V_n_2 V_k_2 V_m_2 (hBOOL(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 15.82/15.65  all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 15.82/15.65  all V_n_2 V_m_2 (hBOOL(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))).
% 15.82/15.65  all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 15.82/15.65  all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))).
% 15.82/15.65  all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))).
% 15.82/15.65  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)).
% 15.82/15.65  all T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))=hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.82/15.65  all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(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))))).
% 15.82/15.65  all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))))).
% 15.82/15.65  all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))))).
% 15.82/15.65  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)))).
% 15.82/15.65  all V_y V_x (hAPP(c_Nat_OSuc,V_x)=hAPP(c_Nat_OSuc,V_y)->V_x=V_y).
% 15.82/15.65  all V_nat_H_2 V_nat_2 (hAPP(c_Nat_OSuc,V_nat_2)=hAPP(c_Nat_OSuc,V_nat_H_2)<->V_nat_2=V_nat_H_2).
% 15.82/15.65  all V_n (hAPP(c_Nat_OSuc,V_n)!=V_n).
% 15.82/15.65  all V_n (V_n!=hAPP(c_Nat_OSuc,V_n)).
% 15.82/15.65  all V_P_2 V_n_2 V_m_2 ((hBOOL(hAPP(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)))-> ((hBOOL(hAPP(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))))).
% 15.82/15.65  all V_t V_s (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s),V_t))->V_s!=V_t).
% 15.82/15.65  all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))->V_m!=V_n).
% 15.82/15.65  all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n))).
% 15.82/15.65  all V_y V_x (V_x!=V_y-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y),V_x)))).
% 15.82/15.65  all V_n_2 V_m_2 (V_m_2!=V_n_2<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))).
% 15.82/15.65  all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n))).
% 15.82/15.65  all V_n_2 V_k_2 V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)<->V_m_2=V_n_2).
% 15.82/15.65  all V_n_2 V_m_2 V_k_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)<->V_m_2=V_n_2).
% 15.82/15.65  all V_k V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))).
% 15.82/15.65  all V_z V_y V_x (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z))).
% 15.82/15.65  all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)).
% 15.82/15.65  all V_q_2 V_b_2 V_pa_2 V_a_2 T_b (class_Groups_Ozero(T_b)-> (hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2)=hAPP(hAPP(c_Polynomial_OpCons(T_b),V_b_2),V_q_2)<->V_a_2=V_b_2&V_pa_2=V_q_2)).
% 15.82/15.65  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)).
% 15.82/15.65  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))).
% 15.82/15.65  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))).
% 15.82/15.65  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))).
% 15.82/15.65  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)).
% 15.82/15.65  all V_m (hAPP(c_Nat_OSuc,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.65  all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_m)).
% 15.82/15.65  all V_nat_H_1 (hAPP(c_Nat_OSuc,V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.65  all V_m (hAPP(c_Nat_OSuc,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.65  all V_nat_H (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_nat_H)).
% 15.82/15.65  all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_m)).
% 15.82/15.65  all V_n (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.65  all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 15.82/15.65  all V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))).
% 15.82/15.65  all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n)))-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->V_m=V_n)).
% 15.82/15.65  all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i)),V_k)))).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))-> (hAPP(c_Nat_OSuc,V_m)!=V_n->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)))).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n)))).
% 15.82/15.65  all V_m V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_OSuc,V_m)))->V_m=V_n)).
% 15.82/15.65  all V_m_2 V_n_2 (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,V_m_2)))<->V_n_2=V_m_2)).
% 15.82/15.65  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 15.82/15.65  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=V_n_2).
% 15.82/15.65  all V_n_2 V_m_2 (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,V_m_2)))).
% 15.82/15.65  all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=V_m->V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.65  all V_n_2 V_m_2 (hAPP(hAPP(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)).
% 15.82/15.65  all V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 15.82/15.65  all V_n (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=V_n).
% 15.82/15.65  all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))).
% 15.82/15.65  all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))).
% 15.82/15.65  all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))).
% 15.82/15.65  all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_k))).
% 15.82/15.65  all V_n V_m V_l V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)))).
% 15.82/15.65  all V_l V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))))).
% 15.82/15.65  all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)))).
% 15.82/15.65  all V_m V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)))).
% 15.82/15.65  all V_m V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)))).
% 15.82/15.65  all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 15.82/15.65  all V_i V_j (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i))).
% 15.82/15.65  all V_j V_i (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i))).
% 15.82/15.65  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).
% 15.82/15.65  all V_pa_2 V_a_2 T_b (class_Groups_Ozero(T_b)-> (hAPP(hAPP(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)))).
% 15.82/15.65  all T_a (class_Groups_Ozero(T_a)->hAPP(hAPP(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))).
% 15.82/15.65  all V_q V_b V_p V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_b),V_q))=hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q))).
% 15.82/15.65  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)).
% 15.82/15.65  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))).
% 15.82/15.65  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_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x)=hAPP(hAPP(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))).
% 15.82/15.65  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)).
% 15.82/15.65  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)).
% 15.82/15.65  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))->hBOOL(hAPP(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))))).
% 15.82/15.65  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))).
% 15.82/15.65  all V_n_2 V_m_2 V_a_2 T_b (class_Rings_Olinordered__semidom(T_b)-> (hBOOL(hAPP(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))).
% 15.82/15.65  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)),hAPP(c_Nat_OSuc,V_n))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.82/15.65  all V_n V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(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)).
% 15.82/15.65  all V_n V_a T_a (class_Power_Opower(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(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))).
% 15.82/15.65  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)).
% 15.82/15.65  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_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))).
% 15.82/15.65  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| (exists B_j (V_m_2=hAPP(c_Nat_OSuc,B_j)&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_n_2))))).
% 15.82/15.65  all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.65  all V_n_2 (hBOOL(hAPP(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=hAPP(c_Nat_OSuc,B_m)))).
% 15.82/15.65  all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_m_2=hAPP(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=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.82/15.65  all V_n_2 V_m_2 (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)<->V_m_2=hAPP(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=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.82/15.65  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))).
% 15.82/15.65  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))<-> (exists B_k (V_n_2=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k))))).
% 15.82/15.65  all V_m V_i hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))).
% 15.82/15.65  all V_m V_i hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))).
% 15.82/15.65  c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.65  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))->hBOOL(hAPP(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)))))).
% 15.82/15.65  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))).
% 15.82/15.65  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))->hBOOL(hAPP(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),hAPP(c_Nat_OSuc,V_n)))))).
% 15.82/15.65  all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_n V_m V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))-> (hBOOL(hAPP(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)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))))).
% 15.82/15.65  all T_a (class_Rings_Olinordered__semidom(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))))).
% 15.82/15.65  all V_y_2 V_x_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(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))).
% 15.82/15.65  all V_y V_x T_a (class_Rings_Olinordered__ring(T_a)-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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)))).
% 15.82/15.65  class_Rings_Oidom(t_a)-> -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____))).
% 15.82/15.65  all V_n (hAPP(c_Nat_OSuc,V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 15.82/15.65  all V_n (hAPP(c_Nat_OSuc,V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)).
% 15.82/15.65  all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))->V_x=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.82/15.65  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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q))).
% 15.82/15.65  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)).
% 15.82/15.65  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),hAPP(c_Nat_OSuc,V_q))).
% 15.82/15.65  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),hAPP(c_Nat_OSuc,V_q))).
% 15.82/15.65  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),hAPP(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))).
% 15.82/15.65  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))).
% 15.82/15.65  all V_q T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q)=V_q).
% 15.82/15.65  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))).
% 15.82/15.65  all V_p T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=V_p).
% 15.82/15.65  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)).
% 15.82/15.65  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))).
% 15.82/15.65  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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_r)=hAPP(hAPP(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))).
% 15.82/15.65  all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (V_x!=V_y-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))))).
% 15.82/15.65  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)).
% 15.82/15.65  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))).
% 15.82/15.65  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)).
% 15.82/15.65  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))).
% 15.82/15.65  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)).
% 15.82/15.65  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)))).
% 15.82/15.65  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))).
% 15.82/15.65  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))).
% 15.82/15.65  all V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)).
% 15.82/15.65  all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d))).
% 15.82/15.65  all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d)).
% 15.82/15.65  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))).
% 15.82/15.65  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b)).
% 15.82/15.65  all V_d V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))).
% 15.82/15.65  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))).
% 15.82/15.65  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)).
% 15.82/15.65  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)).
% 15.82/15.65  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)).
% 15.82/15.65  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)).
% 15.82/15.65  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))).
% 15.82/15.65  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)))).
% 15.82/15.65  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))).
% 15.82/15.65  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a).
% 15.82/15.65  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 15.82/15.65  all V_a_2 V_b_2 T_b (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)-> (V_b_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.65  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)).
% 15.82/15.65  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)).
% 15.82/15.65  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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z))=hAPP(hAPP(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))).
% 15.82/15.65  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<->hAPP(hAPP(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))!=hAPP(hAPP(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)))).
% 15.82/15.65  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(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))).
% 15.82/15.65  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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(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))).
% 15.82/15.65  all V_b V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m)).
% 15.82/15.65  all V_c V_b V_e V_a T_a (class_Rings_Osemiring(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c)).
% 15.82/15.65  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)-> (hAPP(hAPP(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))=hAPP(hAPP(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)).
% 15.82/15.65  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).
% 15.82/15.65  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).
% 15.82/15.65  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))).
% 15.82/15.65  all V_n_2 V_x_2 (hBOOL(hAPP(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)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))).
% 15.82/15.65  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).
% 15.82/15.65  all V_a T_a (class_Rings_Olinordered__ring(T_a)-> -hBOOL(hAPP(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)))).
% 15.82/15.65  all V_b_2 V_ca_2 V_a_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (hBOOL(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),V_a_2)))).
% 15.82/15.65  all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (hBOOL(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),V_a_2)))).
% 15.82/15.65  all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))-> (hBOOL(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2))))).
% 15.82/15.65  all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(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)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))))).
% 15.82/15.65  all V_a V_b T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(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)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))))).
% 15.82/15.65  all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))-> (hBOOL(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),V_a_2))))).
% 15.82/15.65  all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_b V_a T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_c V_b V_a T_a (class_Rings_Olinordered__comm__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_c V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))))).
% 15.82/15.65  all V_y_2 V_x_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (hAPP(hAPP(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))).
% 15.82/15.65  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->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d))))).
% 15.82/15.65  all T_a (class_Rings_Olinordered__semidom(T_a)-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a)))).
% 15.82/15.65  all T_a (class_Rings_Olinordered__semidom(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a)))).
% 15.82/15.65  all V_n V_m T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_m))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_n))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_a T_a (class_Rings_Olinordered__semidom(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))))).
% 15.82/15.65  all V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m)).
% 15.82/15.65  all V_a V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m)).
% 15.82/15.65  all V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m)).
% 15.82/15.65  class_Rings_Oidom(t_a)-> (-c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))-> (exists B_k B_a (B_a!=c_Groups_Ozero__class_Ozero(t_a)&B_k!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)& (exists B_q (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,B_q)),B_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,v_cs____)& (all B_z (hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(t_a,v_cs____),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_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),B_a),B_q)),B_z)))))))))).
% 15.82/15.65  all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(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)).
% 15.82/15.65  all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))-> (hBOOL(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)))).
% 15.82/15.65  all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Opcompose(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),V_q)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(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)))).
% 15.82/15.65  all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)))).
% 15.82/15.65  all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))))).
% 15.82/15.65  all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))))).
% 15.82/15.65  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))))).
% 15.82/15.65  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))).
% 15.82/15.65  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))).
% 15.82/15.65  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))).
% 15.82/15.65  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))).
% 15.82/15.65  all V_c V_a V_b T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)->V_b=V_c)).
% 15.82/15.65  all V_c V_b V_a T_a (class_Groups_Ocancel__ab__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)->V_b=V_c)).
% 15.82/15.65  all V_c V_b V_a T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)->V_b=V_c)).
% 15.82/15.65  all V_ca_2 V_a_2 V_b_2 T_b (class_Groups_Ocancel__semigroup__add(T_b)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)<->V_b_2=V_ca_2)).
% 15.82/15.65  all V_ca_2 V_b_2 V_a_2 T_b (class_Groups_Ocancel__semigroup__add(T_b)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)<->V_b_2=V_ca_2)).
% 15.82/15.65  all V_c V_b V_a T_a (class_Groups_Oab__semigroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))).
% 15.82/15.65  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))).
% 15.82/15.65  all V_z V_y V_x (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(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))).
% 15.82/15.65  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))).
% 15.82/15.65  all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (hAPP(hAPP(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))).
% 15.82/15.65  all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 15.82/15.65  all V_a T_a (class_Groups_Omonoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 15.82/15.65  all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (c_Groups_Ozero__class_Ozero(T_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.65  all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a).
% 15.82/15.65  all V_a T_a (class_Groups_Omonoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a).
% 15.82/15.65  all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))).
% 15.82/15.65  all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))).
% 15.82/15.65  all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))))).
% 15.82/15.65  all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))))).
% 15.82/15.65  all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))))).
% 15.82/15.65  all V_b_2 V_a_2 V_ca_2 T_b (class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)))).
% 15.82/15.65  all V_b_2 V_ca_2 V_a_2 T_b (class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)))).
% 15.82/15.65  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).
% 15.82/15.65  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).
% 15.82/15.65  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).
% 15.82/15.65  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).
% 15.82/15.65  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).
% 15.82/15.65  all V_k V_j V_u V_i (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k)).
% 15.82/15.65  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 15.82/15.65  all V_q_2 V_pa_2 T_b (class_Rings_Ocomm__semiring__0(T_b)->c_Polynomial_Opcompose(T_b,V_pa_2,V_q_2)=c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(T_b),T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBK(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBB(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),T_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))))),hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2))),V_pa_2)).
% 15.82/15.65  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))).
% 15.82/15.65  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))).
% 15.82/15.65  class_Rings_Oidom(t_a)-> (exists B_k B_a (B_a!=c_Groups_Ozero__class_Ozero(t_a)& (exists B_q (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,B_q)),B_k))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(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,hAPP(hAPP(c_Polynomial_OpCons(t_a),B_a),B_q)),B_z)))))))).
% 15.82/15.65  all V_y V_z V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))).
% 15.82/15.65  all V_z V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))).
% 15.82/15.65  all V_pa_2 V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Polynomial_Opos__poly(T_b,hAPP(hAPP(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))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)))).
% 15.82/15.65  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).
% 15.82/15.65  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).
% 15.82/15.65  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)).
% 15.82/15.65  all V_z2 V_z1 V_w (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2))=hAPP(hAPP(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))).
% 15.82/15.65  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))).
% 15.82/15.65  all V_w V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w)=hAPP(hAPP(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))).
% 15.82/15.65  all V_n_2 V_m_2 (hBOOL(hAPP(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))).
% 15.82/15.65  all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))->hBOOL(hAPP(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))))).
% 15.82/15.65  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)))).
% 15.82/15.65  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_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q))))).
% 15.82/15.65  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))))).
% 15.82/15.65  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).
% 15.82/15.65  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),hAPP(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))).
% 15.82/15.65  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)).
% 15.82/15.65  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,hAPP(hAPP(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)))).
% 15.82/15.65  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,hAPP(hAPP(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)))).
% 15.82/15.65  all V_q_2 V_pa_2 T_b (class_Rings_Ocomm__semiring__0(T_b)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)=c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(T_b),T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBK(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBB(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),T_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),c_Polynomial_Osmult(T_b)),V_q_2)))),hAPP(c_Polynomial_OpCons(T_b),c_Groups_Ozero__class_Ozero(T_b)))),V_pa_2)).
% 15.82/15.65  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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_b_H))=hAPP(hAPP(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))).
% 15.82/15.65  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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))=hAPP(hAPP(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))).
% 15.82/15.65  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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_a_H)),V_b)=hAPP(hAPP(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))).
% 15.82/15.65  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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya)=hAPP(hAPP(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))).
% 15.82/15.65  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))).
% 15.82/15.65  all V_n V_b V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(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)).
% 15.82/15.65  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)).
% 15.82/15.65  all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x),V_y))|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y),V_x))).
% 15.82/15.65  all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k)))).
% 15.82/15.65  all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))).
% 15.82/15.65  all V_z3 V_z2 V_z1 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3))).
% 15.82/15.65  all V_z V_y V_x (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z))).
% 15.82/15.65  all V_z_2 V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))|V_w_2=V_z_2).
% 15.82/15.65  all V_w V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)).
% 15.82/15.65  all V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z).
% 15.82/15.65  all V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)=V_z).
% 15.82/15.65  hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 15.82/15.65  all V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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)).
% 15.82/15.65  c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.82/15.65  all V_p V_b V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_b),V_p))=hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_p)).
% 15.82/15.65  all V_p T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),c_Groups_Oone__class_Oone(T_a)),V_p)=V_p).
% 15.82/15.65  all V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(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))).
% 15.82/15.65  all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q))).
% 15.82/15.65  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)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_q)=hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))).
% 15.82/15.65  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),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q))=hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))).
% 15.82/15.65  all V_pa_2 V_a_2 T_b (class_Rings_Oidom(T_b)-> (hAPP(hAPP(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)))).
% 15.82/15.65  all V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_p)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.82/15.65  all V_p V_b V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_b),V_p))=hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p))).
% 15.82/15.65  all V_x V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(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))).
% 15.82/15.65  all V_a V_p V_c T_a (class_Rings_Ocomm__semiring__0(T_a)-> (hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),V_p)=hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)->V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.82/15.65  all V_p V_b V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_p)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_b),V_p))).
% 15.82/15.65  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))).
% 15.82/15.65  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))).
% 15.82/15.65  all V_b V_n V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_n)).
% 15.82/15.65  all V_a V_p V_c T_a (class_Rings_Ocomm__semiring__0(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),V_p)),hAPP(hAPP(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)))).
% 15.82/15.65  all V_n V_a T_a (class_Groups_Ozero(T_a)->c_Polynomial_Omonom(T_a,V_a,hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Polynomial_Omonom(T_a,V_a,V_n))).
% 15.82/15.65  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))).
% 15.82/15.65  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))=hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.82/15.65  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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))).
% 15.82/15.65  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)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),V_q)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q)),hAPP(hAPP(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)))).
% 15.82/15.65  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),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_q))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(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)))).
% 15.82/15.65  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)).
% 15.82/15.65  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)).
% 15.82/15.65  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)).
% 15.82/15.65  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)).
% 15.82/15.65  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_Polynomial_Opoly__rec(tc_Polynomial_Opoly(T_b),T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBK(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),T_b),hAPP(c_COMBS(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b))),hAPP(c_Polynomial_Osmult(T_b),V_h_2)))),c_Polynomial_OpCons(T_b))),V_pa_2)).
% 15.82/15.65  all V_r V_q V_c V_p T_a (class_Rings_Ocomm__semiring__0(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),V_q))=hAPP(hAPP(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))).
% 15.82/15.65  all V_c V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)))=hAPP(hAPP(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))).
% 15.82/15.65  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,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),V_h)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_h),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)))).
% 15.82/15.65  all V_n V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->hBOOL(hAPP(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))))))).
% 15.82/15.65  all V_v V_u V_y V_a V_x T_a (class_Rings_Olinordered__semiring__1__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v)=c_Groups_Oone__class_Oone(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)))))))).
% 15.82/15.65  all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)).
% 15.82/15.65  all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_N))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))))).
% 15.82/15.65  all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)))).
% 15.82/15.65  all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)))).
% 15.82/15.65  all V_d V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))))).
% 15.82/15.65  all V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))))).
% 15.82/15.65  all V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))))).
% 15.82/15.65  all V_b_2 V_a_2 V_ca_2 T_b (class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2)))).
% 15.82/15.65  all V_b_2 V_ca_2 V_a_2 T_b (class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2)))).
% 15.82/15.65  all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)).
% 15.82/15.65  all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.65  all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n)),V_n))).
% 15.82/15.65  all V_n_2 V_m_2 (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)),V_m_2))).
% 15.82/15.65  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=hAPP(c_Nat_OSuc,V_n_2)).
% 15.82/15.65  all V_m_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),V_m_2))).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n)))).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n)))-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->V_m=hAPP(c_Nat_OSuc,V_n))).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))).
% 15.82/15.65  all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),V_y))).
% 15.82/15.65  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))&V_m_2!=V_n_2).
% 15.82/15.65  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=V_n_2).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))-> (V_m!=V_n->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)))).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|V_m=V_n->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))).
% 15.82/15.65  all V_y V_z V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))).
% 15.82/15.65  all V_z V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))).
% 15.82/15.65  all V_m V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))).
% 15.82/15.65  all V_m V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))).
% 15.82/15.65  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))<-> (exists B_k (V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)))).
% 15.82/15.65  all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))).
% 15.82/15.65  all V_m V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)))).
% 15.82/15.65  all V_m V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)))).
% 15.82/15.65  all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)))).
% 15.82/15.65  all V_l V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_l))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))))).
% 15.82/15.65  all V_n V_k V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n))).
% 15.82/15.65  all V_n V_k V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))).
% 15.82/15.65  all V_n V_k V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))-> -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n)))).
% 15.82/15.65  all V_w_2 V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),V_w_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2),V_w_2))&V_z_2!=V_w_2).
% 15.82/15.65  all V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))).
% 15.82/15.65  all V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))).
% 15.82/15.65  all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))).
% 15.82/15.65  all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))).
% 15.82/15.65  all V_l V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_l))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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_l))))).
% 15.82/15.65  all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j)))).
% 15.82/15.65  all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_N))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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))))))).
% 15.82/15.65  all V_y_2 V_x_2 V_b_2 T_b (class_Rings_Olinordered__semidom(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b)),V_b_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x_2),V_y_2))))).
% 15.82/15.65  all V_n V_m V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))))).
% 15.82/15.65  all V_a T_a (class_Rings_Olinordered__ring(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)))).
% 15.82/15.65  all V_b_2 V_a_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b)))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2),c_Groups_Ozero__class_Ozero(T_b))))).
% 15.82/15.65  all V_b_2 V_a_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2),c_Groups_Ozero__class_Ozero(T_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b)))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_b_2)))).
% 15.82/15.65  all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))))).
% 15.82/15.65  all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 15.82/15.65  all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 15.82/15.65  all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 15.82/15.65  all V_b V_a T_a (class_Rings_Oordered__ring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))))).
% 15.82/15.65  all V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_c V_b V_a T_a (class_Rings_Oordered__comm__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_c V_a V_b T_a (class_Rings_Oordered__ring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_c V_a V_b T_a (class_Rings_Oordered__ring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(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)))))).
% 15.82/15.65  all V_d V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(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_d)))))))).
% 15.82/15.65  all V_d V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(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_d)))))))).
% 15.82/15.65  all V_b V_a T_a (class_Rings_Oordered__ring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))).
% 15.82/15.65  all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.82/15.65  all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)))).
% 15.82/15.65  all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))))).
% 15.82/15.65  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))))).
% 15.82/15.65  all V_y_2 V_x_2 T_b (class_Groups_Oordered__comm__monoid__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_x_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_y_2))-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_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))))).
% 15.82/15.65  all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))))).
% 15.82/15.65  all V_a V_b V_c T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))))).
% 15.82/15.65  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 15.82/15.65  all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))))).
% 15.82/15.65  all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))))).
% 15.82/15.65  all T_a (class_Rings_Olinordered__semidom(T_a)-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a)))).
% 15.82/15.65  all T_a (class_Rings_Olinordered__semidom(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a)))).
% 15.82/15.65  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 15.82/15.65  all V_n V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))))).
% 15.82/15.65  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 15.82/15.65  all V_m_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)),V_m_2))).
% 15.82/15.65  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))).
% 15.82/15.65  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n)))).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n))).
% 15.82/15.65  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,V_m_2)))<->V_n_2=V_m_2)).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))).
% 15.82/15.65  all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))).
% 15.82/15.65  all V_z V_z_H V_w V_w_H (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H),V_w))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_H),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))))).
% 15.82/15.65  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))).
% 15.82/15.65  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)))).
% 15.82/15.65  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))).
% 15.82/15.65  all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2)=c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2))).
% 15.82/15.65  all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))-> (hBOOL(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2))))).
% 15.82/15.65  all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))-> (hBOOL(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2),V_a_2))))).
% 15.82/15.65  all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(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)))))))).
% 15.82/15.65  all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(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)))))))).
% 15.82/15.65  all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(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)))))))).
% 15.82/15.65  all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(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)))))))).
% 15.82/15.65  all V_b V_c V_a T_a (class_Rings_Olinordered__semiring(T_a)-> (hBOOL(hAPP(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)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))).
% 15.82/15.65  all V_b V_c V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(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)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))).
% 15.82/15.65  all V_b V_a V_c T_a (class_Rings_Olinordered__semiring(T_a)-> (hBOOL(hAPP(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)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))).
% 15.82/15.65  all V_b V_a V_c T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(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)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))).
% 15.82/15.65  all V_b V_c V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(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)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))))).
% 15.82/15.65  all V_b V_a V_c T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(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)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))))).
% 15.82/15.65  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))))).
% 15.82/15.65  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))))).
% 15.82/15.65  all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))))).
% 15.82/15.65  all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))))).
% 15.82/15.65  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 15.82/15.65  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 15.82/15.65  all V_y V_x T_a (class_Rings_Olinordered__ring(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(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))))).
% 15.82/15.65  all V_y_2 V_x_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(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))).
% 15.82/15.65  all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)))))).
% 15.82/15.65  all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)))))).
% 15.82/15.65  all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(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)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))).
% 15.82/15.65  all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))))).
% 15.82/15.65  all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->V_a=V_b)))).
% 15.82/15.65  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2))).
% 15.82/15.65  all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))<-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)))).
% 15.82/15.65  all V_n_2 V_k_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))<-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)))).
% 15.82/15.65  all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)))).
% 15.82/15.65  all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))).
% 15.82/15.65  all V_z_2 V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2))).
% 15.82/15.65  all V_z_2 V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))).
% 15.82/15.65  all V_z V_w (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z))).
% 15.82/15.65  all V_n V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))).
% 15.82/15.65  all V_v V_u V_y V_a V_x T_a (class_Rings_Olinordered__semiring__1(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v)=c_Groups_Oone__class_Oone(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)))))))).
% 15.82/15.65  all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(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)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->V_a=V_b))))).
% 15.82/15.65  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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_h),V_x))).
% 15.82/15.65  all V_c V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osynthetic__div(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),V_c)=hAPP(hAPP(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))).
% 15.82/15.65  all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)))).
% 15.82/15.65  all V_h V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h)=hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.82/15.65  all V_q V_r V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))-> (V_a=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q),c_Groups_Oone__class_Oone(tc_Int_Oint)))))).
% 15.82/15.65  all V_q V_r V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))-> (V_a=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q))))).
% 15.82/15.65  all V_n V_r T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_r))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_r),c_Groups_Oone__class_Oone(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),hAPP(c_Nat_OSuc,V_n))),V_r))))).
% 15.82/15.65  all V_r_H V_q_H V_b_H (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H))))).
% 15.82/15.65  all V_r_H V_q_H V_b_H (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))).
% 15.82/15.65  all V_w hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w),V_w)).
% 15.82/15.65  all V_w V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z),V_w))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w),V_z))).
% 15.82/15.65  all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_j),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i),V_k)))).
% 15.82/15.65  all V_w V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z),V_w))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w),V_z))->V_z=V_w)).
% 15.82/15.65  all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_n)).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))).
% 15.82/15.65  all V_n V_m (V_m=V_n->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))).
% 15.82/15.65  all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_k)))).
% 15.82/15.65  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->V_m=V_n)).
% 15.82/15.65  all V_r_H V_q_H V_b_H V_r V_q V_b (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H),V_q)))))))).
% 15.82/15.65  all V_r V_q V_r_H V_q_H V_b (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r_H))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q),V_q_H)))))).
% 15.82/15.65  all V_r_H V_q_H V_b_H V_r V_q V_b (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q),V_q_H)))))))).
% 15.82/15.65  all V_r V_q V_r_H V_q_H V_b (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H),V_q)))))).
% 15.82/15.65  all V_n V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)))).
% 15.82/15.65  all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))))).
% 15.82/15.65  all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))))).
% 15.82/15.65  hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 15.82/15.65  hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.65  all V_x T_a (class_Orderings_Opreorder(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_x))).
% 15.82/15.65  all V_p V_c T_a (class_Rings_Ocomm__ring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_c)),hAPP(hAPP(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))),hAPP(hAPP(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).
% 15.82/15.65  all V_l_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_l_2))<-> (exists B_n (V_l_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),B_n)))).
% 15.82/15.65  all V_y_2 V_x_2 T_b (class_Orderings_Olinorder(T_b)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_y_2),V_x_2)))).
% 15.82/15.65  all V_p V_a T_b (class_Groups_Oab__group__add(T_b)->c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a),V_p))=hAPP(hAPP(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))).
% 15.82/15.65  all V_p V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p))=hAPP(hAPP(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))).
% 15.82/15.65  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))).
% 15.82/15.65  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)).
% 15.82/15.65  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)).
% 15.82/15.65  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))).
% 15.82/15.65  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).
% 15.82/15.65  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)).
% 15.82/15.65  all V_p V_a T_a (class_Rings_Ocomm__ring(T_a)->hAPP(hAPP(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),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p))).
% 15.82/15.65  all V_p V_a T_a (class_Rings_Ocomm__ring(T_a)->hAPP(hAPP(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),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p))).
% 15.82/15.65  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))).
% 15.82/15.65  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))).
% 15.82/15.65  all V_w V_z (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w))=hAPP(hAPP(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))).
% 15.82/15.65  c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.82/15.65  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=V_b).
% 15.82/15.65  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b))=V_b).
% 15.82/15.65  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=hAPP(hAPP(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))).
% 15.82/15.65  all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=hAPP(hAPP(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))).
% 15.82/15.65  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))).
% 15.82/15.65  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)).
% 15.82/15.65  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))).
% 15.82/15.65  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)).
% 15.82/15.65  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))).
% 15.82/15.65  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))).
% 15.82/15.65  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))).
% 15.82/15.65  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))).
% 15.82/15.65  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))).
% 15.82/15.65  all V_a_2 V_b_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (hBOOL(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)))).
% 15.82/15.65  all V_b_2 V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),V_b_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)),V_a_2)))).
% 15.82/15.65  all V_b_2 V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))))).
% 15.82/15.65  all V_b_2 V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))))).
% 15.82/15.65  all V_b_2 V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),V_b_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)),V_a_2)))).
% 15.82/15.65  all V_a_2 V_b_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2)))).
% 15.82/15.65  all V_b V_a T_a (class_Groups_Oordered__ab__group__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)),c_Groups_Ouminus__class_Ouminus(T_a,V_a))))).
% 15.82/15.65  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))).
% 15.82/15.65  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))).
% 15.82/15.65  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))).
% 15.82/15.66  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)).
% 15.82/15.66  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)).
% 15.82/15.66  all V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))))).
% 15.82/15.66  all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))))).
% 15.82/15.66  all V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)))).
% 15.82/15.66  all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),V_a_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)))).
% 15.82/15.66  all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),V_a_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)))).
% 15.82/15.66  all V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)))).
% 15.82/15.66  all V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))))).
% 15.82/15.66  all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))))).
% 15.82/15.66  all V_y_2 V_x_2 T_b (class_Groups_Ogroup__add(T_b)-> (hAPP(hAPP(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))).
% 15.82/15.66  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)-> (hAPP(hAPP(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)).
% 15.82/15.66  all V_a T_a (class_Groups_Oab__group__add(T_a)->hAPP(hAPP(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)).
% 15.82/15.66  all V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(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)).
% 15.82/15.66  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)<->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.66  all V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(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)).
% 15.82/15.66  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)))).
% 15.82/15.66  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)).
% 15.82/15.66  all V_z (hAPP(hAPP(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)).
% 15.82/15.66  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))).
% 15.82/15.66  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))).
% 15.82/15.66  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),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Nat_OSuc,hAPP(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))).
% 15.82/15.66  all V_g_2 V_f_2 T_b T_c (class_Orderings_Oord(T_c)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,T_c),V_f_2),V_g_2))<-> (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_c,hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))))).
% 15.82/15.66  all V_y V_x T_a (class_Orderings_Olinorder(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))).
% 15.82/15.66  all V_y_2 V_x_2 T_b (class_Orderings_Oorder(T_b)-> (V_x_2=V_y_2<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_y_2),V_x_2)))).
% 15.82/15.66  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (V_x=V_y->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y)))).
% 15.82/15.66  all V_x_2 V_g_2 V_f_2 T_b T_c (class_Orderings_Oord(T_c)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,T_c),V_f_2),V_g_2))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_c,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))))).
% 15.82/15.66  all V_x_2 V_y_2 T_b (class_Orderings_Oorder(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_y_2),V_x_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))<->V_x_2=V_y_2))).
% 15.82/15.66  all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_c))))).
% 15.82/15.66  all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_a))))).
% 15.82/15.66  all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (V_b=V_c->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_c))))).
% 15.82/15.66  all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))-> (V_b=V_c->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_a))))).
% 15.82/15.66  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))->V_x=V_y))).
% 15.82/15.66  all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_z))))).
% 15.82/15.66  all V_x V_y T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))->V_x=V_y))).
% 15.82/15.66  all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_z),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_z),V_x))))).
% 15.82/15.66  all V_x_2 V_g_2 V_f_2 T_b T_c (class_Orderings_Oord(T_c)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,T_c),V_f_2),V_g_2))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_c,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))))).
% 15.82/15.66  all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x)))).
% 15.82/15.66  all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))-> (V_x!=V_y->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))))).
% 15.82/15.66  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))).
% 15.82/15.66  all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x))))).
% 15.82/15.66  all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z))))).
% 15.82/15.66  all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))-> (V_b=V_c->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a))))).
% 15.82/15.66  all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (V_b=V_c->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c))))).
% 15.82/15.66  all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a))))).
% 15.82/15.66  all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c))))).
% 15.82/15.66  all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))).
% 15.82/15.66  all V_b V_a T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)))).
% 15.82/15.66  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->V_y!=V_x)).
% 15.82/15.66  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->V_x!=V_y)).
% 15.82/15.66  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))).
% 15.82/15.66  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))).
% 15.82/15.66  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->V_x!=V_y)).
% 15.82/15.66  all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (V_x!=V_y-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))))).
% 15.82/15.66  all V_x_2 V_y_2 T_b (class_Orderings_Olinorder(T_b)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_y_2),V_x_2))-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))<->V_x_2=V_y_2))).
% 15.82/15.66  all V_y V_x T_a (class_Orderings_Olinorder(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))).
% 15.82/15.66  all V_y_2 V_x_2 T_b (class_Orderings_Olinorder(T_b)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_y_2),V_x_2))|V_x_2=V_y_2)).
% 15.82/15.66  all V_y_2 V_x_2 T_b (class_Orderings_Olinorder(T_b)-> (V_x_2!=V_y_2<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_y_2),V_x_2)))).
% 15.82/15.66  all V_x T_a (class_Orderings_Opreorder(T_a)-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_x))).
% 15.82/15.66  all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x))))).
% 15.82/15.66  all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z))))).
% 15.82/15.66  all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_z),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x))))).
% 15.82/15.66  all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z))))).
% 15.82/15.66  all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))-> (V_a!=V_b->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))))).
% 15.82/15.66  all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (V_a!=V_b->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))).
% 15.82/15.66  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x=V_y)).
% 15.82/15.66  all V_y_2 V_x_2 T_b (class_Orderings_Olinorder(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))<->V_x_2=V_y_2))).
% 15.82/15.66  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y)))).
% 15.82/15.66  all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)))).
% 15.82/15.66  all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))))).
% 15.82/15.66  all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))).
% 15.82/15.66  all V_y_2 V_x_2 T_b (class_Orderings_Olinorder(T_b)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))<->V_x_2=V_y_2))).
% 15.82/15.66  all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)))).
% 15.82/15.66  all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x)))).
% 15.82/15.66  all V_y_2 V_x_2 T_b (class_Orderings_Oorder(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))|V_x_2=V_y_2)).
% 15.82/15.66  all V_y_2 V_x_2 T_b (class_Orderings_Opreorder(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))& -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_y_2),V_x_2)))).
% 15.82/15.66  all V_y_2 V_x_2 T_b (class_Orderings_Oorder(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))&V_x_2!=V_y_2)).
% 15.82/15.66  all V_y V_x T_a (class_Orderings_Olinorder(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))).
% 15.82/15.66  all V_y_2 V_x_2 T_b (class_Orderings_Olinorder(T_b)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_y_2),V_x_2)))).
% 15.82/15.66  all V_a V_p T_a (class_Rings_Oidom(T_a)-> (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),hAPP(hAPP(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))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(T_a,V_a,V_p)))),V_p)))).
% 15.82/15.66  all V_a V_p T_a (class_Rings_Oidom(T_a)-> (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))-> -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(T_a,V_a,V_p)))),V_p)))).
% 15.82/15.66  all V_y_2 V_x_2 T_b (class_Lattices_Oboolean__algebra(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_x_2)),c_Groups_Ouminus__class_Ouminus(T_b,V_y_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_y_2),V_x_2)))).
% 15.82/15.66  all V_y V_x T_a (class_Lattices_Oboolean__algebra(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y)),c_Groups_Ouminus__class_Ouminus(T_a,V_x))))).
% 15.82/15.66  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))).
% 15.82/15.66  all V_y_2 V_x_2 T_b (class_Rings_Ocomm__ring__1(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),c_Groups_Ouminus__class_Ouminus(T_b,V_x_2)),V_y_2))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)))).
% 15.82/15.66  all V_y_2 V_x_2 T_b (class_Rings_Ocomm__ring__1(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),c_Groups_Ouminus__class_Ouminus(T_b,V_y_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)))).
% 15.82/15.66  all V_z (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z))=V_z).
% 15.82/15.66  all V_g_2 V_f_2 T_b T_c (class_Orderings_Oord(T_c)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c),V_f_2),V_g_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,T_c),V_f_2),V_g_2))& -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,T_c),V_g_2),V_f_2)))).
% 15.82/15.66  all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_q))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q)))).
% 15.82/15.66  all V_a V_q V_p T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q))))).
% 15.82/15.66  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a))).
% 15.82/15.66  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))))).
% 15.82/15.66  all V_n V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))->hBOOL(hAPP(hAPP(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))))).
% 15.82/15.66  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))).
% 15.82/15.66  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))))).
% 15.82/15.66  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)))).
% 15.82/15.66  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)))).
% 15.82/15.66  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)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)))).
% 15.82/15.66  all V_d V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))->hBOOL(hAPP(hAPP(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)))))).
% 15.82/15.66  all V_b V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))).
% 15.82/15.66  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))).
% 15.82/15.66  all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))).
% 15.82/15.66  all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))).
% 15.82/15.66  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(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))).
% 15.82/15.66  all V_b_2 V_ca_2 V_a_2 T_b (class_Rings_Oidom(T_b)-> (hBOOL(hAPP(hAPP(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)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)))).
% 15.82/15.66  all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Oidom(T_b)-> (hBOOL(hAPP(hAPP(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)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)))).
% 15.82/15.66  all V_a V_n V_m T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))))).
% 15.82/15.66  all V_m V_n V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->hBOOL(hAPP(hAPP(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_m)))))).
% 15.82/15.66  all V_m V_b V_n V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b))))).
% 15.82/15.66  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)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_q_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2))))).
% 15.82/15.66  all V_a V_q V_p T_a (class_Fields_Ofield(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_q))))).
% 15.82/15.66  all V_q V_a V_p T_a (class_Fields_Ofield(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q)))-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))))).
% 15.82/15.66  all V_q_2 V_pa_2 V_a_2 T_b (class_Fields_Ofield(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(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)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2))))).
% 15.82/15.66  all V_a T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)=V_a).
% 15.82/15.66  all V_x T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)=V_x).
% 15.82/15.66  all V_b V_a T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_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)).
% 15.82/15.66  all V_y_2 V_x_2 T_b (class_Lattices_Oboolean__algebra(T_b)-> (c_Groups_Ouminus__class_Ouminus(T_b,V_x_2)=c_Groups_Ouminus__class_Ouminus(T_b,V_y_2)<->V_x_2=V_y_2)).
% 15.82/15.66  all V_x_2 V_A_2 T_c T_b (class_Groups_Ouminus(T_b)->hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b),V_A_2),V_x_2)=c_Groups_Ouminus__class_Ouminus(T_b,hAPP(V_A_2,V_x_2))).
% 15.82/15.66  all V_x T_a (class_Lattices_Oboolean__algebra(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x))=V_x).
% 15.82/15.66  all V_x V_n T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(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)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))))).
% 15.82/15.66  all V_x_2 V_A_2 T_c T_b (class_Groups_Ouminus(T_b)->hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b),V_A_2),V_x_2)=c_Groups_Ouminus__class_Ouminus(T_b,hAPP(V_A_2,V_x_2))).
% 15.82/15.66  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)<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Ouminus__class_Ouminus(T_b,V_ca_2)),hAPP(hAPP(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)))).
% 15.82/15.66  all V_pa_2 V_ca_2 T_b (class_Rings_Oidom(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),V_ca_2),hAPP(hAPP(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))).
% 15.82/15.66  all V_p V_a T_a (class_Rings_Oidom(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),hAPP(hAPP(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))).
% 15.82/15.66  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 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b))))&hBOOL(hAPP(V_P_2,B_x)))))).
% 15.82/15.66  all V_pa_2 V_a_2 T_b (class_Rings_Oidom(T_b)->c_Polynomial_Oorder(T_b,V_a_2,V_pa_2)=c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot),hAPP(c_COMBC(tc_Nat_Onat,tc_Polynomial_Opoly(T_b),tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_HOL_Obool),tc_Nat_Onat),c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Polynomial_Opoly(T_b),tc_Nat_Onat),hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))))),c_Nat_OSuc))),V_pa_2)))).
% 15.82/15.66  all V_n_2 V_P_2 (-hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))-> (hBOOL(hAPP(V_P_2,V_n_2))-> (exists B_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k),V_n_2))& (all B_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i),B_k))-> -hBOOL(hAPP(V_P_2,B_i))))&hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))).
% 15.82/15.66  all V_k hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)).
% 15.82/15.66  all V_t_2 V_d_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2)))).
% 15.82/15.66  all V_t_2 V_d_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2)),V_t_2))).
% 15.82/15.66  all V_n_2 V_k_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2))).
% 15.82/15.66  all V_m_2 (hBOOL(hAPP(hAPP(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)).
% 15.82/15.66  all V_t_2 V_m_2 V_k_2 (V_k_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))<->hBOOL(hAPP(hAPP(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))))).
% 15.82/15.66  all V_P_2 T_b (class_Orderings_Owellorder(T_b)-> ((exists B_x1 hBOOL(hAPP(V_P_2,B_x1)))->hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))))).
% 15.82/15.66  all V_k_2 V_P_2 T_b (class_Orderings_Owellorder(T_b)-> (hBOOL(hAPP(V_P_2,V_k_2))->hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))))).
% 15.82/15.66  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))->V_m=V_n)))).
% 15.82/15.66  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m),V_n))-> -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)))).
% 15.82/15.66  all V_n V_m V_k (hBOOL(hAPP(hAPP(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)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)))).
% 15.82/15.66  all V_ca_2 V_t_2 V_x_2 V_d_2 V_a_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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))))).
% 15.82/15.66  all V_m_2 V_n_2 V_k_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(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))))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2))).
% 15.82/15.66  all V_m_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))<->V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.82/15.66  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))-> -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)))).
% 15.82/15.66  all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(hAPP(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)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2))).
% 15.82/15.66  all V_k_2 V_P_2 T_b (class_Orderings_Owellorder(T_b)-> (hBOOL(hAPP(V_P_2,V_k_2))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Orderings_Oord__class_OLeast(T_b,V_P_2)),V_k_2)))).
% 15.82/15.66  all V_P_2 V_k_2 T_b (class_Orderings_Owellorder(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_k_2),c_Orderings_Oord__class_OLeast(T_b,V_P_2)))-> -hBOOL(hAPP(V_P_2,V_k_2)))).
% 15.82/15.66  all V_n V_z (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z),V_n)))).
% 15.82/15.66  all V_n V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n)))).
% 15.82/15.66  all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))-> (hBOOL(hAPP(hAPP(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)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)))).
% 15.82/15.66  all V_n V_m V_k (hBOOL(hAPP(hAPP(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)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)))).
% 15.82/15.66  all V_n_2 V_P_2 (hBOOL(hAPP(V_P_2,V_n_2))-> (-hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))->c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2)=hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_OSuc))))).
% 15.82/15.66  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))-> (hBOOL(hAPP(hAPP(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))).
% 15.82/15.66  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))-> (hBOOL(hAPP(hAPP(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))).
% 15.82/15.66  all V_n V_m V_i (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)))).
% 15.82/15.66  all V_b_2 V_a_2 V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (hBOOL(hAPP(hAPP(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)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)))).
% 15.82/15.66  all V_b V_n V_a (hBOOL(hAPP(hAPP(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)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)))).
% 15.82/15.66  all V_b V_n V_a (hBOOL(hAPP(hAPP(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)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b)))).
% 15.82/15.66  all V_x hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)).
% 15.82/15.66  all V_y_2 V_x_2 (V_x_2=V_y_2<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))&hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))).
% 15.82/15.66  all V_y_2 V_x_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))|V_x_2=V_y_2).
% 15.82/15.66  all V_y_2 V_x_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))&V_x_2!=V_y_2).
% 15.82/15.66  all V_b V_a (V_a!=V_b-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)))).
% 15.82/15.66  all V_y V_x (V_x=V_y->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))).
% 15.82/15.66  all V_x_2 V_y_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))<->V_x_2=V_y_2)).
% 15.82/15.66  all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))|V_x=V_y).
% 15.82/15.66  all V_b V_a (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))-> (V_a!=V_b->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)))).
% 15.82/15.66  all V_c V_b V_a (V_a=V_b-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)))).
% 15.82/15.66  all V_c V_b V_a (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))-> (V_b=V_c->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)))).
% 15.82/15.66  all V_n V_m (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))->V_m=V_n)).
% 15.82/15.66  all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))->V_x=V_y)).
% 15.82/15.66  all V_z V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)))).
% 15.82/15.66  all V_c V_b V_a (V_a=V_b-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)))).
% 15.82/15.66  all V_z V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)))).
% 15.82/15.66  all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))->V_x!=V_y).
% 15.82/15.66  all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))-> -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)))).
% 15.82/15.66  all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))).
% 15.82/15.66  all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))-> -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)))).
% 15.82/15.66  all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))->V_x!=V_y).
% 15.82/15.66  all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))->V_y!=V_x).
% 15.82/15.66  all V_c V_b V_a (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))-> (V_b=V_c->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)))).
% 15.82/15.66  all V_z V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)))).
% 15.82/15.66  all V_b V_a (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))-> -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)))).
% 15.82/15.66  all V_z V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)))).
% 15.82/15.66  all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))-> -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)))).
% 15.82/15.66  all V_x hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.82/15.66  all V_x hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x)).
% 15.82/15.66  all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)))).
% 15.82/15.66  all V_b_2 V_a_2 V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (hBOOL(hAPP(hAPP(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)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_b_2)))).
% 15.82/15.66  all V_y_2 V_x_2 V_f_2 T_b (class_Orderings_Oorder(T_b)-> (c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))))).
% 15.82/15.66  all V_k_2 V_P_2 V_d_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))-> ((all B_x (hBOOL(hAPP(V_P_2,B_x))->hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2)))))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))-> (all B_x (hBOOL(hAPP(V_P_2,B_x))->hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2))))))))).
% 15.82/15.66  all V_x V_n T_a (class_Groups_Omonoid__mult(T_a)-> (hBOOL(hAPP(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))).
% 15.82/15.66  all V_n V_m V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))))).
% 15.82/15.66  all V_n V_m V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))))).
% 15.82/15.66  all V_n V_m V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))))).
% 15.82/15.66  all V_z V_y V_x T_a (class_Rings_Ocomm__ring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_z)))))).
% 15.82/15.66  all V_m_2 V_n_2 (hBOOL(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 15.82/15.66  all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_m)))).
% 15.82/15.66  all V_n V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),hAPP(c_Nat_OSuc,V_m))).
% 15.82/15.66  all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.66  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.66  all V_n_2 V_m_2 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))).
% 15.82/15.66  all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)=hAPP(c_Nat_OSuc,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))).
% 15.82/15.66  all V_k_2 V_j_2 V_i_2 (hBOOL(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2))).
% 15.82/15.66  all V_n V_m (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m).
% 15.82/15.66  all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))))).
% 15.82/15.66  all V_c V_b V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_c),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c))))).
% 15.82/15.66  all V_i V_j V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i)).
% 15.82/15.66  all V_i V_j V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k)).
% 15.82/15.66  all V_i V_j V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))).
% 15.82/15.66  all V_k_2 V_j_2 V_i_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_k_2<->V_j_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2))).
% 15.82/15.66  all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_n)=V_m).
% 15.82/15.66  all V_i_2 V_j_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_j_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)))).
% 15.82/15.66  all V_i V_j V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k)).
% 15.82/15.66  all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m).
% 15.82/15.66  all V_m V_n V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_k)))).
% 15.82/15.66  all V_i_2 V_k_2 V_j_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)),V_i_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)))).
% 15.82/15.66  all V_i V_j V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),V_j)).
% 15.82/15.66  all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,hAPP(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)).
% 15.82/15.66  all V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n).
% 15.82/15.66  all V_n V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_m)).
% 15.82/15.66  all V_l V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)))).
% 15.82/15.66  all V_l V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)))).
% 15.82/15.66  all V_n V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_n))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i))=V_i).
% 15.82/15.66  all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)<->V_m_2=V_n_2))).
% 15.82/15.66  all V_n V_m V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_m))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))).
% 15.82/15.66  all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))))).
% 15.82/15.66  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)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_ca_2),V_d_2))))).
% 15.82/15.66  all V_x_2 V_B_2 V_A_2 T_c T_b (class_Groups_Ominus(T_b)->hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b),V_A_2,V_B_2),V_x_2)=c_Groups_Ominus__class_Ominus(T_b,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2))).
% 15.82/15.66  all V_x_2 V_B_2 V_A_2 T_c T_b (class_Groups_Ominus(T_b)->hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b),V_A_2,V_B_2),V_x_2)=c_Groups_Ominus__class_Ominus(T_b,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2))).
% 15.82/15.66  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),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_b),V_q))=hAPP(hAPP(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))).
% 15.82/15.66  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))).
% 15.82/15.66  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)).
% 15.82/15.66  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))).
% 15.82/15.66  all V_p V_b V_a T_a (class_Rings_Ocomm__ring(T_a)->hAPP(hAPP(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),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_b),V_p))).
% 15.82/15.66  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)).
% 15.82/15.66  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))).
% 15.82/15.66  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))).
% 15.82/15.66  all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n),V_n)=V_m).
% 15.82/15.66  all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_n)=V_m).
% 15.82/15.66  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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))).
% 15.82/15.66  all V_n V_m V_k (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 15.82/15.66  all V_n V_k V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 15.82/15.66  all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),hAPP(c_Nat_OSuc,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 15.82/15.66  all V_k V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n),hAPP(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)).
% 15.82/15.66  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)).
% 15.82/15.66  all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 15.82/15.66  all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.66  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)).
% 15.82/15.66  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b)=V_a).
% 15.82/15.66  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),V_b)=V_a).
% 15.82/15.66  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))).
% 15.82/15.66  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))).
% 15.82/15.66  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))).
% 15.82/15.66  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))).
% 15.82/15.66  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)).
% 15.82/15.66  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))).
% 15.82/15.66  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)).
% 15.82/15.66  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).
% 15.82/15.66  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)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),c_Groups_Ouminus__class_Ouminus(T_a,V_y))).
% 15.82/15.66  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))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)).
% 15.82/15.66  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)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 15.82/15.66  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 15.82/15.66  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)).
% 15.82/15.66  all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_2 T_b (class_Rings_Oring(T_b)-> (hAPP(hAPP(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)=hAPP(hAPP(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=hAPP(hAPP(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))).
% 15.82/15.66  all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_2 T_b (class_Rings_Oring(T_b)-> (hAPP(hAPP(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)=hAPP(hAPP(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)<->hAPP(hAPP(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)).
% 15.82/15.66  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))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(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)))).
% 15.82/15.66  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))=hAPP(hAPP(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))).
% 15.82/15.66  all V_b_2 V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2))<->hBOOL(hAPP(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))))).
% 15.82/15.66  all V_b_2 V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_b))))).
% 15.82/15.66  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)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),V_d_2))))).
% 15.82/15.66  all V_l V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_l))->hBOOL(hAPP(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))))).
% 15.82/15.66  all V_n V_k V_j (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n)),V_k))).
% 15.82/15.66  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)).
% 15.82/15.66  all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_2 T_b (class_Rings_Oordered__ring(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(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)),hAPP(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_ca_2),hAPP(hAPP(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))))).
% 15.82/15.66  all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_2 T_b (class_Rings_Oordered__ring(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(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)),hAPP(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(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)))).
% 15.82/15.66  all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_2 T_b (class_Rings_Oordered__ring(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(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)),hAPP(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(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)))).
% 15.82/15.66  all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_2 T_b (class_Rings_Oordered__ring(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(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)),hAPP(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),hAPP(hAPP(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))))).
% 15.82/15.66  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),hAPP(hAPP(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)))).
% 15.82/15.66  all V_t_2 V_D_2 V_d_2 T_b (class_Rings_Ocomm__ring(T_b)&class_Rings_Odvd(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))-> (all B_x B_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(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))))))).
% 15.82/15.66  all V_t_2 V_D_2 V_d_2 T_b (class_Rings_Ocomm__ring(T_b)&class_Rings_Odvd(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))-> (all B_x B_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(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))))))).
% 15.82/15.66  all V_i V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,hAPP(c_Nat_OSuc,V_i))),V_n))).
% 15.82/15.66  all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->hAPP(c_Nat_OSuc,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n).
% 15.82/15.66  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)))<-> (hBOOL(hAPP(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=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)->hBOOL(hAPP(V_P_2,B_d))))).
% 15.82/15.66  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)))<-> -(hBOOL(hAPP(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=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)& -hBOOL(hAPP(V_P_2,B_d)))))).
% 15.82/15.66  all V_m V_j V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_j),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m))).
% 15.82/15.66  all V_m V_j V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),hAPP(c_Nat_OSuc,V_j))).
% 15.82/15.66  all V_n_2 V_m_2 V_u_2 V_i_2 V_j_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)))).
% 15.82/15.66  all V_n V_m V_u V_i V_j (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j),V_i))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u)),V_m),V_n)).
% 15.82/15.66  all V_n_2 V_m_2 V_u_2 V_i_2 V_j_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)<->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)=V_n_2)).
% 15.82/15.66  all V_n_2 V_m_2 V_u_2 V_j_2 V_i_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))))).
% 15.82/15.66  all V_n V_m V_u V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u)),V_n))).
% 15.82/15.66  all V_n_2 V_m_2 V_u_2 V_j_2 V_i_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)<->V_m_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))).
% 15.82/15.66  all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->V_n=hAPP(c_Nat_OSuc,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 15.82/15.66  all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->hAPP(c_Nat_OSuc,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=V_n).
% 15.82/15.66  all V_n V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=V_n)& (V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=hAPP(c_Nat_OSuc,hAPP(hAPP(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)))).
% 15.82/15.66  all V_n_2 V_m_2 V_u_2 V_i_2 V_j_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)))).
% 15.82/15.66  all V_n_2 V_m_2 V_u_2 V_j_2 V_i_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))))).
% 15.82/15.66  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)=hAPP(hAPP(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)))).
% 15.82/15.66  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)))))).
% 15.82/15.66  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),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Nat_OSuc,hAPP(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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))).
% 15.82/15.66  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)))))).
% 15.82/15.66  all V_y V_n V_p T_a (class_Groups_Omonoid__mult(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_p),V_n))->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n),V_p))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y))).
% 15.82/15.66  all V_n V_m V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n)))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)))).
% 15.82/15.66  all V_l_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_l_2))<->hBOOL(hAPP(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)))).
% 15.82/15.66  all V_y_2 V_x_2 T_b (class_Rings_Olinordered__idom(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Polynomial_Opoly(T_b),V_x_2),V_y_2))<->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)))).
% 15.82/15.66  all V_q V_p V_a T_a (class_Rings_Ocomm__ring(T_a)->hAPP(hAPP(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),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q))).
% 15.82/15.66  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).
% 15.82/15.66  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))).
% 15.82/15.66  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))).
% 15.82/15.66  all V_y_2 V_x_2 T_b (class_Rings_Olinordered__idom(T_b)-> (hBOOL(hAPP(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)))).
% 15.82/15.66  all V_w V_z (hAPP(hAPP(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)).
% 15.82/15.66  all V_w V_z (c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))).
% 15.82/15.66  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)).
% 15.82/15.66  all V_z_2 V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))).
% 15.82/15.66  all V_f_2 T_b (class_Orderings_Oorder(T_b)-> (c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)->c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2))).
% 15.82/15.66  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))).
% 15.82/15.66  all V_y_2 V_x_2 V_f_2 T_b (class_Orderings_Oorder(T_b)-> (c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))))).
% 15.82/15.66  all V_x V_y ((hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y),V_x))->c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y))& (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y),V_x))->c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.66  all V_k V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))-> (hBOOL(hAPP(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,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))).
% 15.82/15.66  all V_b V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))->hBOOL(hAPP(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))))).
% 15.82/15.66  all V_a_2 V_b_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)))).
% 15.82/15.66  all V_a_2 V_b_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))-> (hBOOL(hAPP(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)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))).
% 15.82/15.66  all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))->hBOOL(hAPP(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))))).
% 15.82/15.66  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))).
% 15.82/15.66  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))).
% 15.82/15.66  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)).
% 15.82/15.66  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)).
% 15.82/15.66  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))).
% 15.82/15.66  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))).
% 15.82/15.66  all V_b V_a T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(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)).
% 15.82/15.66  all V_a V_b V_c T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(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))).
% 15.82/15.66  all V_b V_a T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(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)).
% 15.82/15.66  all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(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))).
% 15.82/15.66  all V_w V_z V_x V_y T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))-> (hBOOL(hAPP(hAPP(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))))).
% 15.82/15.66  all V_y V_x V_z T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y),V_z)=hAPP(hAPP(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))))).
% 15.82/15.66  all V_x V_y T_a (class_Divides_Oring__div(T_a)-> (hBOOL(hAPP(hAPP(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)))).
% 15.82/15.66  all V_x V_y T_a (class_Divides_Oring__div(T_a)-> (hBOOL(hAPP(hAPP(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)))).
% 15.82/15.66  all V_n V_x V_y T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(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)))).
% 15.82/15.66  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)).
% 15.82/15.66  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)).
% 15.82/15.66  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)).
% 15.82/15.66  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).
% 15.82/15.66  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)).
% 15.82/15.66  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)).
% 15.82/15.66  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)).
% 15.82/15.66  all V_ca_2 V_b_2 V_a_2 T_b (class_Divides_Osemiring__div(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ca_2))-> (hBOOL(hAPP(hAPP(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)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_ca_2)))))).
% 15.82/15.66  all V_m V_n (hBOOL(hAPP(hAPP(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).
% 15.82/15.66  all V_k_2 V_i_2 (c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<->V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_i_2))).
% 15.82/15.66  all V_a_2 V_b_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))-> (hBOOL(hAPP(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_a_2,V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)))).
% 15.82/15.66  all V_i_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2),V_i_2)))).
% 15.82/15.66  all V_b_2 V_a_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_2),V_a_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))).
% 15.82/15.66  all V_b V_b_H V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)))))).
% 15.82/15.66  all V_b V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))).
% 15.82/15.66  all V_b V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),V_b))->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.66  all V_a_2 V_b_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(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_a_2,V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))).
% 15.82/15.66  all V_b V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))).
% 15.82/15.66  all V_b V_b_H V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)))))).
% 15.82/15.66  all V_b V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_a))->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.66  all V_b V_a_H V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),V_a_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b))))).
% 15.82/15.66  all V_b V_a_H V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),V_a_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))))).
% 15.82/15.66  all V_k V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k)),V_x)))).
% 15.82/15.66  all V_b V_a V_c (hBOOL(hAPP(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)).
% 15.82/15.66  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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))).
% 15.82/15.66  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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))).
% 15.82/15.66  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_Oplus__class_Oplus(T_a),V_a),V_b),V_b)=hAPP(hAPP(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)))).
% 15.82/15.66  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_Oplus__class_Oplus(T_a),V_b),V_a),V_b)=hAPP(hAPP(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)))).
% 15.82/15.66  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)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))-> (hBOOL(hAPP(hAPP(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))))))).
% 15.82/15.66  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)-> (hBOOL(hAPP(hAPP(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))))).
% 15.82/15.66  all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y))))).
% 15.82/15.66  all V_k_2 V_n_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))<-> (V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))& (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))-> (all B_i ((exists B_j (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j),V_k_2))&V_n_2=hAPP(hAPP(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(V_P_2,B_i)))))& (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (all B_i ((exists B_j (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),B_j))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&V_n_2=hAPP(hAPP(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(V_P_2,B_i)))))).
% 15.82/15.66  all V_r_1 V_y V_b_1 V_a_1 (V_a_1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)-> ((hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1),V_b_1)))& (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1),V_r_1))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))-> (V_b_1!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1)=V_y))).
% 15.82/15.66  all V_x V_y (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y),V_x))->c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y)).
% 15.82/15.66  all V_k V_l ((hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))->c_SMT_Oz3div(V_k,V_l)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,V_l))& (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))->c_SMT_Oz3div(V_k,V_l)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_l))))).
% 15.82/15.66  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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))=hAPP(hAPP(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))).
% 15.82/15.66  all V_k V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k)))).
% 15.82/15.66  all V_n V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_m)).
% 15.82/15.66  all V_n V_m (hBOOL(hAPP(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)).
% 15.82/15.66  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))).
% 15.82/15.66  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))).
% 15.82/15.66  all V_m (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=V_m).
% 15.82/15.66  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))).
% 15.82/15.66  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)).
% 15.82/15.66  all V_y V_x V_a T_a (class_Fields_Ofield(T_a)->c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_x),V_y)=hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y))).
% 15.82/15.66  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)).
% 15.82/15.66  all V_k V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m))))).
% 15.82/15.66  all V_m V_n (hBOOL(hAPP(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).
% 15.82/15.66  all V_m V_n (hBOOL(hAPP(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).
% 15.82/15.66  all V_n V_m V_k (hBOOL(hAPP(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)).
% 15.82/15.66  all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_m)))).
% 15.82/15.66  all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(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))& (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=hAPP(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)))).
% 15.82/15.66  all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=hAPP(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)))).
% 15.82/15.66  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 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_k_2))-> (V_n_2=hAPP(hAPP(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))))))).
% 15.82/15.66  all V_m_2 V_q_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2))))<->V_q_2=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2))).
% 15.82/15.66  all V_n_2 V_m_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| (exists B_q (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q))))&hBOOL(hAPP(V_P_2,B_q))))).
% 15.82/15.66  all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=hAPP(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)))).
% 15.82/15.66  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))-> (hBOOL(hAPP(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)))& (-hBOOL(hAPP(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)))))).
% 15.82/15.66  all V_k_2 V_P_2 V_d_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))-> ((all B_x (hBOOL(hAPP(V_P_2,B_x))->hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,V_d_2)))))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))-> (all B_x (hBOOL(hAPP(V_P_2,B_x))->hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2))))))))).
% 15.82/15.66  all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)))).
% 15.82/15.66  all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))))).
% 15.82/15.66  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))).
% 15.82/15.66  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)).
% 15.82/15.66  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))).
% 15.82/15.66  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)).
% 15.82/15.66  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))).
% 15.82/15.66  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))).
% 15.82/15.66  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))).
% 15.82/15.66  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)).
% 15.82/15.66  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)).
% 15.82/15.66  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)<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)))).
% 15.82/15.66  all V_a T_a (class_Rings_Olinordered__idom(T_a)-> (hBOOL(hAPP(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))).
% 15.82/15.66  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))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))))).
% 15.82/15.66  all V_a T_a (class_Rings_Olinordered__idom(T_a)-> (hBOOL(hAPP(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)))).
% 15.82/15.66  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)-> (hBOOL(hAPP(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))& (-hBOOL(hAPP(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))))).
% 15.82/15.66  all V_n_2 V_P_2 V_k_2 (hBOOL(hAPP(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 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j),V_k_2))&V_n_2=hAPP(hAPP(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)))))).
% 15.82/15.66  all V_n_2 V_P_2 V_k_2 (hBOOL(hAPP(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 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),B_j))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&V_n_2=hAPP(hAPP(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)))))).
% 15.82/15.66  all V_c V_b V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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,hAPP(hAPP(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))).
% 15.82/15.66  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)).
% 15.82/15.66  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)).
% 15.82/15.66  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).
% 15.82/15.66  all V_b V_a T_a (class_Divides_Osemiring__div(T_a)->hAPP(hAPP(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).
% 15.82/15.66  all V_a V_b T_a (class_Divides_Osemiring__div(T_a)->hAPP(hAPP(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).
% 15.82/15.66  all V_b V_a T_a (class_Divides_Osemiring__div(T_a)->hAPP(hAPP(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).
% 15.82/15.66  all V_c V_a V_b T_a (class_Divides_Osemiring__div(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(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)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)).
% 15.82/15.66  all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(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)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)).
% 15.82/15.66  all V_k V_b V_a (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k)).
% 15.82/15.66  all V_k V_a V_b (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k)).
% 15.82/15.66  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)=hAPP(hAPP(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))).
% 15.82/15.66  all V_b V_a (V_a=hAPP(hAPP(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))).
% 15.82/15.66  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))).
% 15.82/15.66  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))).
% 15.82/15.66  all V_m_2 V_n_2 V_k_2 T_b (class_Divides_Osemiring__div(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2))))).
% 15.82/15.66  all V_a V_b V_c T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(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))).
% 15.82/15.66  all V_n V_m V_f (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))))).
% 15.82/15.66  all V_n V_m V_k T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))))).
% 15.82/15.66  all V_n V_m V_k T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))))).
% 15.82/15.66  all V_n V_m V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)))).
% 15.82/15.66  all V_b V_a T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(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))).
% 15.82/15.66  all V_b_2 V_a_2 T_b (class_Divides_Osemiring__div(T_b)-> (hBOOL(hAPP(hAPP(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))).
% 15.82/15.66  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)).
% 15.82/15.66  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)).
% 15.82/15.66  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)).
% 15.82/15.66  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)).
% 15.82/15.66  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)).
% 15.82/15.66  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_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)).
% 15.82/15.66  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_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)).
% 15.82/15.66  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)).
% 15.82/15.66  all V_a (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.82/15.66  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)).
% 15.82/15.66  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).
% 15.82/15.66  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)).
% 15.82/15.66  all V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b)).
% 15.82/15.66  all V_a V_b T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b)).
% 15.82/15.66  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_Oplus__class_Oplus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)).
% 15.82/15.66  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_Oplus__class_Oplus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c)).
% 15.82/15.66  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_Oplus__class_Oplus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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)).
% 15.82/15.66  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_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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)).
% 15.82/15.66  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_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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)).
% 15.82/15.66  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_Oplus__class_Oplus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c)))).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Groups_Ocancel__ab__semigroup__add(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Rings_Oring__1__no__zero__divisors(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Rings_Oring__no__zero__divisors(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Groups_Ocancel__semigroup__add(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Groups_Oab__semigroup__mult(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Groups_Ocomm__monoid__mult(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Groups_Oab__semigroup__add(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Rings_Ono__zero__divisors(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Groups_Ocomm__monoid__add(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Rings_Ocomm__semiring__1(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Rings_Ocomm__semiring__0(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Rings_Ocomm__semiring(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Groups_Oab__group__add(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Rings_Ozero__ne_q__one(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Groups_Omonoid__mult(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Rings_Ocomm__ring__1(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Groups_Omonoid__add(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Rings_Osemiring__0(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Groups_Ogroup__add(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Rings_Omult__zero(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Rings_Ocomm__ring(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Rings_Osemiring(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Groups_Ouminus(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Rings_Oring__1(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Groups_Ominus(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Power_Opower(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Groups_Ozero(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Rings_Oring(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Groups_Oone(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Rings_Odvd(T)).
% 15.82/15.66  all T (class_Rings_Oidom(T)->class_Groups_Ocancel__comm__monoid__add(T)).
% 15.82/15.66  all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat).
% 15.82/15.66  class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint).
% 15.82/15.66  all T_2 T_1 (class_Lattices_Oboolean__algebra(T_1)->class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))).
% 15.82/15.66  all T_2 T_1 (class_Orderings_Opreorder(T_1)->class_Orderings_Opreorder(tc_fun(T_2,T_1))).
% 15.82/15.66  all T_2 T_1 (class_Orderings_Oorder(T_1)->class_Orderings_Oorder(tc_fun(T_2,T_1))).
% 15.82/15.66  all T_2 T_1 (class_Orderings_Oord(T_1)->class_Orderings_Oord(tc_fun(T_2,T_1))).
% 15.82/15.66  all T_2 T_1 (class_Groups_Ouminus(T_1)->class_Groups_Ouminus(tc_fun(T_2,T_1))).
% 15.82/15.66  all T_2 T_1 (class_Groups_Ominus(T_1)->class_Groups_Ominus(tc_fun(T_2,T_1))).
% 15.82/15.66  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 15.82/15.66  class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 15.82/15.66  class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 15.82/15.66  class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 15.82/15.66  class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint).
% 15.82/15.66  class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 15.82/15.66  class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint).
% 15.82/15.66  class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 15.82/15.66  class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 15.82/15.66  class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 15.82/15.66  class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 15.82/15.66  class_Rings_Oordered__cancel__semiring(tc_Int_Oint).
% 15.82/15.66  class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 15.82/15.66  class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 15.82/15.66  class_Rings_Oordered__comm__semiring(tc_Int_Oint).
% 15.82/15.66  class_Rings_Olinordered__semiring__1(tc_Int_Oint).
% 15.82/15.66  class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 15.82/15.66  class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 15.82/15.66  class_Rings_Olinordered__semiring(tc_Int_Oint).
% 15.82/15.66  class_Rings_Olinordered__semidom(tc_Int_Oint).
% 15.82/15.66  class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 15.82/15.66  class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 15.82/15.66  class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 15.82/15.66  class_Rings_Oordered__semiring(tc_Int_Oint).
% 15.82/15.66  class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 15.82/15.66  class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 15.82/15.66  class_Rings_Olinordered__ring(tc_Int_Oint).
% 15.82/15.66  class_Rings_Olinordered__idom(tc_Int_Oint).
% 15.82/15.66  class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 15.82/15.66  class_Rings_Ocomm__semiring__0(tc_Int_Oint).
% 15.82/15.66  class_Divides_Osemiring__div(tc_Int_Oint).
% 15.82/15.66  class_Rings_Ocomm__semiring(tc_Int_Oint).
% 15.82/15.66  class_Groups_Oab__group__add(tc_Int_Oint).
% 15.82/15.66  class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 15.82/15.66  class_Rings_Oordered__ring(tc_Int_Oint).
% 15.82/15.66  class_Orderings_Opreorder(tc_Int_Oint).
% 15.82/15.66  class_Orderings_Olinorder(tc_Int_Oint).
% 15.82/15.66  class_Groups_Omonoid__mult(tc_Int_Oint).
% 15.82/15.66  class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 15.82/15.66  class_Groups_Omonoid__add(tc_Int_Oint).
% 15.82/15.66  class_Rings_Osemiring__0(tc_Int_Oint).
% 15.82/15.66  class_Groups_Ogroup__add(tc_Int_Oint).
% 15.82/15.66  class_Divides_Oring__div(tc_Int_Oint).
% 15.82/15.66  class_Rings_Omult__zero(tc_Int_Oint).
% 15.82/15.66  class_Rings_Ocomm__ring(tc_Int_Oint).
% 15.82/15.66  class_Orderings_Oorder(tc_Int_Oint).
% 15.82/15.66  class_Int_Oring__char__0(tc_Int_Oint).
% 15.82/15.66  class_Rings_Osemiring(tc_Int_Oint).
% 15.82/15.66  class_Orderings_Oord(tc_Int_Oint).
% 15.82/15.66  class_Groups_Ouminus(tc_Int_Oint).
% 15.82/15.66  class_Groups_Osgn__if(tc_Int_Oint).
% 15.82/15.66  class_Rings_Oring__1(tc_Int_Oint).
% 15.82/15.66  class_Groups_Ominus(tc_Int_Oint).
% 15.82/15.66  class_Power_Opower(tc_Int_Oint).
% 15.82/15.66  class_Groups_Ozero(tc_Int_Oint).
% 15.82/15.66  class_Rings_Oring(tc_Int_Oint).
% 15.82/15.66  class_Rings_Oidom(tc_Int_Oint).
% 15.82/15.66  class_Groups_Oone(tc_Int_Oint).
% 15.82/15.66  class_Rings_Odvd(tc_Int_Oint).
% 15.82/15.66  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 15.82/15.66  class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 15.82/15.66  class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 15.82/15.66  class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 15.82/15.66  class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 15.82/15.66  class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 15.82/15.66  class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 15.82/15.66  class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 15.82/15.66  class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 15.82/15.66  class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 15.82/15.66  class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 15.82/15.66  class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 15.82/15.66  class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 15.82/15.66  class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 15.82/15.66  class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 15.82/15.66  class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 15.82/15.66  class_Rings_Oordered__semiring(tc_Nat_Onat).
% 15.82/15.66  class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 15.82/15.66  class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 15.82/15.66  class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 15.82/15.66  class_Rings_Ocomm__semiring__0(tc_Nat_Onat).
% 15.82/15.66  class_Divides_Osemiring__div(tc_Nat_Onat).
% 15.82/15.66  class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 15.82/15.66  class_Orderings_Owellorder(tc_Nat_Onat).
% 15.82/15.66  class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 15.82/15.66  class_Orderings_Opreorder(tc_Nat_Onat).
% 15.82/15.66  class_Orderings_Olinorder(tc_Nat_Onat).
% 15.82/15.66  class_Groups_Omonoid__mult(tc_Nat_Onat).
% 15.82/15.66  class_Groups_Omonoid__add(tc_Nat_Onat).
% 15.82/15.66  class_Rings_Osemiring__0(tc_Nat_Onat).
% 15.82/15.66  class_Rings_Omult__zero(tc_Nat_Onat).
% 15.82/15.66  class_Orderings_Oorder(tc_Nat_Onat).
% 15.82/15.66  class_Rings_Osemiring(tc_Nat_Onat).
% 15.82/15.66  class_Orderings_Oord(tc_Nat_Onat).
% 15.82/15.66  class_Groups_Ominus(tc_Nat_Onat).
% 15.82/15.66  class_Power_Opower(tc_Nat_Onat).
% 15.82/15.66  class_Groups_Ozero(tc_Nat_Onat).
% 15.82/15.66  class_Groups_Oone(tc_Nat_Onat).
% 15.82/15.66  class_Rings_Odvd(tc_Nat_Onat).
% 15.82/15.66  class_Lattices_Oboolean__algebra(tc_HOL_Obool).
% 15.82/15.66  class_Orderings_Opreorder(tc_HOL_Obool).
% 15.82/15.66  class_Orderings_Oorder(tc_HOL_Obool).
% 15.82/15.66  class_Orderings_Oord(tc_HOL_Obool).
% 15.82/15.66  class_Groups_Ouminus(tc_HOL_Obool).
% 15.82/15.66  class_Groups_Ominus(tc_HOL_Obool).
% 15.82/15.66  all T_1 (class_Rings_Oidom(T_1)->class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Fields_Ofield(T_1)->class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1))).
% 15.82/15.66  all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Fields_Ofield(T_1)->class_Divides_Oring__div(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Oorder(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Osemiring(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Oord(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ouminus(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Oring__1(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ominus(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Power_Opower(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Groups_Ozero(T_1)->class_Groups_Ozero(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Oring(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oidom(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Oone(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Odvd(tc_Polynomial_Opoly(T_1))).
% 15.82/15.67  all V_Q V_P T_b T_a (hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q)=V_P).
% 15.82/15.67  all V_R_2 V_Q_2 V_P_2 T_d T_b T_c (hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_P_2),V_Q_2),V_R_2)=hAPP(V_P_2,hAPP(V_Q_2,V_R_2))).
% 15.82/15.67  all V_R_2 V_Q_2 V_P_2 T_b T_d T_c (hAPP(hAPP(c_COMBC(T_c,T_d,T_b,V_P_2),V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),V_Q_2)).
% 15.82/15.67  all V_R_2 V_Q_2 V_P_2 T_b T_d T_c (hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2))).
% 15.82/15.67  all V_y_2 V_x_2 (-hBOOL(c_fe_qual(V_x_2,V_y_2))|V_x_2=V_y_2).
% 15.82/15.67  all V_y_2 V_x_2 (V_x_2!=V_y_2|hBOOL(c_fe_qual(V_x_2,V_y_2))).
% 15.82/15.67  all V_P_2 (-hBOOL(hAPP(c_fNot,V_P_2))| -hBOOL(V_P_2)).
% 15.82/15.67  all V_P_2 (-(-hBOOL(V_P_2))|hBOOL(hAPP(c_fNot,V_P_2))).
% 15.82/15.67  all V_Q_2 V_P_2 (-hBOOL(V_P_2)| -hBOOL(V_Q_2)|hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))).
% 15.82/15.67  all V_Q_2 V_P_2 (-hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))|hBOOL(V_P_2)).
% 15.82/15.67  all V_Q_2 V_P_2 (-hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))|hBOOL(V_Q_2)).
% 15.82/15.67  v_a!=c_Groups_Ozero__class_Ozero(t_a).
% 15.82/15.67  hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,v_q)),v_k))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,v_cs____).
% 15.82/15.67  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),v_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),B_z),hAPP(c_Polynomial_Opoly(t_a,v_q),B_z))))).
% 15.82/15.67  -(exists B_a (B_a!=c_Groups_Ozero__class_Ozero(t_a)&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))& (exists B_q (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,B_q)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____))& (all B_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),B_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),v_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),B_z),hAPP(c_Polynomial_Opoly(t_a,v_q),B_z)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),B_z),hAPP(c_Polynomial_Opoly(t_a,B_q),B_z)))))))))).
% 15.82/15.67  class_Rings_Oidom(t_a).
% 15.82/15.67  end_of_list.
% 15.82/15.67  
% 15.82/15.67  -------> usable clausifies to:
% 15.82/15.67  
% 15.82/15.67  list(usable).
% 15.82/15.67  0 [] A=A.
% 15.82/15.67  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.
% 15.82/15.67  0 [] -class_Rings_Oidom(t_a)| -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_p)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))).
% 15.82/15.67  0 [] -class_Rings_Oidom(t_a)|$c1!=c_Groups_Ozero__class_Ozero(t_a).
% 15.82/15.67  0 [] -class_Rings_Oidom(t_a)|hAPP(c_Polynomial_Opoly(t_a,v_cs____),$c1)!=c_Groups_Ozero__class_Ozero(t_a).
% 15.82/15.67  0 [] -class_Rings_Oidom(t_a)|$c2!=c_Groups_Ozero__class_Ozero(t_a).
% 15.82/15.67  0 [] -class_Rings_Oidom(t_a)|hAPP(c_Polynomial_Opoly(t_a,v_cs____),$c2)!=c_Groups_Ozero__class_Ozero(t_a).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_OSuc,V_n))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),V_x)=hAPP(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b)),V_b_2))| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2),V_y_2)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b)),V_b_2))|hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2),V_y_2)).
% 15.82/15.67  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).
% 15.82/15.67  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.
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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.
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)|V_m_2=V_n_2.
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)|V_m_2!=V_n_2.
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(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)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(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)).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)=V_n.
% 15.82/15.67  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)).
% 15.82/15.67  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)).
% 15.82/15.67  0 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)|hAPP(V_f_2,B_x)=hAPP(V_f_2,B_y).
% 15.82/15.67  0 [] c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)|hAPP(V_f_2,$f3(V_f_2,T_c,T_b))!=hAPP(V_f_2,$f2(V_f_2,T_c,T_b)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2)!=hAPP(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=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.67  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_x_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 15.82/15.67  0 [] -hBOOL(hAPP(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)))|hBOOL(hAPP(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).
% 15.82/15.67  0 [] hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(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).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 15.82/15.67  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).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))=hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(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))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))).
% 15.82/15.67  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)).
% 15.82/15.67  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)).
% 15.82/15.67  0 [] hAPP(c_Nat_OSuc,V_x)!=hAPP(c_Nat_OSuc,V_y)|V_x=V_y.
% 15.82/15.67  0 [] hAPP(c_Nat_OSuc,V_nat_2)!=hAPP(c_Nat_OSuc,V_nat_H_2)|V_nat_2=V_nat_H_2.
% 15.82/15.67  0 [] hAPP(c_Nat_OSuc,V_nat_2)=hAPP(c_Nat_OSuc,V_nat_H_2)|V_nat_2!=V_nat_H_2.
% 15.82/15.67  0 [] hAPP(c_Nat_OSuc,V_n)!=V_n.
% 15.82/15.67  0 [] V_n!=hAPP(c_Nat_OSuc,V_n).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=V_n_2|hBOOL(hAPP(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)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s),V_t))|V_s!=V_t.
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))|V_m!=V_n.
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n)).
% 15.82/15.67  0 [] V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y),V_x)).
% 15.82/15.67  0 [] V_m_2=V_n_2|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)).
% 15.82/15.67  0 [] V_m_2!=V_n_2| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] V_m_2!=V_n_2| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)|V_m_2=V_n_2.
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)|V_m_2!=V_n_2.
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2=V_n_2.
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2!=V_n_2.
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m).
% 15.82/15.67  0 [] -class_Groups_Ozero(T_b)|hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2)!=hAPP(hAPP(c_Polynomial_OpCons(T_b),V_b_2),V_q_2)|V_a_2=V_b_2.
% 15.82/15.67  0 [] -class_Groups_Ozero(T_b)|hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2)!=hAPP(hAPP(c_Polynomial_OpCons(T_b),V_b_2),V_q_2)|V_pa_2=V_q_2.
% 15.82/15.67  0 [] -class_Groups_Ozero(T_b)|hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2)=hAPP(hAPP(c_Polynomial_OpCons(T_b),V_b_2),V_q_2)|V_a_2!=V_b_2|V_pa_2!=V_q_2.
% 15.82/15.67  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.
% 15.82/15.67  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.
% 15.82/15.67  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).
% 15.82/15.67  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)).
% 15.82/15.67  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)).
% 15.82/15.67  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).
% 15.82/15.67  0 [] hAPP(c_Nat_OSuc,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.67  0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_m).
% 15.82/15.67  0 [] hAPP(c_Nat_OSuc,V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.67  0 [] hAPP(c_Nat_OSuc,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.67  0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_nat_H).
% 15.82/15.67  0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_m).
% 15.82/15.67  0 [] V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.82/15.67  0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 15.82/15.67  0 [] V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|V_m=V_n.
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i)),V_k)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hAPP(c_Nat_OSuc,V_m)=V_n|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_OSuc,V_m)))|V_m=V_n.
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,V_m_2)))|V_n_2=V_m_2.
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,V_m_2)))|V_n_2!=V_m_2.
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=V_n_2.
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))|V_m_2!=V_n_2.
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,V_m_2))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,V_m_2))).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)!=V_m|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.67  0 [] hAPP(hAPP(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).
% 15.82/15.67  0 [] hAPP(hAPP(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).
% 15.82/15.67  0 [] hAPP(hAPP(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).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=V_n.
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_k)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)).
% 15.82/15.67  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.
% 15.82/15.67  0 [] -class_Groups_Ozero(T_b)|hAPP(hAPP(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).
% 15.82/15.67  0 [] -class_Groups_Ozero(T_b)|hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Groups_Ozero(T_b)|hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Groups_Ozero(T_a)|hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_b),V_q))=hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 15.82/15.67  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).
% 15.82/15.67  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)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x)=hAPP(hAPP(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)).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))|hBOOL(hAPP(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))).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_b)| -hBOOL(hAPP(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.
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_b)| -hBOOL(hAPP(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.
% 15.82/15.67  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)),hAPP(c_Nat_OSuc,V_n))=c_Groups_Ozero__class_Ozero(T_a).
% 15.82/15.67  0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(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).
% 15.82/15.67  0 [] -class_Power_Opower(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(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)).
% 15.82/15.67  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).
% 15.82/15.67  0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(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)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=hAPP(c_Nat_OSuc,$f4(V_n_2,V_m_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f4(V_n_2,V_m_2)),V_n_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))|V_m_2!=hAPP(c_Nat_OSuc,B_j)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_n_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|V_n_2=hAPP(c_Nat_OSuc,$f5(V_n_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|V_n_2!=hAPP(c_Nat_OSuc,B_m).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=hAPP(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).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=hAPP(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=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=hAPP(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!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.67  0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.67  0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.67  0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(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).
% 15.82/15.67  0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(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=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.67  0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.67  0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(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!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_n_2=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),$f6(V_n_2,V_m_2))).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_n_2!=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))).
% 15.82/15.67  0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))|hBOOL(hAPP(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)))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))|hBOOL(hAPP(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)))).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))|hBOOL(hAPP(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),hAPP(c_Nat_OSuc,V_n)))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(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).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(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).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(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).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Oidom(t_a)| -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____))).
% 15.82/15.67  0 [] hAPP(c_Nat_OSuc,V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 15.82/15.67  0 [] hAPP(c_Nat_OSuc,V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))|V_x=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.67  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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)).
% 15.82/15.67  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).
% 15.82/15.67  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),hAPP(c_Nat_OSuc,V_q)).
% 15.82/15.67  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),hAPP(c_Nat_OSuc,V_q)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(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)).
% 15.82/15.67  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)).
% 15.82/15.67  0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q)=V_q.
% 15.82/15.67  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)).
% 15.82/15.67  0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=V_p.
% 15.82/15.67  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).
% 15.82/15.67  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)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_r)=hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__idom(T_a)|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 15.82/15.67  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).
% 15.82/15.67  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)).
% 15.82/15.67  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).
% 15.82/15.67  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)).
% 15.82/15.67  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).
% 15.82/15.67  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))).
% 15.82/15.67  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)).
% 15.82/15.67  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)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)).
% 15.82/15.67  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)).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 15.82/15.67  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|V_b_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.82/15.67  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|V_b_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.82/15.67  0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a).
% 15.82/15.67  0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z))=hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|V_a_2=V_b_2|V_ca_2=V_d_2|hAPP(hAPP(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))!=hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|V_a_2!=V_b_2|hAPP(hAPP(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))=hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|V_ca_2!=V_d_2|hAPP(hAPP(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))=hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m).
% 15.82/15.67  0 [] -class_Rings_Osemiring(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c).
% 15.82/15.67  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|hAPP(hAPP(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))!=hAPP(hAPP(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.
% 15.82/15.67  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|hAPP(hAPP(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))=hAPP(hAPP(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.
% 15.82/15.67  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|hAPP(hAPP(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))=hAPP(hAPP(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.
% 15.82/15.67  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.
% 15.82/15.67  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.
% 15.82/15.67  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)).
% 15.82/15.67  0 [] -hBOOL(hAPP(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)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(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).
% 15.82/15.67  0 [] hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)).
% 15.82/15.67  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.
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring(T_a)| -hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),V_a_2)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),V_a_2)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)|hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)|hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),V_a_2)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),V_a_2)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),V_a_2)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)|hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)|hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),V_a_2)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))|hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),V_a_2)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))|hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),V_a_2)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__comm__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)|hAPP(hAPP(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).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)|hAPP(hAPP(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).
% 15.82/15.67  0 [] -class_Rings_Olinordered__ring__strict(T_b)|hAPP(hAPP(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).
% 15.82/15.67  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|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_m))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_n))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m).
% 15.82/15.67  0 [] -class_Rings_Oidom(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))|$c4!=c_Groups_Ozero__class_Ozero(t_a).
% 15.82/15.67  0 [] -class_Rings_Oidom(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))|$c5!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.67  0 [] -class_Rings_Oidom(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,$c3)),$c5)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,v_cs____).
% 15.82/15.67  0 [] -class_Rings_Oidom(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))|hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(t_a,v_cs____),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_z),$c5)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),$c4),$c3)),B_z))).
% 15.82/15.67  0 [] -hBOOL(hAPP(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.
% 15.82/15.67  0 [] -hBOOL(hAPP(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.
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))|hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Opcompose(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),V_q)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(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))).
% 15.82/15.67  0 [] -class_Groups_Olinordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.67  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__idom(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__idom(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.67  0 [] -class_Groups_Olinordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.67  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.67  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))).
% 15.82/15.67  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)).
% 15.82/15.67  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)).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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)).
% 15.82/15.67  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)|V_b=V_c.
% 15.82/15.67  0 [] -class_Groups_Ocancel__ab__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)|V_b=V_c.
% 15.82/15.67  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)|V_b=V_c.
% 15.82/15.67  0 [] -class_Groups_Ocancel__semigroup__add(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)|V_b_2=V_ca_2.
% 15.82/15.67  0 [] -class_Groups_Ocancel__semigroup__add(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)|V_b_2!=V_ca_2.
% 15.82/15.67  0 [] -class_Groups_Ocancel__semigroup__add(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)|V_b_2=V_ca_2.
% 15.82/15.67  0 [] -class_Groups_Ocancel__semigroup__add(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)|V_b_2!=V_ca_2.
% 15.82/15.67  0 [] -class_Groups_Oab__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(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)).
% 15.82/15.67  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)).
% 15.82/15.67  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|hAPP(hAPP(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).
% 15.82/15.67  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|hAPP(hAPP(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).
% 15.82/15.67  0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 15.82/15.67  0 [] -class_Groups_Omonoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 15.82/15.67  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|c_Groups_Ozero__class_Ozero(T_b)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.82/15.67  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|c_Groups_Ozero__class_Ozero(T_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.82/15.67  0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 15.82/15.67  0 [] -class_Groups_Omonoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 15.82/15.67  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 15.82/15.67  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 15.82/15.67  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))).
% 15.82/15.67  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))).
% 15.82/15.67  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))).
% 15.82/15.67  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)).
% 15.82/15.67  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)).
% 15.82/15.67  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)).
% 15.82/15.67  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)).
% 15.82/15.67  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.
% 15.82/15.67  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.
% 15.82/15.67  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.
% 15.82/15.67  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.
% 15.82/15.67  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.
% 15.82/15.67  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).
% 15.82/15.67  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.
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k).
% 15.82/15.67  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_b)|c_Polynomial_Opcompose(T_b,V_pa_2,V_q_2)=c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(T_b),T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBK(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBB(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),T_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))))),hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2))),V_pa_2).
% 15.82/15.67  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).
% 15.82/15.67  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)).
% 15.82/15.67  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).
% 15.82/15.67  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)).
% 15.82/15.67  0 [] -class_Rings_Oidom(t_a)|$c7!=c_Groups_Ozero__class_Ozero(t_a).
% 15.82/15.67  0 [] -class_Rings_Oidom(t_a)|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,$c6)),$c8))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,v_cs____).
% 15.82/15.67  0 [] -class_Rings_Oidom(t_a)|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),$c8)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),$c7),$c6)),B_z)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__idom(T_b)| -c_Polynomial_Opos__poly(T_b,hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__idom(T_b)| -c_Polynomial_Opos__poly(T_b,hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2))|c_Polynomial_Opos__poly(T_b,V_pa_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__idom(T_b)|c_Polynomial_Opos__poly(T_b,hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2))| -c_Polynomial_Opos__poly(T_b,V_pa_2).
% 15.82/15.67  0 [] -class_Rings_Olinordered__idom(T_b)|c_Polynomial_Opos__poly(T_b,hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2))|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)=V_z.
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z.
% 15.82/15.67  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).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2))=hAPP(hAPP(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)).
% 15.82/15.67  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)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w)=hAPP(hAPP(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)).
% 15.82/15.67  0 [] -hBOOL(hAPP(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).
% 15.82/15.67  0 [] -hBOOL(hAPP(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).
% 15.82/15.67  0 [] -hBOOL(hAPP(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).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.82/15.67  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_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 15.82/15.67  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)).
% 15.82/15.67  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.
% 15.82/15.67  0 [] hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),hAPP(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)).
% 15.82/15.67  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.
% 15.82/15.67  0 [] -class_Groups_Ozero(T_c)|c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,hAPP(hAPP(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))).
% 15.82/15.67  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,hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)=c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(T_b),T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBK(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBB(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),T_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),c_Polynomial_Osmult(T_b)),V_q_2)))),hAPP(c_Polynomial_OpCons(T_b),c_Groups_Ozero__class_Ozero(T_b)))),V_pa_2).
% 15.82/15.67  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_b_H))=hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))=hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_a_H)),V_b)=hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya)=hAPP(hAPP(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)).
% 15.82/15.67  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)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(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).
% 15.82/15.67  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.
% 15.82/15.67  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.
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x),V_y))|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y),V_x)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))|V_w_2=V_z_2.
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(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.
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z.
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)=V_z.
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 15.82/15.67  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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).
% 15.82/15.67  0 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_b),V_p))=hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_p).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),c_Groups_Oone__class_Oone(T_a)),V_p)=V_p.
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_q)=hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q))=hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 15.82/15.67  0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(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).
% 15.82/15.67  0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_p)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_b),V_p))=hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),V_p)!=hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_p)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_b),V_p)).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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)).
% 15.82/15.67  0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_n).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),V_p)),hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,V_a,hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Polynomial_Omonom(T_a,V_a,V_n)).
% 15.82/15.67  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)).
% 15.82/15.67  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.82/15.67  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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),V_q)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q)),hAPP(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_q))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(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))).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  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).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_b)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_b,V_pa_2,V_h_2)=c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(T_b),T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBK(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),T_b),hAPP(c_COMBS(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b))),hAPP(c_Polynomial_Osmult(T_b),V_h_2)))),c_Polynomial_OpCons(T_b))),V_pa_2).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),V_q))!=hAPP(hAPP(c_Polynomial_OpCons(T_a),V_r),V_q)|V_r=hAPP(c_Polynomial_Opoly(T_a,V_p),V_c).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),V_q))!=hAPP(hAPP(c_Polynomial_OpCons(T_a),V_r),V_q)|V_q=c_Polynomial_Osynthetic__div(T_a,V_p,V_c).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)))=hAPP(hAPP(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)).
% 15.82/15.67  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),V_h)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_h),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|hBOOL(hAPP(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))).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semiring__1__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v)!=c_Groups_Oone__class_Oone(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)).
% 15.82/15.67  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_N))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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))).
% 15.82/15.67  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)).
% 15.82/15.67  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)).
% 15.82/15.67  0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))).
% 15.82/15.67  0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))).
% 15.82/15.67  0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))).
% 15.82/15.67  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2)).
% 15.82/15.67  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2)).
% 15.82/15.67  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2)).
% 15.82/15.67  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n)),V_n)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)),V_m_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)),V_m_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=hAPP(c_Nat_OSuc,V_n_2).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))|V_m_2!=hAPP(c_Nat_OSuc,V_n_2).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),V_m_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),V_m_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|V_m=hAPP(c_Nat_OSuc,V_n).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),V_y)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2!=V_n_2.
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=V_n_2.
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=V_n_2.
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2!=V_n_2.
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|V_m=V_n|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 15.82/15.67  0 [] V_m!=V_n|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),$f7(V_n_2,V_m_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|V_n_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_l))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),V_w_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2),V_w_2)).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),V_w_2))|V_z_2!=V_w_2.
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),V_w_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2),V_w_2))|V_z_2=V_w_2.
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))).
% 15.82/15.67  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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))).
% 15.82/15.67  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_l))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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_l))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_N))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semidom(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b)),V_b_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x_2),V_y_2)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semidom(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b)),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x_2),V_y_2)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_b_2)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_b_2)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2),c_Groups_Ozero__class_Ozero(T_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2),c_Groups_Ozero__class_Ozero(T_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_b_2)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_b_2)).
% 15.82/15.68  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 15.82/15.68  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 15.82/15.68  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))).
% 15.82/15.68  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 15.82/15.68  0 [] -class_Rings_Oordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 15.82/15.68  0 [] -class_Rings_Oordered__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Oordered__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Oordered__comm__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Oordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Oordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Oordered__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(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_d))).
% 15.82/15.68  0 [] -class_Rings_Oordered__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(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_d))).
% 15.82/15.68  0 [] -class_Rings_Oordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 15.82/15.68  0 [] -class_Rings_Oordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 15.82/15.68  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 15.82/15.68  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 15.82/15.68  0 [] -class_Groups_Olinordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.68  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.68  0 [] -class_Groups_Olinordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))).
% 15.82/15.68  0 [] -class_Groups_Oordered__comm__monoid__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_y_2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_x_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.82/15.68  0 [] -class_Groups_Oordered__comm__monoid__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_y_2))|hAPP(hAPP(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_Ozero__class_Ozero(T_b).
% 15.82/15.68  0 [] -class_Groups_Oordered__comm__monoid__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_y_2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_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).
% 15.82/15.68  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))).
% 15.82/15.68  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))).
% 15.82/15.68  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 15.82/15.68  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))).
% 15.82/15.68  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semidom(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)),V_m_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)),V_m_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,V_m_2)))|V_n_2=V_m_2.
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,V_m_2)))|V_n_2!=V_m_2.
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H),V_w))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_H),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))).
% 15.82/15.68  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)).
% 15.82/15.68  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)).
% 15.82/15.68  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)).
% 15.82/15.68  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)).
% 15.82/15.68  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2)=c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))|hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2),V_a_2)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))|hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2),V_a_2)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semiring(T_a)| -hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semiring(T_a)| -hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)).
% 15.82/15.68  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))).
% 15.82/15.68  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))).
% 15.82/15.68  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))).
% 15.82/15.68  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))).
% 15.82/15.68  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 15.82/15.68  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(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)))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Rings_Olinordered__ring__strict(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Rings_Olinordered__idom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__idom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semidom(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))!=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|V_a=V_b.
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semiring__1(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v)!=c_Groups_Oone__class_Oone(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semidom(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)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|V_a=V_b.
% 15.82/15.68  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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_h),V_x)).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osynthetic__div(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),V_c)=hAPP(hAPP(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)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h)=hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))|V_a!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))|V_a!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_r))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_r),c_Groups_Oone__class_Oone(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),hAPP(c_Nat_OSuc,V_n))),V_r)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w),V_w)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z),V_w))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w),V_z)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_j),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i),V_k)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z),V_w))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w),V_z))|V_z=V_w.
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_n)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m)).
% 15.82/15.68  0 [] V_m!=V_n|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_k)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|V_m=V_n.
% 15.82/15.68  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H),V_q)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r_H))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q),V_q_H)).
% 15.82/15.68  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q),V_q_H)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H),V_q)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] -class_Orderings_Opreorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_x)).
% 15.82/15.68  0 [] -class_Rings_Ocomm__ring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_c)),hAPP(hAPP(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))),hAPP(hAPP(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.
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_l_2))|V_l_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),$f8(V_l_2,V_k_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_l_2))|V_l_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),B_n).
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_y_2),V_x_2)).
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_y_2),V_x_2)).
% 15.82/15.68  0 [] -class_Groups_Oab__group__add(T_b)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a),V_p))=hAPP(hAPP(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)).
% 15.82/15.68  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p))=hAPP(hAPP(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)).
% 15.82/15.68  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)).
% 15.82/15.68  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.
% 15.82/15.68  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.
% 15.82/15.68  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.
% 15.82/15.68  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.
% 15.82/15.68  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).
% 15.82/15.68  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).
% 15.82/15.68  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.
% 15.82/15.68  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).
% 15.82/15.68  0 [] -class_Rings_Ocomm__ring(T_a)|hAPP(hAPP(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),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)).
% 15.82/15.68  0 [] -class_Rings_Ocomm__ring(T_a)|hAPP(hAPP(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),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)).
% 15.82/15.68  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)).
% 15.82/15.68  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)).
% 15.82/15.68  0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w))=hAPP(hAPP(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)).
% 15.82/15.68  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).
% 15.82/15.68  0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=V_b.
% 15.82/15.68  0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b))=V_b.
% 15.82/15.68  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=hAPP(hAPP(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)).
% 15.82/15.68  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=hAPP(hAPP(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)).
% 15.82/15.68  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)).
% 15.82/15.68  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).
% 15.82/15.68  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)).
% 15.82/15.68  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).
% 15.82/15.68  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).
% 15.82/15.68  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.
% 15.82/15.68  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).
% 15.82/15.68  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)).
% 15.82/15.68  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)).
% 15.82/15.68  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)).
% 15.82/15.68  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)).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)|hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2)).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)),V_a_2)).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),V_b_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)),V_a_2)).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_b_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2))).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)),V_a_2)).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),V_b_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)),V_a_2)).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2)).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2)).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)),c_Groups_Ouminus__class_Ouminus(T_a,V_a))).
% 15.82/15.68  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).
% 15.82/15.68  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).
% 15.82/15.68  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).
% 15.82/15.68  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).
% 15.82/15.68  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).
% 15.82/15.68  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).
% 15.82/15.68  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.
% 15.82/15.68  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.
% 15.82/15.68  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).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Groups_Olinordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.68  0 [] -class_Groups_Olinordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),V_a_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.68  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),V_a_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.68  0 [] -class_Groups_Olinordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),V_a_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.68  0 [] -class_Groups_Olinordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),V_a_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__idom(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__idom(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Groups_Ogroup__add(T_b)|hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Groups_Ogroup__add(T_b)|hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(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.
% 15.82/15.68  0 [] -class_Groups_Oab__group__add(T_a)|hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Groups_Ogroup__add(T_b)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_b).
% 15.82/15.68  0 [] -class_Groups_Ogroup__add(T_b)|V_a_2=c_Groups_Ouminus__class_Ouminus(T_b,V_b_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)!=c_Groups_Ozero__class_Ozero(T_b).
% 15.82/15.68  0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(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).
% 15.82/15.68  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)).
% 15.82/15.68  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).
% 15.82/15.68  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)).
% 15.82/15.68  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).
% 15.82/15.68  0 [] hAPP(hAPP(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).
% 15.82/15.68  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)).
% 15.82/15.68  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)).
% 15.82/15.68  0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))!=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Nat_OSuc,hAPP(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).
% 15.82/15.68  0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x_2!=V_y_2.
% 15.82/15.68  0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x_2!=c_Groups_Ouminus__class_Ouminus(T_b,V_y_2).
% 15.82/15.68  0 [] -class_Orderings_Oord(T_c)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,T_c),V_f_2),V_g_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_c,hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))).
% 15.82/15.68  0 [] -class_Orderings_Oord(T_c)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,T_c),V_f_2),V_g_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_c,hAPP(V_f_2,$f9(V_g_2,V_f_2,T_b,T_c))),hAPP(V_g_2,$f9(V_g_2,V_f_2,T_b,T_c)))).
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_b)|V_x_2!=V_y_2|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_b)|V_x_2!=V_y_2|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_y_2),V_x_2)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_b)|V_x_2=V_y_2| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_y_2),V_x_2)).
% 15.82/15.68  0 [] -class_Orderings_Opreorder(T_a)|V_x!=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y)).
% 15.82/15.68  0 [] -class_Orderings_Oord(T_c)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,T_c),V_f_2),V_g_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_c,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_y_2),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))|V_x_2=V_y_2.
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_y_2),V_x_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 15.82/15.68  0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_c)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_a)).
% 15.82/15.68  0 [] -class_Orderings_Oord(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))|V_b!=V_c|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_c)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))|V_b!=V_c|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_a)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))|V_x=V_y.
% 15.82/15.68  0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_z)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|V_x=V_y.
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_z),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_z),V_x)).
% 15.82/15.68  0 [] -class_Orderings_Oord(T_c)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,T_c),V_f_2),V_g_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_c,hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))).
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x)).
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 15.82/15.68  0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)).
% 15.82/15.68  0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))|V_b!=V_c|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)).
% 15.82/15.68  0 [] -class_Orderings_Oord(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))|V_b!=V_c|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)).
% 15.82/15.68  0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 15.82/15.68  0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_y!=V_x.
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x!=V_y.
% 15.82/15.68  0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 15.82/15.68  0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x!=V_y.
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_y_2),V_x_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))|V_x_2=V_y_2.
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_y_2),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_y_2),V_x_2))|V_x_2=V_y_2.
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_y_2),V_x_2)).
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_b)|V_x_2=V_y_2|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_y_2),V_x_2)).
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_b)|V_x_2!=V_y_2| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2)).
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_b)|V_x_2!=V_y_2| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_y_2),V_x_2)).
% 15.82/15.68  0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_x)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)).
% 15.82/15.68  0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_z),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)).
% 15.82/15.68  0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))|V_a=V_b|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))|V_a=V_b|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x=V_y.
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))|V_x_2=V_y_2.
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 15.82/15.68  0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y)).
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))|V_x_2=V_y_2.
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)).
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))|V_x_2=V_y_2.
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 15.82/15.68  0 [] -class_Orderings_Opreorder(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2)).
% 15.82/15.68  0 [] -class_Orderings_Opreorder(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_y_2),V_x_2)).
% 15.82/15.68  0 [] -class_Orderings_Opreorder(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_y_2),V_x_2)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))|V_x_2=V_y_2.
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_y_2),V_x_2)).
% 15.82/15.68  0 [] -class_Orderings_Olinorder(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_y_2),V_x_2)).
% 15.82/15.68  0 [] -class_Rings_Oidom(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),hAPP(hAPP(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)).
% 15.82/15.68  0 [] -class_Rings_Oidom(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(T_a,V_a,V_p)))),V_p)).
% 15.82/15.68  0 [] -class_Rings_Oidom(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(T_a,V_a,V_p)))),V_p)).
% 15.82/15.68  0 [] -class_Lattices_Oboolean__algebra(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_x_2)),c_Groups_Ouminus__class_Ouminus(T_b,V_y_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_y_2),V_x_2)).
% 15.82/15.68  0 [] -class_Lattices_Oboolean__algebra(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_x_2)),c_Groups_Ouminus__class_Ouminus(T_b,V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_y_2),V_x_2)).
% 15.82/15.68  0 [] -class_Lattices_Oboolean__algebra(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y)),c_Groups_Ouminus__class_Ouminus(T_a,V_x))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__ring__1(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),c_Groups_Ouminus__class_Ouminus(T_b,V_x_2)),V_y_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)).
% 15.82/15.68  0 [] -class_Rings_Ocomm__ring__1(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),c_Groups_Ouminus__class_Ouminus(T_b,V_x_2)),V_y_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)).
% 15.82/15.68  0 [] -class_Rings_Ocomm__ring__1(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),c_Groups_Ouminus__class_Ouminus(T_b,V_y_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)).
% 15.82/15.68  0 [] -class_Rings_Ocomm__ring__1(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),c_Groups_Ouminus__class_Ouminus(T_b,V_y_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)).
% 15.82/15.68  0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z))=V_z.
% 15.82/15.68  0 [] -class_Orderings_Oord(T_c)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c),V_f_2),V_g_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,T_c),V_f_2),V_g_2)).
% 15.82/15.68  0 [] -class_Orderings_Oord(T_c)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c),V_f_2),V_g_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,T_c),V_g_2),V_f_2)).
% 15.82/15.68  0 [] -class_Orderings_Oord(T_c)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c),V_f_2),V_g_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,T_c),V_f_2),V_g_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,T_c),V_g_2),V_f_2)).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_q))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))|hBOOL(hAPP(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)).
% 15.82/15.68  0 [] -class_Rings_Odvd(T_a)|V_a!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))|hBOOL(hAPP(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Rings_Oidom(T_b)| -hBOOL(hAPP(hAPP(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)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)).
% 15.82/15.68  0 [] -class_Rings_Oidom(T_b)|hBOOL(hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Rings_Oidom(T_b)|hBOOL(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)).
% 15.82/15.68  0 [] -class_Rings_Oidom(T_b)| -hBOOL(hAPP(hAPP(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)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)).
% 15.82/15.68  0 [] -class_Rings_Oidom(T_b)|hBOOL(hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Rings_Oidom(T_b)|hBOOL(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|hBOOL(hAPP(hAPP(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_m))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b)).
% 15.82/15.68  0 [] -class_Fields_Ofield(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_q_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)).
% 15.82/15.68  0 [] -class_Fields_Ofield(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_q_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)).
% 15.82/15.68  0 [] -class_Fields_Ofield(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))|V_a=c_Groups_Ozero__class_Ozero(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_q)).
% 15.82/15.68  0 [] -class_Fields_Ofield(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q)))|V_a=c_Groups_Ozero__class_Ozero(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 15.82/15.68  0 [] -class_Fields_Ofield(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(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)).
% 15.82/15.68  0 [] -class_Fields_Ofield(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_pa_2)),V_q_2))|V_a_2=c_Groups_Ozero__class_Ozero(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)).
% 15.82/15.68  0 [] -class_Fields_Ofield(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_pa_2)),V_q_2))|V_a_2=c_Groups_Ozero__class_Ozero(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)).
% 15.82/15.68  0 [] -class_Fields_Ofield(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Fields_Ofield(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(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))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)).
% 15.82/15.68  0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)=V_a.
% 15.82/15.68  0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)=V_x.
% 15.82/15.68  0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_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).
% 15.82/15.68  0 [] -class_Lattices_Oboolean__algebra(T_b)|c_Groups_Ouminus__class_Ouminus(T_b,V_x_2)!=c_Groups_Ouminus__class_Ouminus(T_b,V_y_2)|V_x_2=V_y_2.
% 15.82/15.68  0 [] -class_Lattices_Oboolean__algebra(T_b)|c_Groups_Ouminus__class_Ouminus(T_b,V_x_2)=c_Groups_Ouminus__class_Ouminus(T_b,V_y_2)|V_x_2!=V_y_2.
% 15.82/15.68  0 [] -class_Groups_Ouminus(T_b)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b),V_A_2),V_x_2)=c_Groups_Ouminus__class_Ouminus(T_b,hAPP(V_A_2,V_x_2)).
% 15.82/15.68  0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x))=V_x.
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__semiring__1(T_a)|V_x!=c_Groups_Oone__class_Oone(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))).
% 15.82/15.68  0 [] -class_Groups_Ouminus(T_b)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b),V_A_2),V_x_2)=c_Groups_Ouminus__class_Ouminus(T_b,hAPP(V_A_2,V_x_2)).
% 15.82/15.68  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)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Ouminus__class_Ouminus(T_b,V_ca_2)),hAPP(hAPP(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)).
% 15.82/15.68  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)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Ouminus__class_Ouminus(T_b,V_ca_2)),hAPP(hAPP(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)).
% 15.82/15.68  0 [] -class_Rings_Oidom(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),V_ca_2),hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Rings_Oidom(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),V_ca_2),hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Rings_Oidom(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),hAPP(hAPP(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)).
% 15.82/15.68  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(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),$f10(V_l_2,V_P_2,T_b)),c_Groups_Ozero__class_Ozero(T_b)))).
% 15.82/15.68  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,$f10(V_l_2,V_P_2,T_b))).
% 15.82/15.68  0 [] -class_Rings_Odvd(T_b)| -class_Rings_Osemiring__0(T_b)|hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),$f11(V_l_2,V_P_2,T_b))))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),X1),c_Groups_Ozero__class_Ozero(T_b))))| -hBOOL(hAPP(V_P_2,X1)).
% 15.82/15.68  0 [] -class_Rings_Oidom(T_b)|c_Polynomial_Oorder(T_b,V_a_2,V_pa_2)=c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot),hAPP(c_COMBC(tc_Nat_Onat,tc_Polynomial_Opoly(T_b),tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_HOL_Obool),tc_Nat_Onat),c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Polynomial_Opoly(T_b),tc_Nat_Onat),hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Ouminus__class_Ouminus(T_b,V_a_2)),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))))),c_Nat_OSuc))),V_pa_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f12(V_n_2,V_P_2)),V_n_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i),$f12(V_n_2,V_P_2)))| -hBOOL(hAPP(V_P_2,B_i)).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))|hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),$f12(V_n_2,V_P_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 15.82/15.68  0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2))).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2)),V_t_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2)),V_t_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(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).
% 15.82/15.68  0 [] hBOOL(hAPP(hAPP(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).
% 15.82/15.68  0 [] V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))|hBOOL(hAPP(hAPP(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))).
% 15.82/15.68  0 [] V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))| -hBOOL(hAPP(hAPP(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))).
% 15.82/15.68  0 [] -class_Orderings_Owellorder(T_b)| -hBOOL(hAPP(V_P_2,B_x1))|hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))).
% 15.82/15.68  0 [] -class_Orderings_Owellorder(T_b)| -hBOOL(hAPP(V_P_2,V_k_2))|hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))|V_m=V_n.
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m),V_n))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(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)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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))).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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))).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(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))))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(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))))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.68  0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_m_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(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)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(hAPP(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).
% 15.82/15.68  0 [] hBOOL(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)).
% 15.82/15.68  0 [] -class_Orderings_Owellorder(T_b)| -hBOOL(hAPP(V_P_2,V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Orderings_Oord__class_OLeast(T_b,V_P_2)),V_k_2)).
% 15.82/15.68  0 [] -class_Orderings_Owellorder(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_k_2),c_Orderings_Oord__class_OLeast(T_b,V_P_2)))| -hBOOL(hAPP(V_P_2,V_k_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z),V_n)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))| -hBOOL(hAPP(hAPP(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)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))|hBOOL(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)).
% 15.82/15.68  0 [] -hBOOL(hAPP(V_P_2,V_n_2))|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2)=hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_OSuc))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))| -hBOOL(hAPP(hAPP(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).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))|hBOOL(hAPP(hAPP(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).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))| -hBOOL(hAPP(hAPP(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).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))|hBOOL(hAPP(hAPP(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).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 15.82/15.68  0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(hAPP(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)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)).
% 15.82/15.68  0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(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)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(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)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b)).
% 15.82/15.68  0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)).
% 15.82/15.68  0 [] V_x_2!=V_y_2|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)).
% 15.82/15.68  0 [] V_x_2!=V_y_2|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)).
% 15.82/15.68  0 [] V_x_2=V_y_2| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))|V_x_2=V_y_2.
% 15.82/15.68  0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))|V_x_2!=V_y_2.
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))|V_x_2!=V_y_2.
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))|V_x_2=V_y_2.
% 15.82/15.68  0 [] V_a=V_b| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)).
% 15.82/15.68  0 [] V_x!=V_y|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))|V_x_2=V_y_2.
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))|V_x_2!=V_y_2.
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))|V_x=V_y.
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))|V_a=V_b| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)).
% 15.82/15.68  0 [] V_a!=V_b| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))|V_b!=V_c|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))|V_m=V_n.
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))|V_x=V_y.
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)).
% 15.82/15.68  0 [] V_a!=V_b| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)).
% 15.82/15.68  0 [] V_a!=V_b| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))|V_x!=V_y.
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))|V_x!=V_y.
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))|V_y!=V_x.
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))|V_b!=V_c|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))|V_b!=V_c| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)).
% 15.82/15.68  0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.82/15.68  0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)).
% 15.82/15.68  0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(hAPP(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)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_b_2)).
% 15.82/15.68  0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_b_2)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_b)| -c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))|hBOOL(hAPP(V_P_2,$f13(V_k_2,V_P_2,V_d_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))| -hBOOL(hAPP(V_P_2,B_x))|hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))| -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),$f13(V_k_2,V_P_2,V_d_2)),V_d_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))| -hBOOL(hAPP(V_P_2,B_x))|hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))).
% 15.82/15.68  0 [] -class_Groups_Omonoid__mult(T_a)| -hBOOL(hAPP(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).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__ring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_z))).
% 15.82/15.68  0 [] -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_m)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),hAPP(c_Nat_OSuc,V_m))).
% 15.82/15.68  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.68  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)=hAPP(c_Nat_OSuc,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 15.82/15.68  0 [] -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m.
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_c),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)!=V_k_2|V_j_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_k_2|V_j_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_n)=V_m.
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_j_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_j_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m.
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_k))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)),V_i_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)),V_i_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),V_j).
% 15.82/15.68  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,hAPP(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).
% 15.82/15.68  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_m)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_n))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i))=V_i.
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)|V_m_2=V_n_2.
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)|V_m_2!=V_n_2.
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_m))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 15.82/15.68  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)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_ca_2),V_d_2)).
% 15.82/15.68  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)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_ca_2),V_d_2)).
% 15.82/15.68  0 [] -class_Groups_Ominus(T_b)|hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b),V_A_2,V_B_2),V_x_2)=c_Groups_Ominus__class_Ominus(T_b,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)).
% 15.82/15.68  0 [] -class_Groups_Ominus(T_b)|hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b),V_A_2,V_B_2),V_x_2)=c_Groups_Ominus__class_Ominus(T_b,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)).
% 15.82/15.68  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_b),V_q))=hAPP(hAPP(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)).
% 15.82/15.68  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)).
% 15.82/15.68  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).
% 15.82/15.68  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.
% 15.82/15.68  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.
% 15.82/15.68  0 [] -class_Rings_Ocomm__ring(T_a)|hAPP(hAPP(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),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_b),V_p)).
% 15.82/15.68  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).
% 15.82/15.68  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)).
% 15.82/15.68  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)).
% 15.82/15.68  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n),V_n)=V_m.
% 15.82/15.68  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_n)=V_m.
% 15.82/15.68  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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)).
% 15.82/15.68  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 15.82/15.68  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 15.82/15.68  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),hAPP(c_Nat_OSuc,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 15.82/15.68  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n),hAPP(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).
% 15.82/15.68  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).
% 15.82/15.68  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 15.82/15.68  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.68  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.
% 15.82/15.68  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b)=V_a.
% 15.82/15.68  0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),V_b)=V_a.
% 15.82/15.68  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)).
% 15.82/15.68  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)).
% 15.82/15.68  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)).
% 15.82/15.68  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)).
% 15.82/15.68  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.
% 15.82/15.68  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.
% 15.82/15.68  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).
% 15.82/15.68  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).
% 15.82/15.68  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).
% 15.82/15.68  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.
% 15.82/15.68  0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),c_Groups_Ouminus__class_Ouminus(T_a,V_y)).
% 15.82/15.68  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))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b).
% 15.82/15.68  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 15.82/15.68  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 15.82/15.68  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).
% 15.82/15.68  0 [] -class_Rings_Oring(T_b)|hAPP(hAPP(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)!=hAPP(hAPP(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=hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Rings_Oring(T_b)|hAPP(hAPP(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)=hAPP(hAPP(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!=hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Rings_Oring(T_b)|hAPP(hAPP(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)!=hAPP(hAPP(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)|hAPP(hAPP(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.
% 15.82/15.68  0 [] -class_Rings_Oring(T_b)|hAPP(hAPP(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)=hAPP(hAPP(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)|hAPP(hAPP(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.
% 15.82/15.68  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))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(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))).
% 15.82/15.68  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))=hAPP(hAPP(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)).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2))|hBOOL(hAPP(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))).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2))| -hBOOL(hAPP(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))).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  0 [] -class_Groups_Oordered__ab__group__add(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2),V_b_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.68  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)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),V_d_2)).
% 15.82/15.68  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)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),V_b_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),V_d_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_l))|hBOOL(hAPP(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))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n)),V_k)).
% 15.82/15.68  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).
% 15.82/15.68  0 [] -class_Rings_Oordered__ring(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(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)),hAPP(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_ca_2),hAPP(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Oordered__ring(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(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)),hAPP(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,V_ca_2),hAPP(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Oordered__ring(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(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)),hAPP(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(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)).
% 15.82/15.68  0 [] -class_Rings_Oordered__ring(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(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)),hAPP(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(hAPP(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)).
% 15.82/15.68  0 [] -class_Rings_Oordered__ring(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(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)),hAPP(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(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)).
% 15.82/15.68  0 [] -class_Rings_Oordered__ring(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(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)),hAPP(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(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)).
% 15.82/15.68  0 [] -class_Rings_Oordered__ring(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(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)),hAPP(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),hAPP(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Oordered__ring(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(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)),hAPP(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_ca_2),hAPP(hAPP(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))).
% 15.82/15.68  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),hAPP(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__ring(T_b)| -class_Rings_Odvd(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__ring(T_b)| -class_Rings_Odvd(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__ring(T_b)| -class_Rings_Odvd(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Ocomm__ring(T_b)| -class_Rings_Odvd(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(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))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,hAPP(c_Nat_OSuc,V_i))),V_n)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|hAPP(c_Nat_OSuc,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n.
% 15.82/15.68  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(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))).
% 15.82/15.68  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|V_a_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))|V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),$f14(V_b_2,V_a_2,V_P_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))| -hBOOL(hAPP(V_P_2,$f14(V_b_2,V_a_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),$f14(V_b_2,V_a_2,V_P_2)).
% 15.82/15.68  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,$f14(V_b_2,V_a_2,V_P_2))).
% 15.82/15.68  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.82/15.68  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|V_a_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))|V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),$f15(V_b_2,V_a_2,V_P_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))| -hBOOL(hAPP(V_P_2,$f15(V_b_2,V_a_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),$f15(V_b_2,V_a_2,V_P_2)).
% 15.82/15.68  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,$f15(V_b_2,V_a_2,V_P_2))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_j),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),hAPP(c_Nat_OSuc,V_j)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j),V_i))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u)),V_m),V_n).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)=V_n_2.
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)!=V_n_2.
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u)),V_n)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)|V_m_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)|V_m_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|V_n=hAPP(c_Nat_OSuc,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|hAPP(c_Nat_OSuc,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=V_n.
% 15.82/15.68  0 [] V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=V_n.
% 15.82/15.68  0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=hAPP(c_Nat_OSuc,hAPP(hAPP(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)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))).
% 15.82/15.68  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).
% 15.82/15.68  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)=hAPP(hAPP(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)).
% 15.82/15.68  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).
% 15.82/15.68  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)))).
% 15.82/15.68  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),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Nat_OSuc,hAPP(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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)).
% 15.82/15.68  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).
% 15.82/15.68  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)))).
% 15.82/15.68  0 [] -class_Groups_Omonoid__mult(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_p),V_n))|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n),V_p))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_l_2))|hBOOL(hAPP(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))).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_l_2))| -hBOOL(hAPP(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))).
% 15.82/15.68  0 [] -class_Rings_Olinordered__idom(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Polynomial_Opoly(T_b),V_x_2),V_y_2))|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)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__idom(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Polynomial_Opoly(T_b),V_x_2),V_y_2))|V_x_2!=V_y_2.
% 15.82/15.68  0 [] -class_Rings_Olinordered__idom(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(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)).
% 15.82/15.68  0 [] -class_Rings_Ocomm__ring(T_a)|hAPP(hAPP(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),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q)).
% 15.82/15.68  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.
% 15.82/15.68  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)).
% 15.82/15.68  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)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__idom(T_b)| -hBOOL(hAPP(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)).
% 15.82/15.68  0 [] -class_Rings_Olinordered__idom(T_b)|hBOOL(hAPP(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)).
% 15.82/15.68  0 [] hAPP(hAPP(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).
% 15.82/15.68  0 [] c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)).
% 15.82/15.68  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).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_b)| -c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)|c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2).
% 15.82/15.68  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)).
% 15.82/15.68  0 [] -class_Orderings_Oorder(T_b)| -c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y),V_x))|c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y).
% 15.82/15.68  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y),V_x))|c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))| -hBOOL(hAPP(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,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))|hBOOL(hAPP(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))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))| -hBOOL(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))|hBOOL(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))|hBOOL(hAPP(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))).
% 15.82/15.68  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).
% 15.82/15.68  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).
% 15.82/15.68  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.
% 15.82/15.68  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.
% 15.82/15.68  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).
% 15.82/15.68  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).
% 15.82/15.68  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).
% 15.82/15.68  0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(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.
% 15.82/15.68  0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(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.
% 15.82/15.68  0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))| -hBOOL(hAPP(hAPP(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)).
% 15.82/15.68  0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y),V_z)=hAPP(hAPP(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)).
% 15.82/15.68  0 [] -class_Divides_Oring__div(T_a)| -hBOOL(hAPP(hAPP(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)).
% 15.82/15.68  0 [] -class_Divides_Oring__div(T_a)| -hBOOL(hAPP(hAPP(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)).
% 15.82/15.68  0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(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)).
% 15.82/15.68  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).
% 15.82/15.68  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).
% 15.82/15.68  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).
% 15.82/15.68  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.
% 15.82/15.68  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).
% 15.82/15.68  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).
% 15.82/15.68  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).
% 15.82/15.68  0 [] -class_Divides_Osemiring__div(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ca_2))| -hBOOL(hAPP(hAPP(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)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_ca_2)).
% 15.82/15.68  0 [] -class_Divides_Osemiring__div(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ca_2))|hBOOL(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_ca_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(hAPP(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.
% 15.82/15.68  0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_i_2)).
% 15.82/15.68  0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_i_2)).
% 15.82/15.68  0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.82/15.68  0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2),V_k_2)).
% 15.82/15.68  0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_i_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))| -hBOOL(hAPP(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_a_2,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))|hBOOL(hAPP(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_a_2,V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2),V_i_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2),V_i_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_2),V_a_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_2),V_a_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),V_b))|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(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_a_2,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(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_a_2,V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_a))|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),V_a_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),V_a_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k)),V_x)).
% 15.82/15.68  0 [] -hBOOL(hAPP(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).
% 15.82/15.68  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_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)).
% 15.82/15.68  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_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)).
% 15.82/15.68  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_Oplus__class_Oplus(T_a),V_a),V_b),V_b)=hAPP(hAPP(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)).
% 15.82/15.68  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_Oplus__class_Oplus(T_a),V_b),V_a),V_b)=hAPP(hAPP(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)).
% 15.82/15.68  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)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))| -hBOOL(hAPP(hAPP(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).
% 15.82/15.68  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)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))| -hBOOL(hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Divides_Osemiring__div(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)| -hBOOL(hAPP(hAPP(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).
% 15.82/15.68  0 [] -class_Divides_Osemiring__div(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)| -hBOOL(hAPP(hAPP(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).
% 15.82/15.68  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y))).
% 15.82/15.68  0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j),V_k_2))|V_n_2!=hAPP(hAPP(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(V_P_2,B_i)).
% 15.82/15.68  0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),X3))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_n_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),X2)),X3)|hBOOL(hAPP(V_P_2,X2)).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f18(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f18(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f19(V_k_2,V_n_2,V_P_2))),$f18(V_k_2,V_n_2,V_P_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))| -hBOOL(hAPP(V_P_2,$f19(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f16(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f16(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f18(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f16(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f18(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f16(V_k_2,V_n_2,V_P_2)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f19(V_k_2,V_n_2,V_P_2))),$f18(V_k_2,V_n_2,V_P_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f16(V_k_2,V_n_2,V_P_2)))| -hBOOL(hAPP(V_P_2,$f19(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f16(V_k_2,V_n_2,V_P_2)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f16(V_k_2,V_n_2,V_P_2)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f18(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f16(V_k_2,V_n_2,V_P_2)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f18(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f16(V_k_2,V_n_2,V_P_2)),V_k_2))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f19(V_k_2,V_n_2,V_P_2))),$f18(V_k_2,V_n_2,V_P_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f16(V_k_2,V_n_2,V_P_2)),V_k_2))| -hBOOL(hAPP(V_P_2,$f19(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f17(V_k_2,V_n_2,V_P_2))),$f16(V_k_2,V_n_2,V_P_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f17(V_k_2,V_n_2,V_P_2))),$f16(V_k_2,V_n_2,V_P_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f18(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f17(V_k_2,V_n_2,V_P_2))),$f16(V_k_2,V_n_2,V_P_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f18(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f17(V_k_2,V_n_2,V_P_2))),$f16(V_k_2,V_n_2,V_P_2))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f19(V_k_2,V_n_2,V_P_2))),$f18(V_k_2,V_n_2,V_P_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f17(V_k_2,V_n_2,V_P_2))),$f16(V_k_2,V_n_2,V_P_2))| -hBOOL(hAPP(V_P_2,$f19(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(V_P_2,$f17(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(V_P_2,$f17(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f18(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(V_P_2,$f17(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f18(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(V_P_2,$f17(V_k_2,V_n_2,V_P_2)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f19(V_k_2,V_n_2,V_P_2))),$f18(V_k_2,V_n_2,V_P_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(V_P_2,$f17(V_k_2,V_n_2,V_P_2)))| -hBOOL(hAPP(V_P_2,$f19(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f18(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f18(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f19(V_k_2,V_n_2,V_P_2))),$f18(V_k_2,V_n_2,V_P_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))| -hBOOL(hAPP(V_P_2,$f19(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f16(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f16(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f18(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f16(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f18(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f16(V_k_2,V_n_2,V_P_2)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f19(V_k_2,V_n_2,V_P_2))),$f18(V_k_2,V_n_2,V_P_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f16(V_k_2,V_n_2,V_P_2)))| -hBOOL(hAPP(V_P_2,$f19(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f16(V_k_2,V_n_2,V_P_2)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f16(V_k_2,V_n_2,V_P_2)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f18(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f16(V_k_2,V_n_2,V_P_2)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f18(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f16(V_k_2,V_n_2,V_P_2)),V_k_2))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f19(V_k_2,V_n_2,V_P_2))),$f18(V_k_2,V_n_2,V_P_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f16(V_k_2,V_n_2,V_P_2)),V_k_2))| -hBOOL(hAPP(V_P_2,$f19(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f17(V_k_2,V_n_2,V_P_2))),$f16(V_k_2,V_n_2,V_P_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f17(V_k_2,V_n_2,V_P_2))),$f16(V_k_2,V_n_2,V_P_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f18(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f17(V_k_2,V_n_2,V_P_2))),$f16(V_k_2,V_n_2,V_P_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f18(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f17(V_k_2,V_n_2,V_P_2))),$f16(V_k_2,V_n_2,V_P_2))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f19(V_k_2,V_n_2,V_P_2))),$f18(V_k_2,V_n_2,V_P_2)).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f17(V_k_2,V_n_2,V_P_2))),$f16(V_k_2,V_n_2,V_P_2))| -hBOOL(hAPP(V_P_2,$f19(V_k_2,V_n_2,V_P_2))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(V_P_2,$f17(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.68  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(V_P_2,$f17(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f18(V_k_2,V_n_2,V_P_2))).
% 15.82/15.69  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(V_P_2,$f17(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f18(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.69  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(V_P_2,$f17(V_k_2,V_n_2,V_P_2)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f19(V_k_2,V_n_2,V_P_2))),$f18(V_k_2,V_n_2,V_P_2)).
% 15.82/15.69  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(V_P_2,$f17(V_k_2,V_n_2,V_P_2)))| -hBOOL(hAPP(V_P_2,$f19(V_k_2,V_n_2,V_P_2))).
% 15.82/15.69  0 [] V_a_1!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1),V_r_1))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_b_1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1)=V_y.
% 15.82/15.69  0 [] V_a_1!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1),V_b_1))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))|V_b_1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1)=V_y.
% 15.82/15.69  0 [] V_a_1!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1),V_b_1))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1),V_r_1))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_b_1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1)=V_y.
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y),V_x))|c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))|c_SMT_Oz3div(V_k,V_l)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,V_l).
% 15.82/15.69  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))|c_SMT_Oz3div(V_k,V_l)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_l))).
% 15.82/15.69  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))=hAPP(hAPP(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)).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k))).
% 15.82/15.69  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_m)).
% 15.82/15.69  0 [] -hBOOL(hAPP(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).
% 15.82/15.69  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)).
% 15.82/15.69  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)).
% 15.82/15.69  0 [] c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=V_m.
% 15.82/15.69  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).
% 15.82/15.69  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).
% 15.82/15.69  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).
% 15.82/15.69  0 [] -class_Fields_Ofield(T_a)|c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_x),V_y)=hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.82/15.69  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).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m))).
% 15.82/15.69  0 [] -hBOOL(hAPP(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.
% 15.82/15.69  0 [] -hBOOL(hAPP(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.
% 15.82/15.69  0 [] -hBOOL(hAPP(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).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_m)).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(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).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=hAPP(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)).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=hAPP(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)).
% 15.82/15.69  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))).
% 15.82/15.69  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(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_k_2))|V_n_2!=hAPP(hAPP(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)).
% 15.82/15.69  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(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f20(V_k_2,V_n_2,V_P_2)),V_k_2)).
% 15.82/15.69  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=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),$f21(V_k_2,V_n_2,V_P_2))),$f20(V_k_2,V_n_2,V_P_2)).
% 15.82/15.69  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,$f21(V_k_2,V_n_2,V_P_2))).
% 15.82/15.69  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.69  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f20(V_k_2,V_n_2,V_P_2)),V_k_2)).
% 15.82/15.69  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=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),$f21(V_k_2,V_n_2,V_P_2))),$f20(V_k_2,V_n_2,V_P_2)).
% 15.82/15.69  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,$f21(V_k_2,V_n_2,V_P_2))).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2))))|V_q_2=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2))|V_q_2!=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2))))|V_q_2!=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2).
% 15.82/15.69  0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),$f22(V_n_2,V_m_2,V_P_2))),V_m_2)).
% 15.82/15.69  0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,$f22(V_n_2,V_m_2,V_P_2))))).
% 15.82/15.69  0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(V_P_2,$f22(V_n_2,V_m_2,V_P_2))).
% 15.82/15.69  0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),$f22(V_n_2,V_m_2,V_P_2))),V_m_2)).
% 15.82/15.69  0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,$f22(V_n_2,V_m_2,V_P_2))))).
% 15.82/15.69  0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(V_P_2,$f22(V_n_2,V_m_2,V_P_2))).
% 15.82/15.69  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.82/15.69  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q))))| -hBOOL(hAPP(V_P_2,B_q)).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=hAPP(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)).
% 15.82/15.69  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)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_a)|V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))| -hBOOL(hAPP(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)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_a)|V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hBOOL(hAPP(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))).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))|hBOOL(hAPP(V_P_2,$f23(V_k_2,V_P_2,V_d_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))| -hBOOL(hAPP(V_P_2,B_x))|hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))| -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,$f23(V_k_2,V_P_2,V_d_2),V_d_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))| -hBOOL(hAPP(V_P_2,B_x))|hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.69  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)).
% 15.82/15.69  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).
% 15.82/15.69  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).
% 15.82/15.69  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).
% 15.82/15.69  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).
% 15.82/15.69  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).
% 15.82/15.69  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).
% 15.82/15.69  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)).
% 15.82/15.69  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)).
% 15.82/15.69  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).
% 15.82/15.69  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).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_a_2)!=c_Groups_Oone__class_Oone(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_a_2)=c_Groups_Oone__class_Oone(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b)),V_a_2)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_a)| -hBOOL(hAPP(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).
% 15.82/15.69  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))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.69  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))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_a)| -hBOOL(hAPP(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)).
% 15.82/15.69  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).
% 15.82/15.69  0 [] -class_Groups_Osgn__if(T_a)|V_x=c_Groups_Ozero__class_Ozero(T_a)| -hBOOL(hAPP(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).
% 15.82/15.69  0 [] -class_Groups_Osgn__if(T_a)|V_x=c_Groups_Ozero__class_Ozero(T_a)|hBOOL(hAPP(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)).
% 15.82/15.69  0 [] -hBOOL(hAPP(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(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j),V_k_2))|V_n_2!=hAPP(hAPP(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)).
% 15.82/15.69  0 [] -hBOOL(hAPP(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(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f24(V_n_2,V_P_2,V_k_2))).
% 15.82/15.69  0 [] -hBOOL(hAPP(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(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f24(V_n_2,V_P_2,V_k_2)),V_k_2)).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f25(V_n_2,V_P_2,V_k_2))),$f24(V_n_2,V_P_2,V_k_2)).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(hAPP(V_P_2,$f25(V_n_2,V_P_2,V_k_2)),$f24(V_n_2,V_P_2,V_k_2))).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),B_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_n_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)|hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f26(V_n_2,V_P_2,V_k_2))).
% 15.82/15.69  0 [] -hBOOL(hAPP(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(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f26(V_n_2,V_P_2,V_k_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f27(V_n_2,V_P_2,V_k_2))),$f26(V_n_2,V_P_2,V_k_2)).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(hAPP(V_P_2,$f27(V_n_2,V_P_2,V_k_2)),$f26(V_n_2,V_P_2,V_k_2))).
% 15.82/15.69  0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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,hAPP(hAPP(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)).
% 15.82/15.69  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).
% 15.82/15.69  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).
% 15.82/15.69  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).
% 15.82/15.69  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_a.
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(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.
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(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.
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(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.
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(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)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(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)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c).
% 15.82/15.69  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k).
% 15.82/15.69  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k).
% 15.82/15.69  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)=hAPP(hAPP(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)).
% 15.82/15.69  0 [] V_a=hAPP(hAPP(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)).
% 15.82/15.69  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)).
% 15.82/15.69  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)).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(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).
% 15.82/15.69  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)).
% 15.82/15.69  0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(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).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_b)| -hBOOL(hAPP(hAPP(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).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_b)|hBOOL(hAPP(hAPP(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).
% 15.82/15.69  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).
% 15.82/15.69  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).
% 15.82/15.69  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).
% 15.82/15.69  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).
% 15.82/15.69  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).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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).
% 15.82/15.69  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).
% 15.82/15.69  0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.82/15.69  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).
% 15.82/15.69  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.
% 15.82/15.69  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).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c).
% 15.82/15.69  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c).
% 15.82/15.69  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_Oplus__class_Oplus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Groups_Ocancel__ab__semigroup__add(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Rings_Oring__1__no__zero__divisors(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Rings_Oring__no__zero__divisors(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Groups_Ocancel__semigroup__add(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Groups_Oab__semigroup__mult(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Groups_Ocomm__monoid__mult(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Groups_Oab__semigroup__add(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Rings_Ono__zero__divisors(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Groups_Ocomm__monoid__add(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Rings_Ocomm__semiring__1(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Rings_Ocomm__semiring__0(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Rings_Ocomm__semiring(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Groups_Oab__group__add(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Rings_Ozero__ne_q__one(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Groups_Omonoid__mult(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Rings_Ocomm__ring__1(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Groups_Omonoid__add(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Rings_Osemiring__0(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Groups_Ogroup__add(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Rings_Omult__zero(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Rings_Ocomm__ring(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Rings_Osemiring(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Groups_Ouminus(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Rings_Oring__1(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Groups_Ominus(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Power_Opower(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Groups_Ozero(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Rings_Oring(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Groups_Oone(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Rings_Odvd(T).
% 15.82/15.69  0 [] -class_Rings_Oidom(T)|class_Groups_Ocancel__comm__monoid__add(T).
% 15.82/15.69  0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint).
% 15.82/15.69  0 [] -class_Lattices_Oboolean__algebra(T_1)|class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)).
% 15.82/15.69  0 [] -class_Orderings_Opreorder(T_1)|class_Orderings_Opreorder(tc_fun(T_2,T_1)).
% 15.82/15.69  0 [] -class_Orderings_Oorder(T_1)|class_Orderings_Oorder(tc_fun(T_2,T_1)).
% 15.82/15.69  0 [] -class_Orderings_Oord(T_1)|class_Orderings_Oord(tc_fun(T_2,T_1)).
% 15.82/15.69  0 [] -class_Groups_Ouminus(T_1)|class_Groups_Ouminus(tc_fun(T_2,T_1)).
% 15.82/15.69  0 [] -class_Groups_Ominus(T_1)|class_Groups_Ominus(tc_fun(T_2,T_1)).
% 15.82/15.69  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Oordered__cancel__semiring(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Oordered__comm__semiring(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Olinordered__semiring__1(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Olinordered__semiring(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Olinordered__semidom(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Oordered__semiring(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Olinordered__ring(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Olinordered__idom(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Ocomm__semiring__0(tc_Int_Oint).
% 15.82/15.69  0 [] class_Divides_Osemiring__div(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Ocomm__semiring(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Oab__group__add(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Oordered__ring(tc_Int_Oint).
% 15.82/15.69  0 [] class_Orderings_Opreorder(tc_Int_Oint).
% 15.82/15.69  0 [] class_Orderings_Olinorder(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Omonoid__mult(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Omonoid__add(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Osemiring__0(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Ogroup__add(tc_Int_Oint).
% 15.82/15.69  0 [] class_Divides_Oring__div(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Omult__zero(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Ocomm__ring(tc_Int_Oint).
% 15.82/15.69  0 [] class_Orderings_Oorder(tc_Int_Oint).
% 15.82/15.69  0 [] class_Int_Oring__char__0(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Osemiring(tc_Int_Oint).
% 15.82/15.69  0 [] class_Orderings_Oord(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Ouminus(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Osgn__if(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Oring__1(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Ominus(tc_Int_Oint).
% 15.82/15.69  0 [] class_Power_Opower(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Ozero(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Oring(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Oidom(tc_Int_Oint).
% 15.82/15.69  0 [] class_Groups_Oone(tc_Int_Oint).
% 15.82/15.69  0 [] class_Rings_Odvd(tc_Int_Oint).
% 15.82/15.69  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Rings_Oordered__semiring(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Rings_Ocomm__semiring__0(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Divides_Osemiring__div(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Orderings_Owellorder(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Orderings_Opreorder(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Orderings_Olinorder(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Groups_Omonoid__mult(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Groups_Omonoid__add(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Rings_Osemiring__0(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Rings_Omult__zero(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Orderings_Oorder(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Rings_Osemiring(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Orderings_Oord(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Groups_Ominus(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Power_Opower(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Groups_Ozero(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Groups_Oone(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Rings_Odvd(tc_Nat_Onat).
% 15.82/15.69  0 [] class_Lattices_Oboolean__algebra(tc_HOL_Obool).
% 15.82/15.69  0 [] class_Orderings_Opreorder(tc_HOL_Obool).
% 15.82/15.69  0 [] class_Orderings_Oorder(tc_HOL_Obool).
% 15.82/15.69  0 [] class_Orderings_Oord(tc_HOL_Obool).
% 15.82/15.69  0 [] class_Groups_Ouminus(tc_HOL_Obool).
% 15.82/15.69  0 [] class_Groups_Ominus(tc_HOL_Obool).
% 15.82/15.69  0 [] -class_Rings_Oidom(T_1)|class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Oidom(T_1)|class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Oidom(T_1)|class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Oidom(T_1)|class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Fields_Ofield(T_1)|class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Fields_Ofield(T_1)|class_Divides_Oring__div(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Oord(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ominus(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Power_Opower(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Groups_Ozero(T_1)|class_Groups_Ozero(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Oring(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Oidom(T_1)|class_Rings_Oidom(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Oone(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Odvd(tc_Polynomial_Opoly(T_1)).
% 15.82/15.69  0 [] hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q)=V_P.
% 15.82/15.69  0 [] hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_P_2),V_Q_2),V_R_2)=hAPP(V_P_2,hAPP(V_Q_2,V_R_2)).
% 15.82/15.69  0 [] hAPP(hAPP(c_COMBC(T_c,T_d,T_b,V_P_2),V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),V_Q_2).
% 15.82/15.69  0 [] hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)).
% 15.82/15.69  0 [] -hBOOL(c_fe_qual(V_x_2,V_y_2))|V_x_2=V_y_2.
% 15.82/15.69  0 [] V_x_2!=V_y_2|hBOOL(c_fe_qual(V_x_2,V_y_2)).
% 15.82/15.69  0 [] -hBOOL(hAPP(c_fNot,V_P_2))| -hBOOL(V_P_2).
% 15.82/15.69  0 [] hBOOL(V_P_2)|hBOOL(hAPP(c_fNot,V_P_2)).
% 15.82/15.69  0 [] -hBOOL(V_P_2)| -hBOOL(V_Q_2)|hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)).
% 15.82/15.69  0 [] -hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))|hBOOL(V_P_2).
% 15.82/15.69  0 [] -hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))|hBOOL(V_Q_2).
% 15.82/15.69  0 [] v_a!=c_Groups_Ozero__class_Ozero(t_a).
% 15.82/15.69  0 [] hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,v_q)),v_k))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,v_cs____).
% 15.82/15.69  0 [] 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),v_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),B_z),hAPP(c_Polynomial_Opoly(t_a,v_q),B_z)))).
% 15.82/15.69  0 [] B_a=c_Groups_Ozero__class_Ozero(t_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,B_q)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))!=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),$f28(B_a,B_q)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),$f28(B_a,B_q)),v_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),v_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),$f28(B_a,B_q)),hAPP(c_Polynomial_Opoly(t_a,v_q),$f28(B_a,B_q))))))!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),$f28(B_a,B_q)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),$f28(B_a,B_q)),hAPP(c_Polynomial_Opoly(t_a,B_q),$f28(B_a,B_q))))).
% 15.82/15.69  0 [] class_Rings_Oidom(t_a).
% 15.82/15.69  end_of_list.
% 15.82/15.69  
% 15.82/15.69  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 15.82/15.69  
% 15.82/15.69  This ia a non-Horn set with equality.  The strategy will be
% 15.82/15.69  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 15.82/15.69  deletion, with positive clauses in sos and nonpositive
% 15.82/15.69  clauses in usable.
% 15.82/15.69  
% 15.82/15.69     dependent: set(knuth_bendix).
% 15.82/15.69     dependent: set(anl_eq).
% 15.82/15.69     dependent: set(para_from).
% 15.82/15.69     dependent: set(para_into).
% 15.82/15.69     dependent: clear(para_from_right).
% 15.82/15.69     dependent: clear(para_into_right).
% 15.82/15.69     dependent: set(para_from_vars).
% 15.82/15.69     dependent: set(eq_units_both_ways).
% 15.82/15.69     dependent: set(dynamic_demod_all).
% 15.82/15.69     dependent: set(dynamic_demod).
% 15.82/15.69     dependent: set(order_eq).
% 15.82/15.69     dependent: set(back_demod).
% 15.82/15.69     dependent: set(lrpo).
% 15.82/15.69     dependent: set(hyper_res).
% 15.82/15.69     dependent: set(unit_deletion).
% 15.82/15.69     dependent: set(factor).
% 15.82/15.69  
% 15.82/15.69  ------------> process usable:
% 15.82/15.69  ** KEPT (pick-wt=14): 1 [] hAPP(A,$f1(B,A))!=hAPP(B,$f1(B,A))|A=B.
% 15.82/15.69  ** KEPT (pick-wt=8): 2 [] -class_Rings_Oidom(t_a)| -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_p)).
% 15.82/15.69  ** KEPT (pick-wt=6): 4 [copy,3,flip.2] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=$c1.
% 15.82/15.69  ** KEPT (pick-wt=10): 6 [copy,5,flip.2] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=hAPP(c_Polynomial_Opoly(t_a,v_cs____),$c1).
% 15.82/15.69  ** KEPT (pick-wt=6): 8 [copy,7,flip.2] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=$c2.
% 15.82/15.69  ** KEPT (pick-wt=10): 10 [copy,9,flip.2] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=hAPP(c_Polynomial_Opoly(t_a,v_cs____),$c2).
% 15.82/15.69  ** KEPT (pick-wt=16): 11 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),hAPP(c_Nat_OSuc,B))).
% 15.82/15.69  ** KEPT (pick-wt=7): 12 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.82/15.69  ** KEPT (pick-wt=28): 13 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))).
% 15.82/15.69  ** KEPT (pick-wt=38): 14 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),c_Groups_Oone__class_Oone(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B))).
% 15.82/15.69  ** KEPT (pick-wt=30): 15 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Oone__class_Oone(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C))),c_Groups_Oone__class_Oone(A))).
% 15.82/15.69  ** KEPT (pick-wt=37): 16 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Oone__class_Oone(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))).
% 15.82/15.69  ** KEPT (pick-wt=28): 17 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,hAPP(hAPP(c_Polynomial_OpCons(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),hAPP(c_Polynomial_Opoly(A,C),D))).
% 15.82/15.69  ** KEPT (pick-wt=31): 18 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)).
% 15.82/15.69  ** KEPT (pick-wt=31): 19 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)).
% 15.82/15.69  ** KEPT (pick-wt=20): 20 [] 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).
% 15.82/15.69  ** KEPT (pick-wt=16): 21 [] 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.
% 15.82/15.69  ** KEPT (pick-wt=17): 22 [] 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).
% 15.82/15.69  ** KEPT (pick-wt=20): 23 [] 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).
% 15.82/15.69  ** KEPT (pick-wt=16): 24 [] 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.
% 15.82/15.69  ** KEPT (pick-wt=17): 25 [] 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).
% 15.82/15.69  ** KEPT (pick-wt=17): 26 [] 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).
% 15.82/15.69  ** KEPT (pick-wt=13): 27 [] 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).
% 15.82/15.69  ** KEPT (pick-wt=13): 28 [] 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).
% 15.82/15.69  ** KEPT (pick-wt=25): 30 [copy,29,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)).
% 15.82/15.69  ** KEPT (pick-wt=20): 31 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),C)|B=C.
% 15.82/15.69    Following clause subsumed by 24 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),C)|B!=C.
% 15.82/15.69  ** KEPT (pick-wt=13): 32 [] 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).
% 15.82/15.69  ** KEPT (pick-wt=13): 33 [] 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).
% 15.82/15.69  ** KEPT (pick-wt=17): 34 [] 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).
% 15.82/15.69    Following clause subsumed by 32 during input processing: 0 [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).
% 15.82/15.69    Following clause subsumed by 33 during input processing: 0 [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).
% 15.82/15.69    Following clause subsumed by 34 during input processing: 0 [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).
% 15.82/15.69  ** KEPT (pick-wt=18): 35 [] -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)).
% 15.82/15.69  ** KEPT (pick-wt=18): 36 [] -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)).
% 15.82/15.69  ** KEPT (pick-wt=11): 37 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(A,B,C)|hAPP(C,D)=hAPP(C,E).
% 15.82/15.69  ** KEPT (pick-wt=17): 38 [] c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(A,B,C)|hAPP(C,$f3(C,B,A))!=hAPP(C,$f2(C,B,A)).
% 15.82/15.69  ** KEPT (pick-wt=21): 39 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.69  ** KEPT (pick-wt=15): 40 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.69  ** KEPT (pick-wt=17): 41 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.69  ** KEPT (pick-wt=29): 42 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 15.82/15.69  ** KEPT (pick-wt=23): 43 [] -hBOOL(hAPP(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),A),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.69  ** KEPT (pick-wt=19): 44 [] hBOOL(hAPP(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),A),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 15.82/15.69  ** KEPT (pick-wt=16): 45 [] hBOOL(hAPP(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),A),B)))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.69  ** KEPT (pick-wt=17): 46 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.69  ** KEPT (pick-wt=17): 47 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.69  ** KEPT (pick-wt=23): 48 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.69  ** KEPT (pick-wt=29): 49 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))).
% 15.82/15.69  ** KEPT (pick-wt=29): 50 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C))).
% 15.82/15.69  ** KEPT (pick-wt=23): 51 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)).
% 15.82/15.69  ** KEPT (pick-wt=22): 52 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),C)).
% 15.82/15.69    Following clause subsumed by 50 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),C)).
% 15.82/15.69  ** KEPT (pick-wt=23): 53 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 15.82/15.69  ** KEPT (pick-wt=22): 54 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 15.82/15.69    Following clause subsumed by 49 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 15.82/15.69  ** KEPT (pick-wt=19): 55 [] -hBOOL(hAPP(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),A),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 15.82/15.69  ** KEPT (pick-wt=19): 56 [] -hBOOL(hAPP(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),A),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)).
% 15.82/15.69  ** KEPT (pick-wt=26): 57 [] hBOOL(hAPP(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),A),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)).
% 15.82/15.69    Following clause subsumed by 54 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 15.82/15.69  ** KEPT (pick-wt=26): 58 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 15.82/15.69  ** KEPT (pick-wt=16): 60 [copy,59,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).
% 15.82/15.69  ** KEPT (pick-wt=15): 62 [copy,61,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(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)).
% 15.82/15.69  ** KEPT (pick-wt=32): 63 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A))).
% 15.82/15.69  ** KEPT (pick-wt=29): 64 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))).
% 15.82/15.69  ** KEPT (pick-wt=29): 65 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A))).
% 15.82/15.69  ** KEPT (pick-wt=13): 66 [] -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)).
% 15.82/15.69  ** KEPT (pick-wt=13): 67 [] -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)).
% 15.82/15.69  ** KEPT (pick-wt=10): 68 [] hAPP(c_Nat_OSuc,A)!=hAPP(c_Nat_OSuc,B)|A=B.
% 15.82/15.69    Following clause subsumed by 68 during input processing: 0 [] hAPP(c_Nat_OSuc,A)!=hAPP(c_Nat_OSuc,B)|A=B.
% 15.82/15.69  ** KEPT (pick-wt=10): 69 [] hAPP(c_Nat_OSuc,A)=hAPP(c_Nat_OSuc,B)|A!=B.
% 15.82/15.69  ** KEPT (pick-wt=5): 70 [] hAPP(c_Nat_OSuc,A)!=A.
% 15.82/15.69    Following clause subsumed by 70 during input processing: 0 [flip.1] hAPP(c_Nat_OSuc,A)!=A.
% 15.82/15.69  ** KEPT (pick-wt=9): 71 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|A!=B.
% 15.82/15.69  ** KEPT (pick-wt=9): 72 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|B!=A.
% 15.82/15.69  ** KEPT (pick-wt=6): 73 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),A)).
% 15.82/15.69    Following clause subsumed by 71 during input processing: 0 [] A!=B| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 15.82/15.69    Following clause subsumed by 72 during input processing: 0 [] A!=B| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),A)).
% 15.82/15.69    Following clause subsumed by 73 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),A)).
% 15.82/15.69  ** KEPT (pick-wt=16): 74 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)|A=C.
% 15.82/15.69  ** KEPT (pick-wt=16): 75 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)|A!=C.
% 15.82/15.69  ** KEPT (pick-wt=16): 76 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)|B=C.
% 15.82/15.69  ** KEPT (pick-wt=16): 77 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)|B!=C.
% 15.82/15.69  ** KEPT (pick-wt=18): 78 [] -class_Groups_Ozero(A)|hAPP(hAPP(c_Polynomial_OpCons(A),B),C)!=hAPP(hAPP(c_Polynomial_OpCons(A),D),E)|B=D.
% 15.82/15.69  ** KEPT (pick-wt=18): 79 [] -class_Groups_Ozero(A)|hAPP(hAPP(c_Polynomial_OpCons(A),B),C)!=hAPP(hAPP(c_Polynomial_OpCons(A),D),E)|C=E.
% 15.82/15.69  ** KEPT (pick-wt=21): 80 [] -class_Groups_Ozero(A)|hAPP(hAPP(c_Polynomial_OpCons(A),B),C)=hAPP(hAPP(c_Polynomial_OpCons(A),D),E)|B!=D|C!=E.
% 15.82/15.69  ** KEPT (pick-wt=14): 81 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)!=c_Polynomial_Opoly(A,C)|B=C.
% 15.82/15.69  ** KEPT (pick-wt=14): 82 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)=c_Polynomial_Opoly(A,C)|B!=C.
% 15.82/15.69  ** KEPT (pick-wt=15): 83 [] -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).
% 15.82/15.69  ** KEPT (pick-wt=30): 84 [] -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)).
% 15.82/15.69  ** KEPT (pick-wt=25): 85 [] -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)).
% 15.82/15.69  ** KEPT (pick-wt=12): 86 [] -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).
% 15.82/15.69  ** KEPT (pick-wt=6): 87 [] hAPP(c_Nat_OSuc,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.69  ** KEPT (pick-wt=6): 88 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,A).
% 15.82/15.69    Following clause subsumed by 87 during input processing: 0 [] hAPP(c_Nat_OSuc,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.69    Following clause subsumed by 87 during input processing: 0 [] hAPP(c_Nat_OSuc,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.69    Following clause subsumed by 88 during input processing: 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,A).
% 15.82/15.69    Following clause subsumed by 88 during input processing: 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,A).
% 15.82/15.69  ** KEPT (pick-wt=10): 89 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.69    Following clause subsumed by 12 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.82/15.69    Following clause subsumed by 89 during input processing: 0 [] A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 15.82/15.69    Following clause subsumed by 12 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.82/15.69  ** KEPT (pick-wt=16): 90 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),hAPP(c_Nat_OSuc,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 15.82/15.69  ** KEPT (pick-wt=14): 91 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 15.82/15.69  ** KEPT (pick-wt=17): 92 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|A=B.
% 15.82/15.69  ** KEPT (pick-wt=20): 93 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),C)).
% 15.82/15.69  ** KEPT (pick-wt=19): 94 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hAPP(c_Nat_OSuc,A)=B|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),B)).
% 15.82/15.69  ** KEPT (pick-wt=14): 95 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B))).
% 15.82/15.69  ** KEPT (pick-wt=17): 96 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|B=A.
% 15.82/15.69    Following clause subsumed by 92 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|A=B.
% 15.82/15.69  ** KEPT (pick-wt=17): 97 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|A!=B.
% 15.82/15.69    Following clause subsumed by 90 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),hAPP(c_Nat_OSuc,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 15.82/15.69    Following clause subsumed by 11 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),hAPP(c_Nat_OSuc,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 15.82/15.69    Following clause subsumed by 92 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|A=B.
% 15.82/15.69    Following clause subsumed by 95 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 15.82/15.69  ** KEPT (pick-wt=11): 98 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|A!=B.
% 15.82/15.69  ** KEPT (pick-wt=14): 99 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),hAPP(c_Nat_OSuc,A))).
% 15.82/15.69  ** KEPT (pick-wt=12): 100 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=A|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.69  ** KEPT (pick-wt=13): 101 [] hAPP(hAPP(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).
% 15.82/15.69  ** KEPT (pick-wt=13): 102 [] hAPP(hAPP(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).
% 15.82/15.69  ** KEPT (pick-wt=17): 103 [] hAPP(hAPP(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).
% 15.82/15.69  ** KEPT (pick-wt=17): 104 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),C)).
% 15.82/15.69  ** KEPT (pick-wt=25): 105 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),D)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)).
% 15.82/15.69  ** KEPT (pick-wt=28): 106 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D))).
% 15.82/15.69  ** KEPT (pick-wt=22): 107 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C))).
% 15.82/15.69  ** KEPT (pick-wt=17): 108 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))).
% 15.82/15.69  ** KEPT (pick-wt=17): 109 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C))).
% 15.82/15.69  ** KEPT (pick-wt=22): 110 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 15.82/15.69  ** KEPT (pick-wt=22): 111 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 15.82/15.69  ** KEPT (pick-wt=11): 112 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),B)).
% 15.82/15.69  ** KEPT (pick-wt=11): 113 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),A)).
% 15.82/15.69  ** KEPT (pick-wt=11): 114 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat))=B.
% 15.82/15.69  ** KEPT (pick-wt=16): 115 [] -class_Groups_Ozero(A)|hAPP(hAPP(c_Polynomial_OpCons(A),B),C)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.69  ** KEPT (pick-wt=17): 116 [] -class_Groups_Ozero(A)|hAPP(hAPP(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)).
% 15.82/15.69  ** KEPT (pick-wt=21): 117 [] -class_Groups_Ozero(A)|hAPP(hAPP(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)).
% 15.82/15.69  ** KEPT (pick-wt=15): 118 [] -class_Groups_Ozero(A)|hAPP(hAPP(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)).
% 15.82/15.69  ** KEPT (pick-wt=37): 119 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),B),C)),hAPP(hAPP(c_Polynomial_OpCons(A),D),E))=hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),E)).
% 15.82/15.69  ** KEPT (pick-wt=12): 120 [] -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).
% 15.82/15.69  ** KEPT (pick-wt=28): 121 [] -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)).
% 15.82/15.69  ** KEPT (pick-wt=28): 122 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Polynomial_Opoly(A,B),D)),hAPP(c_Polynomial_Opoly(A,C),D)).
% 15.82/15.69  ** KEPT (pick-wt=12): 123 [] -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).
% 15.82/15.69  ** KEPT (pick-wt=24): 124 [] -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).
% 15.82/15.69  ** KEPT (pick-wt=21): 125 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))).
% 15.82/15.69  ** KEPT (pick-wt=21): 126 [] -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).
% 15.82/15.69  ** KEPT (pick-wt=21): 127 [] -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).
% 15.82/15.69  ** KEPT (pick-wt=25): 128 [] -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).
% 15.82/15.69  ** KEPT (pick-wt=25): 129 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)|C=D.
% 15.82/15.69  ** KEPT (pick-wt=25): 130 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)|C!=D.
% 15.82/15.69  ** KEPT (pick-wt=16): 131 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Nat_OSuc,B))=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.69  ** KEPT (pick-wt=22): 133 [copy,132,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)),B)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)).
% 15.82/15.69  ** KEPT (pick-wt=22): 134 [] -class_Power_Opower(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 15.82/15.69  ** KEPT (pick-wt=12): 135 [] -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).
% 15.82/15.69  ** KEPT (pick-wt=30): 137 [copy,136,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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)).
% 15.82/15.69  ** KEPT (pick-wt=19): 139 [copy,138,flip.3] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_OSuc,$f4(B,A))=A.
% 15.82/15.69  ** KEPT (pick-wt=20): 140 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f4(B,A)),B)).
% 15.82/15.69  ** KEPT (pick-wt=12): 141 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.69  ** KEPT (pick-wt=19): 142 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|A!=hAPP(c_Nat_OSuc,C)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),B)).
% 15.82/15.69  ** KEPT (pick-wt=13): 143 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.69    Following clause subsumed by 141 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.69  ** KEPT (pick-wt=13): 145 [copy,144,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hAPP(c_Nat_OSuc,$f5(A))=A.
% 15.82/15.69  ** KEPT (pick-wt=12): 146 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|A!=hAPP(c_Nat_OSuc,B).
% 15.82/15.69  ** KEPT (pick-wt=21): 147 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.69  ** KEPT (pick-wt=23): 148 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.69  ** KEPT (pick-wt=19): 149 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=hAPP(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).
% 15.82/15.69  ** KEPT (pick-wt=21): 150 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.69  ** KEPT (pick-wt=21): 151 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.69  ** KEPT (pick-wt=21): 152 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.69  ** KEPT (pick-wt=21): 153 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)|A=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.69  ** KEPT (pick-wt=23): 154 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)|A=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.69  ** KEPT (pick-wt=19): 155 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(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).
% 15.82/15.69  ** KEPT (pick-wt=21): 156 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.69  ** KEPT (pick-wt=21): 157 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)|A!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.69  ** KEPT (pick-wt=21): 158 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.69  ** KEPT (pick-wt=26): 159 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)).
% 15.82/15.69    Following clause subsumed by 109 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 15.82/15.69    Following clause subsumed by 108 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)).
% 15.82/15.69  ** KEPT (pick-wt=18): 161 [copy,160,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),$f6(B,A)))=B.
% 15.82/15.69  ** KEPT (pick-wt=16): 162 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|B!=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)).
% 15.82/15.69  ** KEPT (pick-wt=30): 163 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)))).
% 15.82/15.69  ** KEPT (pick-wt=26): 164 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)))).
% 15.82/15.69  ** KEPT (pick-wt=18): 165 [] -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).
% 15.82/15.69  ** KEPT (pick-wt=18): 166 [] -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).
% 15.82/15.69  ** KEPT (pick-wt=23): 167 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)))).
% 15.82/15.69    Following clause subsumed by 19 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))).
% 15.82/15.69    Following clause subsumed by 18 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)).
% 15.82/15.69  ** KEPT (pick-wt=16): 168 [] -class_Rings_Olinordered__semidom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),c_Groups_Oone__class_Oone(A)))).
% 15.82/15.69  ** KEPT (pick-wt=32): 169 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(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))))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.69  ** KEPT (pick-wt=28): 170 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(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))))|B=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.69  ** KEPT (pick-wt=28): 171 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(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=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.69  ** KEPT (pick-wt=24): 172 [] -class_Rings_Olinordered__ring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(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))).
% 15.82/15.69  ** KEPT (pick-wt=13): 173 [] -class_Rings_Oidom(t_a)| -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____))).
% 15.82/15.69  ** KEPT (pick-wt=21): 174 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.82/15.69  ** KEPT (pick-wt=30): 175 [] -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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)).
% 15.82/15.69  ** KEPT (pick-wt=12): 176 [] -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).
% 15.82/15.69  ** KEPT (pick-wt=22): 177 [] -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),hAPP(c_Nat_OSuc,C)).
% 15.82/15.69  ** KEPT (pick-wt=22): 179 [copy,178,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 15.82/15.69    Following clause subsumed by 179 during input processing: 0 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 15.82/15.69  ** KEPT (pick-wt=15): 180 [] -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)).
% 15.82/15.69  ** KEPT (pick-wt=13): 181 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)=B.
% 15.82/15.69  ** KEPT (pick-wt=15): 182 [] -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)).
% 15.82/15.69  ** KEPT (pick-wt=13): 183 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=B.
% 15.82/15.69  ** KEPT (pick-wt=35): 184 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),D)=hAPP(hAPP(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)).
% 15.82/15.69  ** KEPT (pick-wt=17): 185 [] -class_Rings_Olinordered__idom(A)|B=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.69  ** KEPT (pick-wt=15): 186 [] -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).
% 15.82/15.69  ** KEPT (pick-wt=25): 187 [] -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)).
% 15.82/15.69  ** KEPT (pick-wt=25): 189 [copy,188,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)).
% 15.82/15.69    Following clause subsumed by 189 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)).
% 15.82/15.69  ** KEPT (pick-wt=25): 190 [] -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).
% 15.82/15.69    Following clause subsumed by 189 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))).
% 15.82/15.70    Following clause subsumed by 187 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)).
% 15.82/15.70  ** KEPT (pick-wt=35): 191 [] -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)).
% 15.82/15.70  ** KEPT (pick-wt=15): 192 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),B).
% 15.82/15.70  ** KEPT (pick-wt=25): 193 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)).
% 15.82/15.70  ** KEPT (pick-wt=25): 195 [copy,194,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 15.82/15.70    Following clause subsumed by 195 during input processing: 0 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 15.82/15.70  ** KEPT (pick-wt=25): 196 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),C).
% 15.82/15.70  ** KEPT (pick-wt=35): 197 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E)).
% 15.82/15.70  ** KEPT (pick-wt=25): 198 [] -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)).
% 15.82/15.70  ** KEPT (pick-wt=12): 199 [] -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).
% 15.82/15.70  ** KEPT (pick-wt=12): 200 [] -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).
% 15.82/15.70  ** KEPT (pick-wt=12): 201 [] -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).
% 15.82/15.70  ** KEPT (pick-wt=12): 202 [] -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).
% 15.82/15.70  ** KEPT (pick-wt=19): 203 [] -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).
% 15.82/15.70  ** KEPT (pick-wt=15): 204 [] -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).
% 15.82/15.70  ** KEPT (pick-wt=15): 205 [] -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).
% 15.82/15.70  ** KEPT (pick-wt=19): 206 [] -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).
% 15.82/15.70    Following clause subsumed by 206 during input processing: 0 [] -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).
% 15.82/15.70  ** KEPT (pick-wt=11): 207 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B)=B.
% 15.82/15.70  ** KEPT (pick-wt=11): 208 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A))=B.
% 15.82/15.70  ** KEPT (pick-wt=14): 210 [copy,209,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=B|C=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.70  ** KEPT (pick-wt=14): 212 [copy,211,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=B|C!=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.70  ** KEPT (pick-wt=7): 214 [copy,213,flip.2] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 15.82/15.70    Following clause subsumed by 214 during input processing: 0 [] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 15.82/15.70  ** KEPT (pick-wt=30): 216 [copy,215,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(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))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 15.82/15.70  ** KEPT (pick-wt=41): 217 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B=C|D=E|hAPP(hAPP(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))!=hAPP(hAPP(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)).
% 15.82/15.70  ** KEPT (pick-wt=38): 218 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B!=C|hAPP(hAPP(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))=hAPP(hAPP(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)).
% 15.82/15.70  ** KEPT (pick-wt=38): 219 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B!=C|hAPP(hAPP(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))=hAPP(hAPP(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)).
% 15.82/15.70  ** KEPT (pick-wt=30): 220 [] -class_Rings_Ocomm__semiring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(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)).
% 15.82/15.70  ** KEPT (pick-wt=30): 221 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(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)).
% 15.82/15.70  ** KEPT (pick-wt=30): 222 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(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))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),C).
% 15.82/15.70  ** KEPT (pick-wt=40): 224 [copy,223,flip.2] -class_Rings_Osemiring(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)),E)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),E)).
% 15.82/15.70    Following clause subsumed by 217 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(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))!=hAPP(hAPP(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.
% 15.82/15.70    Following clause subsumed by 218 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(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))=hAPP(hAPP(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.
% 15.82/15.70    Following clause subsumed by 219 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(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))=hAPP(hAPP(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.
% 15.82/15.70  ** KEPT (pick-wt=11): 225 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 15.82/15.70  ** KEPT (pick-wt=11): 226 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 15.82/15.70  ** KEPT (pick-wt=30): 227 [] -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)).
% 15.82/15.70    Following clause subsumed by 43 during input processing: 0 [] -hBOOL(hAPP(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),A),B)))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 15.82/15.70    Following clause subsumed by 45 during input processing: 0 [] hBOOL(hAPP(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),A),B)))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.70    Following clause subsumed by 44 during input processing: 0 [] hBOOL(hAPP(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),A),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 15.82/15.70  ** KEPT (pick-wt=11): 228 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat))=B.
% 15.82/15.70  ** KEPT (pick-wt=14): 229 [] -class_Rings_Olinordered__ring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.70  ** KEPT (pick-wt=32): 230 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.70  ** KEPT (pick-wt=31): 231 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),B)).
% 15.82/15.70  ** KEPT (pick-wt=31): 232 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.70  ** KEPT (pick-wt=30): 233 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),B)).
% 15.82/15.70  ** KEPT (pick-wt=31): 234 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 15.82/15.70  ** KEPT (pick-wt=31): 235 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),B)).
% 15.82/15.70  ** KEPT (pick-wt=32): 236 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.70  ** KEPT (pick-wt=31): 237 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 15.82/15.70  ** KEPT (pick-wt=31): 238 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.70  ** KEPT (pick-wt=30): 239 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 15.82/15.70  ** KEPT (pick-wt=31): 240 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 15.82/15.70  ** KEPT (pick-wt=31): 241 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 15.82/15.70  ** KEPT (pick-wt=31): 242 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 15.82/15.70    Following clause subsumed by 240 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 15.82/15.70  ** KEPT (pick-wt=28): 243 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))).
% 15.82/15.70  ** KEPT (pick-wt=28): 244 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.70  ** KEPT (pick-wt=28): 245 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.70  ** KEPT (pick-wt=28): 246 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C)).
% 15.82/15.70  ** KEPT (pick-wt=28): 247 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 15.82/15.70  ** KEPT (pick-wt=31): 248 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 15.82/15.70    Following clause subsumed by 241 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 15.82/15.70    Following clause subsumed by 245 during input processing: 0 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.70  ** KEPT (pick-wt=28): 249 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))).
% 15.82/15.70  ** KEPT (pick-wt=31): 250 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))).
% 15.82/15.70  ** KEPT (pick-wt=31): 251 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))).
% 15.82/15.70  ** KEPT (pick-wt=31): 252 [] -class_Rings_Olinordered__comm__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))).
% 15.82/15.70    Following clause subsumed by 235 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))).
% 15.82/15.70    Following clause subsumed by 241 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B))).
% 15.82/15.70  ** KEPT (pick-wt=26): 253 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))).
% 15.82/15.70  ** KEPT (pick-wt=25): 254 [] -class_Rings_Olinordered__ring__strict(A)|hAPP(hAPP(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).
% 15.82/15.70  ** KEPT (pick-wt=25): 255 [] -class_Rings_Olinordered__ring__strict(A)|hAPP(hAPP(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).
% 15.82/15.70  ** KEPT (pick-wt=29): 256 [] -class_Rings_Olinordered__ring__strict(A)|hAPP(hAPP(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).
% 15.82/15.70  ** KEPT (pick-wt=35): 257 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B=c_Groups_Ozero__class_Ozero(A)|C!=D|E=F|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),F)).
% 15.82/15.70  ** KEPT (pick-wt=10): 258 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.70  ** KEPT (pick-wt=10): 259 [] -class_Rings_Olinordered__semidom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Oone__class_Oone(A))).
% 15.82/15.70  ** KEPT (pick-wt=28): 260 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))).
% 15.82/15.70  ** KEPT (pick-wt=14): 261 [] -class_Rings_Olinordered__semidom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Oone__class_Oone(A)))).
% 15.82/15.70  ** KEPT (pick-wt=22): 262 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),c_Groups_Oone__class_Oone(A))),B).
% 15.82/15.70  ** KEPT (pick-wt=26): 263 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),c_Groups_Oone__class_Oone(A))),B).
% 15.82/15.70  ** KEPT (pick-wt=26): 264 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),C)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Oone__class_Oone(A))),C).
% 15.82/15.70  ** KEPT (pick-wt=12): 266 [copy,265,flip.3] -class_Rings_Oidom(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))|c_Groups_Ozero__class_Ozero(t_a)!=$c4.
% 15.82/15.70  ** KEPT (pick-wt=12): 268 [copy,267,flip.3] -class_Rings_Oidom(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=$c5.
% 15.82/15.70  ** KEPT (pick-wt=26): 269 [] -class_Rings_Oidom(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,$c3)),$c5)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,v_cs____).
% 15.82/15.70  ** KEPT (pick-wt=44): 271 [copy,270,flip.3] -class_Rings_Oidom(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(t_a,v_cs____),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),A),$c5)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),$c4),$c3)),A)))=hAPP(c_Polynomial_Opoly(t_a,v_cs____),A).
% 15.82/15.70  ** KEPT (pick-wt=23): 272 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|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.
% 15.82/15.70    Following clause subsumed by 24 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|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.
% 15.82/15.70    Following clause subsumed by 54 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 15.82/15.70    Following clause subsumed by 49 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 15.82/15.70  ** KEPT (pick-wt=35): 274 [copy,273,flip.2] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(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)),C),c_Polynomial_Opcompose(A,D,C)))=c_Polynomial_Opcompose(A,hAPP(hAPP(c_Polynomial_OpCons(A),B),D),C).
% 15.82/15.70  ** KEPT (pick-wt=21): 275 [] -class_Groups_Olinordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 15.82/15.70  ** KEPT (pick-wt=21): 276 [] -class_Groups_Olinordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 15.82/15.70  ** KEPT (pick-wt=21): 277 [] -class_Rings_Olinordered__idom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.70  ** KEPT (pick-wt=21): 278 [] -class_Rings_Olinordered__idom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.70  ** KEPT (pick-wt=21): 279 [] -class_Groups_Olinordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.70  ** KEPT (pick-wt=21): 280 [] -class_Groups_Olinordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.70  ** KEPT (pick-wt=28): 281 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))).
% 15.82/15.70  ** KEPT (pick-wt=12): 282 [] -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)).
% 15.82/15.70  ** KEPT (pick-wt=20): 283 [] -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)).
% 15.82/15.70  ** KEPT (pick-wt=10): 284 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.70  ** KEPT (pick-wt=10): 285 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.70  ** KEPT (pick-wt=25): 286 [] -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)).
% 15.82/15.70  ** KEPT (pick-wt=18): 287 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)|B=D.
% 15.82/15.70  ** KEPT (pick-wt=18): 288 [] -class_Groups_Ocancel__ab__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)|C=D.
% 15.82/15.70  ** KEPT (pick-wt=18): 289 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)|C=D.
% 15.82/15.70    Following clause subsumed by 287 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)|B=D.
% 15.82/15.70  ** KEPT (pick-wt=18): 290 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)|B!=D.
% 15.82/15.70    Following clause subsumed by 289 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)|C=D.
% 15.82/15.70  ** KEPT (pick-wt=18): 291 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)|C!=D.
% 15.82/15.70  ** KEPT (pick-wt=25): 292 [] -class_Groups_Oab__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 15.82/15.70  ** KEPT (pick-wt=10): 293 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)!=B|B=c_Groups_Oone__class_Oone(A).
% 15.82/15.70  ** KEPT (pick-wt=10): 294 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)=B|B!=c_Groups_Oone__class_Oone(A).
% 15.82/15.70  ** KEPT (pick-wt=15): 295 [] -class_Groups_Olinordered__ab__group__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.70  ** KEPT (pick-wt=15): 296 [] -class_Groups_Olinordered__ab__group__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.70  ** KEPT (pick-wt=11): 297 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A))=B.
% 15.82/15.70  ** KEPT (pick-wt=11): 298 [] -class_Groups_Omonoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A))=B.
% 15.82/15.70  ** KEPT (pick-wt=15): 299 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)|B=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.70  ** KEPT (pick-wt=15): 300 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)|B!=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.70  ** KEPT (pick-wt=11): 301 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B)=B.
% 15.82/15.70  ** KEPT (pick-wt=11): 302 [] -class_Groups_Omonoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B)=B.
% 15.82/15.70  ** KEPT (pick-wt=24): 303 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 15.82/15.70  ** KEPT (pick-wt=24): 304 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 15.82/15.70  ** KEPT (pick-wt=30): 305 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E))).
% 15.82/15.70  ** KEPT (pick-wt=24): 306 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))).
% 15.82/15.70  ** KEPT (pick-wt=24): 307 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D))).
% 15.82/15.70    Following clause subsumed by 303 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 15.82/15.70  ** KEPT (pick-wt=24): 308 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 15.82/15.70    Following clause subsumed by 304 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 15.82/15.70  ** KEPT (pick-wt=24): 309 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 15.82/15.70  ** KEPT (pick-wt=11): 310 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 15.82/15.70  ** KEPT (pick-wt=11): 311 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 15.82/15.70  ** KEPT (pick-wt=11): 312 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 15.82/15.70  ** KEPT (pick-wt=11): 313 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 15.82/15.70    Following clause subsumed by 23 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.
% 15.82/15.70    Following clause subsumed by 25 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).
% 15.82/15.70    Following clause subsumed by 24 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.
% 15.82/15.70  ** KEPT (pick-wt=28): 314 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.70  ** KEPT (pick-wt=111): 315 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Opcompose(A,B,C)=c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(A),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_Polynomial_Opoly(A),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A))),A),c_COMBK(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A))),hAPP(c_COMBC(A,tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A))),A),c_COMBB(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(A),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A))),hAPP(c_COMBC(A,tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))))),hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C))),B).
% 15.82/15.70  ** KEPT (pick-wt=22): 316 [] -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).
% 15.82/15.70  ** KEPT (pick-wt=15): 317 [] -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)).
% 15.82/15.70  ** KEPT (pick-wt=17): 318 [] -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).
% 15.82/15.70  ** KEPT (pick-wt=11): 319 [] -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)).
% 15.82/15.70  ** KEPT (pick-wt=6): 321 [copy,320,flip.2] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=$c7.
% 15.82/15.70  ** KEPT (pick-wt=16): 322 [] -class_Rings_Oidom(t_a)|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,$c6)),$c8))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,v_cs____).
% 15.82/15.70  ** KEPT (pick-wt=28): 324 [copy,323,flip.2] -class_Rings_Oidom(t_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),A),$c8)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),$c7),$c6)),A))=hAPP(c_Polynomial_Opoly(t_a,v_cs____),A).
% 15.82/15.70    Following clause subsumed by 108 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))).
% 15.82/15.70    Following clause subsumed by 109 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C))).
% 15.82/15.70  ** KEPT (pick-wt=18): 325 [] -class_Rings_Olinordered__idom(A)| -c_Polynomial_Opos__poly(A,hAPP(hAPP(c_Polynomial_OpCons(A),B),C))|c_Polynomial_Opos__poly(A,C)|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.82/15.70  ** KEPT (pick-wt=20): 326 [] -class_Rings_Olinordered__idom(A)| -c_Polynomial_Opos__poly(A,hAPP(hAPP(c_Polynomial_OpCons(A),B),C))|c_Polynomial_Opos__poly(A,C)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 15.82/15.70  ** KEPT (pick-wt=13): 327 [] -class_Rings_Olinordered__idom(A)|c_Polynomial_Opos__poly(A,hAPP(hAPP(c_Polynomial_OpCons(A),B),C))| -c_Polynomial_Opos__poly(A,C).
% 15.82/15.70  ** KEPT (pick-wt=22): 328 [] -class_Rings_Olinordered__idom(A)|c_Polynomial_Opos__poly(A,hAPP(hAPP(c_Polynomial_OpCons(A),B),C))|C!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 15.82/15.70  ** KEPT (pick-wt=20): 329 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|A=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.82/15.70  ** KEPT (pick-wt=20): 330 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|B=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.82/15.70  ** KEPT (pick-wt=24): 331 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)=c_Groups_Oone__class_Oone(tc_Int_Oint)|A!=c_Groups_Oone__class_Oone(tc_Int_Oint)|B!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.82/15.70  ** KEPT (pick-wt=29): 332 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))).
% 15.82/15.70  ** KEPT (pick-wt=7): 333 [] -class_Rings_Olinordered__idom(A)| -c_Polynomial_Opos__poly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).
% 15.82/15.70  ** KEPT (pick-wt=17): 334 [] -class_Rings_Olinordered__idom(A)| -c_Polynomial_Opos__poly(A,B)| -c_Polynomial_Opos__poly(A,C)|c_Polynomial_Opos__poly(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)).
% 15.82/15.70  ** KEPT (pick-wt=17): 335 [] -class_Rings_Olinordered__idom(A)| -c_Polynomial_Opos__poly(A,B)| -c_Polynomial_Opos__poly(A,C)|c_Polynomial_Opos__poly(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)).
% 15.82/15.70  ** KEPT (pick-wt=24): 336 [] -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.
% 15.82/15.70  ** KEPT (pick-wt=34): 337 [] -class_Groups_Ozero(A)|c_Polynomial_Opoly__rec(B,A,C,D,hAPP(hAPP(c_Polynomial_OpCons(A),E),F))=hAPP(hAPP(hAPP(D,E),F),c_If(B,c_fe_qual(F,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C,c_Polynomial_Opoly__rec(B,A,C,D,F))).
% 15.82/15.70  ** KEPT (pick-wt=38): 338 [] -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,hAPP(hAPP(c_Polynomial_OpCons(A),E),F))=hAPP(hAPP(hAPP(B,E),F),c_Polynomial_Opoly__rec(D,A,C,B,F)).
% 15.82/15.70  ** KEPT (pick-wt=112): 339 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)=c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(A),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_Polynomial_Opoly(A),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A))),A),c_COMBK(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A))),hAPP(c_COMBC(A,tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A))),A),c_COMBB(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(A),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A))),hAPP(c_COMBC(A,tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A)),C)))),hAPP(c_Polynomial_OpCons(A),c_Groups_Ozero__class_Ozero(A)))),B).
% 15.82/15.70  ** KEPT (pick-wt=30): 341 [copy,340,flip.2] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(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))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 15.82/15.70    Following clause subsumed by 341 during input processing: 0 [flip.2] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(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))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 15.82/15.70  ** KEPT (pick-wt=30): 342 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(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)).
% 15.82/15.70    Following clause subsumed by 342 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(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)).
% 15.82/15.70  ** KEPT (pick-wt=33): 343 [] -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)).
% 15.82/15.70  ** KEPT (pick-wt=21): 344 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(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).
% 15.82/15.70  ** KEPT (pick-wt=14): 345 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,B,C)!=c_Polynomial_Omonom(A,D,C)|B=D.
% 15.82/15.70  ** KEPT (pick-wt=14): 346 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,B,C)=c_Polynomial_Omonom(A,D,C)|B!=D.
% 15.82/15.70  ** KEPT (pick-wt=22): 347 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C))).
% 15.82/15.70  ** KEPT (pick-wt=25): 348 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.70  ** KEPT (pick-wt=25): 349 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.70  ** KEPT (pick-wt=21): 350 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))|A=B.
% 15.82/15.70  ** KEPT (pick-wt=18): 351 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint))))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)).
% 15.82/15.70  ** KEPT (pick-wt=15): 352 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint))))|A!=B.
% 15.82/15.70  ** KEPT (pick-wt=15): 353 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(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).
% 15.82/15.70  ** KEPT (pick-wt=5): 354 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.82/15.70  ** KEPT (pick-wt=25): 356 [copy,355,flip.2] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Polynomial_Osmult(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Polynomial_Osmult(A),B),hAPP(hAPP(c_Polynomial_Osmult(A),C),D)).
% 15.82/15.70  ** KEPT (pick-wt=11): 357 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Polynomial_Osmult(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 15.82/15.70  ** KEPT (pick-wt=14): 358 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Polynomial_Osmult(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.82/15.70  ** KEPT (pick-wt=32): 360 [copy,359,flip.2] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),hAPP(hAPP(c_Polynomial_Osmult(A),B),D))=hAPP(hAPP(c_Polynomial_Osmult(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),D)).
% 15.82/15.70  ** KEPT (pick-wt=27): 361 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),D)=hAPP(hAPP(c_Polynomial_Osmult(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)).
% 15.82/15.70  ** KEPT (pick-wt=27): 362 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Polynomial_Osmult(A),C),D))=hAPP(hAPP(c_Polynomial_Osmult(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)).
% 15.82/15.70  ** KEPT (pick-wt=21): 363 [] -class_Rings_Oidom(A)|hAPP(hAPP(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)).
% 15.82/15.70  ** KEPT (pick-wt=16): 364 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Polynomial_Osmult(A),B),C)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B!=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.70  ** KEPT (pick-wt=17): 365 [] -class_Rings_Oidom(A)|hAPP(hAPP(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)).
% 15.82/15.70  ** KEPT (pick-wt=13): 366 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Polynomial_Osmult(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.82/15.70  ** KEPT (pick-wt=30): 367 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Polynomial_Osmult(A),B),hAPP(hAPP(c_Polynomial_OpCons(A),C),D))=hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Polynomial_Osmult(A),B),D)).
% 15.82/15.70  ** KEPT (pick-wt=23): 368 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Polynomial_Opoly(A,C),D)).
% 15.82/15.70  ** KEPT (pick-wt=20): 369 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Polynomial_Osmult(A),B),C)!=hAPP(hAPP(c_Polynomial_OpCons(A),D),C)|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.82/15.70  ** KEPT (pick-wt=31): 370 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Polynomial_Osmult(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),D)),hAPP(hAPP(c_Polynomial_Osmult(A),C),D)).
% 15.82/15.70  ** KEPT (pick-wt=14): 371 [] -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).
% 15.82/15.70  ** KEPT (pick-wt=14): 372 [] -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).
% 15.82/15.70  ** KEPT (pick-wt=11): 373 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.82/15.70  ** KEPT (pick-wt=25): 374 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),C).
% 15.82/15.70  ** KEPT (pick-wt=28): 375 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),hAPP(hAPP(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)).
% 15.82/15.70  ** KEPT (pick-wt=19): 377 [copy,376,flip.2] -class_Groups_Ozero(A)|hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Ozero__class_Ozero(A)),c_Polynomial_Omonom(A,B,C))=c_Polynomial_Omonom(A,B,hAPP(c_Nat_OSuc,C)).
% 15.82/15.70  ** KEPT (pick-wt=22): 378 [] -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)).
% 15.82/15.70  ** KEPT (pick-wt=16): 380 [copy,379,flip.2] -class_Groups_Ozero(A)|hAPP(hAPP(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)).
% 15.82/15.70  ** KEPT (pick-wt=30): 381 [] -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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),E)).
% 15.82/15.70  ** KEPT (pick-wt=39): 382 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),D)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D))).
% 15.82/15.70  ** KEPT (pick-wt=39): 383 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Polynomial_OpCons(A),C),D))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),C),B)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D))).
% 15.82/15.70  ** KEPT (pick-wt=12): 384 [] -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).
% 15.82/15.70    Following clause subsumed by 384 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).
% 15.82/15.70  ** KEPT (pick-wt=12): 385 [] -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).
% 15.82/15.70    Following clause subsumed by 385 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).
% 15.82/15.70  ** KEPT (pick-wt=83): 386 [] -class_Rings_Ocomm__semiring__0(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,B,C)=c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(A),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_Polynomial_Opoly(A),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A))),A),c_COMBK(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A))),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),A),hAPP(c_COMBS(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(A),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A))),hAPP(c_Polynomial_Osmult(A),C)))),c_Polynomial_OpCons(A))),B).
% 15.82/15.70  ** KEPT (pick-wt=28): 387 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Polynomial_Osmult(A),C),D))!=hAPP(hAPP(c_Polynomial_OpCons(A),E),D)|E=hAPP(c_Polynomial_Opoly(A,B),C).
% 15.82/15.70  ** KEPT (pick-wt=27): 388 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Polynomial_Osmult(A),C),D))!=hAPP(hAPP(c_Polynomial_OpCons(A),E),D)|D=c_Polynomial_Osynthetic__div(A,B,C).
% 15.82/15.70  ** KEPT (pick-wt=31): 389 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Polynomial_Osmult(A),C),c_Polynomial_Osynthetic__div(A,B,C)))=hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(c_Polynomial_Opoly(A,B),C)),c_Polynomial_Osynthetic__div(A,B,C)).
% 15.82/15.70  ** KEPT (pick-wt=35): 391 [copy,390,flip.2] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,C,B))),hAPP(hAPP(c_Polynomial_OpCons(A),D),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,C,B)))=c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,hAPP(hAPP(c_Polynomial_OpCons(A),D),C),B).
% 15.82/15.70  ** KEPT (pick-wt=38): 392 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D))).
% 15.82/15.70  ** KEPT (pick-wt=58): 393 [] -class_Rings_Olinordered__semiring__1__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),F))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),E),F)!=c_Groups_Oone__class_Oone(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D))),C)).
% 15.82/15.70  ** KEPT (pick-wt=31): 394 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))).
% 15.82/15.70  ** KEPT (pick-wt=24): 395 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D)).
% 15.82/15.70  ** KEPT (pick-wt=24): 396 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 15.82/15.70  ** KEPT (pick-wt=30): 397 [] -class_Groups_Oordered__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),E))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E))).
% 15.82/15.70  ** KEPT (pick-wt=24): 398 [] -class_Groups_Oordered__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))).
% 15.82/15.70  ** KEPT (pick-wt=24): 399 [] -class_Groups_Oordered__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D))).
% 15.82/15.71    Following clause subsumed by 395 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D)).
% 15.82/15.71  ** KEPT (pick-wt=24): 400 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D)).
% 15.82/15.71    Following clause subsumed by 396 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 15.82/15.71  ** KEPT (pick-wt=24): 401 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 15.82/15.71  ** KEPT (pick-wt=11): 402 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.71  ** KEPT (pick-wt=11): 403 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.82/15.71  ** KEPT (pick-wt=8): 404 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),A)).
% 15.82/15.71  ** KEPT (pick-wt=14): 405 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,B)),A)).
% 15.82/15.71  ** KEPT (pick-wt=19): 406 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|A=hAPP(c_Nat_OSuc,B).
% 15.82/15.71  ** KEPT (pick-wt=14): 407 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 15.82/15.71  ** KEPT (pick-wt=13): 408 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|A!=hAPP(c_Nat_OSuc,B).
% 15.82/15.71  ** KEPT (pick-wt=16): 409 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),hAPP(c_Nat_OSuc,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 15.82/15.71  ** KEPT (pick-wt=16): 410 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),hAPP(c_Nat_OSuc,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 15.82/15.71    Following clause subsumed by 407 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B))).
% 15.82/15.71    Following clause subsumed by 406 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|A=hAPP(c_Nat_OSuc,B).
% 15.82/15.71  ** KEPT (pick-wt=14): 411 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 15.82/15.71  ** KEPT (pick-wt=12): 412 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 15.82/15.71    Following clause subsumed by 412 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 15.82/15.71    Following clause subsumed by 71 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|A!=B.
% 15.82/15.71  ** KEPT (pick-wt=15): 413 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|A=B.
% 15.82/15.71    Following clause subsumed by 413 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|A=B.
% 15.82/15.71    Following clause subsumed by 412 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 15.82/15.71  ** KEPT (pick-wt=9): 414 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|A!=B.
% 15.82/15.71    Following clause subsumed by 412 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 15.82/15.71    Following clause subsumed by 413 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|A=B|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 15.82/15.71    Following clause subsumed by 412 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 15.82/15.71    Following clause subsumed by 414 during input processing: 0 [] A!=B|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 15.82/15.71  ** KEPT (pick-wt=17): 415 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))).
% 15.82/15.71  ** KEPT (pick-wt=17): 416 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C))).
% 15.82/15.71  ** KEPT (pick-wt=16): 418 [copy,417,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),$f7(B,A))=B.
% 15.82/15.71  ** KEPT (pick-wt=14): 419 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|B!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C).
% 15.82/15.71  ** KEPT (pick-wt=22): 420 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 15.82/15.71  ** KEPT (pick-wt=22): 421 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 15.82/15.71    Following clause subsumed by 416 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C))).
% 15.82/15.71    Following clause subsumed by 415 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))).
% 15.82/15.71  ** KEPT (pick-wt=22): 422 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C))).
% 15.82/15.71  ** KEPT (pick-wt=28): 423 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D))).
% 15.82/15.71  ** KEPT (pick-wt=17): 424 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 15.82/15.71  ** KEPT (pick-wt=17): 425 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),C)).
% 15.82/15.71    Following clause subsumed by 425 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),C)).
% 15.82/15.71    Following clause subsumed by 424 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 15.82/15.71  ** KEPT (pick-wt=12): 426 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B)).
% 15.82/15.71  ** KEPT (pick-wt=9): 427 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))|A!=B.
% 15.82/15.71  ** KEPT (pick-wt=15): 428 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B))|A=B.
% 15.82/15.71  ** KEPT (pick-wt=22): 429 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C))).
% 15.82/15.71  ** KEPT (pick-wt=22): 430 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))).
% 15.82/15.71  ** KEPT (pick-wt=28): 431 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D))).
% 15.82/15.71  ** KEPT (pick-wt=22): 432 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B))).
% 15.82/15.71  ** KEPT (pick-wt=38): 433 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),c_Groups_Oone__class_Oone(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B))).
% 15.82/15.71  ** KEPT (pick-wt=31): 434 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C),D)).
% 15.82/15.71  ** KEPT (pick-wt=31): 435 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C),D)).
% 15.82/15.71    Following clause subsumed by 434 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C),D)).
% 15.82/15.71  ** KEPT (pick-wt=14): 436 [] -class_Rings_Olinordered__ring(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B))).
% 15.82/15.71  ** KEPT (pick-wt=28): 437 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71  ** KEPT (pick-wt=28): 438 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71  ** KEPT (pick-wt=28): 439 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71  ** KEPT (pick-wt=28): 440 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71  ** KEPT (pick-wt=28): 441 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C)).
% 15.82/15.71  ** KEPT (pick-wt=28): 442 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71  ** KEPT (pick-wt=28): 443 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71  ** KEPT (pick-wt=28): 444 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C)).
% 15.82/15.71  ** KEPT (pick-wt=28): 445 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71  ** KEPT (pick-wt=28): 446 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C)).
% 15.82/15.71  ** KEPT (pick-wt=28): 447 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71  ** KEPT (pick-wt=28): 448 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C)).
% 15.82/15.71  ** KEPT (pick-wt=28): 449 [] -class_Rings_Oordered__cancel__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))).
% 15.82/15.71  ** KEPT (pick-wt=28): 450 [] -class_Rings_Oordered__cancel__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71  ** KEPT (pick-wt=28): 451 [] -class_Rings_Oordered__cancel__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71    Following clause subsumed by 451 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71  ** KEPT (pick-wt=28): 452 [] -class_Rings_Oordered__ring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))).
% 15.82/15.71  ** KEPT (pick-wt=31): 453 [] -class_Rings_Oordered__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))).
% 15.82/15.71  ** KEPT (pick-wt=31): 454 [] -class_Rings_Oordered__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))).
% 15.82/15.71  ** KEPT (pick-wt=31): 455 [] -class_Rings_Oordered__comm__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))).
% 15.82/15.71  ** KEPT (pick-wt=31): 456 [] -class_Rings_Oordered__ring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))).
% 15.82/15.71  ** KEPT (pick-wt=31): 457 [] -class_Rings_Oordered__ring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B))).
% 15.82/15.71  ** KEPT (pick-wt=44): 458 [] -class_Rings_Oordered__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))).
% 15.82/15.71  ** KEPT (pick-wt=44): 459 [] -class_Rings_Oordered__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))).
% 15.82/15.71  ** KEPT (pick-wt=28): 460 [] -class_Rings_Oordered__ring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))).
% 15.82/15.71    Following clause subsumed by 452 during input processing: 0 [] -class_Rings_Oordered__ring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))).
% 15.82/15.71    Following clause subsumed by 450 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71    Following clause subsumed by 451 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71  ** KEPT (pick-wt=21): 461 [] -class_Groups_Olinordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 15.82/15.71  ** KEPT (pick-wt=21): 462 [] -class_Groups_Olinordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 15.82/15.71  ** KEPT (pick-wt=21): 463 [] -class_Groups_Olinordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71  ** KEPT (pick-wt=21): 464 [] -class_Groups_Olinordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71  ** KEPT (pick-wt=28): 465 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))).
% 15.82/15.71  ** KEPT (pick-wt=29): 466 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.71  ** KEPT (pick-wt=29): 467 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.71  ** KEPT (pick-wt=33): 468 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.71  ** KEPT (pick-wt=26): 469 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))).
% 15.82/15.71  ** KEPT (pick-wt=26): 470 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B))).
% 15.82/15.71  ** KEPT (pick-wt=28): 471 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71  ** KEPT (pick-wt=30): 472 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),E))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E))).
% 15.82/15.71  ** KEPT (pick-wt=30): 473 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E))).
% 15.82/15.71  ** KEPT (pick-wt=10): 474 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71  ** KEPT (pick-wt=10): 475 [] -class_Rings_Olinordered__semidom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Oone__class_Oone(A))).
% 15.82/15.71  ** KEPT (pick-wt=21): 476 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))).
% 15.82/15.71  ** KEPT (pick-wt=31): 477 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D))).
% 15.82/15.71  ** KEPT (pick-wt=21): 478 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))).
% 15.82/15.71  ** KEPT (pick-wt=14): 479 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),B)).
% 15.82/15.71  ** KEPT (pick-wt=14): 480 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),B)).
% 15.82/15.71  ** KEPT (pick-wt=14): 481 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 15.82/15.71  ** KEPT (pick-wt=14): 482 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 15.82/15.71    Following clause subsumed by 480 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 15.82/15.71    Following clause subsumed by 479 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 15.82/15.71    Following clause subsumed by 482 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B))).
% 15.82/15.71    Following clause subsumed by 479 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),B)).
% 15.82/15.71  ** KEPT (pick-wt=17): 483 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),hAPP(c_Nat_OSuc,A)))|B=A.
% 15.82/15.71    Following clause subsumed by 98 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),hAPP(c_Nat_OSuc,A)))|B!=A.
% 15.82/15.71    Following clause subsumed by 480 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 15.82/15.71  ** KEPT (pick-wt=26): 484 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 15.82/15.71    Following clause subsumed by 430 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 15.82/15.71  ** KEPT (pick-wt=28): 485 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),D))).
% 15.82/15.71  ** KEPT (pick-wt=12): 486 [] -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)).
% 15.82/15.71  ** KEPT (pick-wt=15): 487 [] -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)).
% 15.82/15.71  ** KEPT (pick-wt=15): 488 [] -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)).
% 15.82/15.71  ** KEPT (pick-wt=12): 489 [] -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)).
% 15.82/15.71  ** KEPT (pick-wt=31): 490 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D)).
% 15.82/15.71  ** KEPT (pick-wt=31): 491 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D)).
% 15.82/15.71  ** KEPT (pick-wt=31): 492 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),C)).
% 15.82/15.71  ** KEPT (pick-wt=31): 493 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),C)).
% 15.82/15.71  ** KEPT (pick-wt=44): 494 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))).
% 15.82/15.71  ** KEPT (pick-wt=44): 495 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))).
% 15.82/15.71  ** KEPT (pick-wt=44): 496 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))).
% 15.82/15.71  ** KEPT (pick-wt=44): 497 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))).
% 15.82/15.71  ** KEPT (pick-wt=31): 498 [] -class_Rings_Olinordered__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 15.82/15.71  ** KEPT (pick-wt=31): 499 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 15.82/15.71  ** KEPT (pick-wt=31): 500 [] -class_Rings_Olinordered__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 15.82/15.71  ** KEPT (pick-wt=31): 501 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 15.82/15.71  ** KEPT (pick-wt=31): 502 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 15.82/15.71  ** KEPT (pick-wt=31): 503 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D)).
% 15.82/15.71  ** KEPT (pick-wt=28): 504 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))).
% 15.82/15.71  ** KEPT (pick-wt=28): 505 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))).
% 15.82/15.71  ** KEPT (pick-wt=26): 506 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))).
% 15.82/15.71  ** KEPT (pick-wt=26): 507 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))).
% 15.82/15.71  ** KEPT (pick-wt=28): 508 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71  ** KEPT (pick-wt=28): 509 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.71  ** KEPT (pick-wt=24): 510 [] -class_Rings_Olinordered__ring(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(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)))).
% 15.82/15.71  ** KEPT (pick-wt=28): 511 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(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).
% 15.82/15.71  ** KEPT (pick-wt=28): 512 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(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).
% 15.82/15.71  ** KEPT (pick-wt=32): 513 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(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).
% 15.82/15.71  ** KEPT (pick-wt=34): 514 [] -class_Rings_Olinordered__idom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Oone__class_Oone(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),B)).
% 15.82/15.71  ** KEPT (pick-wt=34): 515 [] -class_Rings_Olinordered__idom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Oone__class_Oone(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)),B)).
% 15.82/15.71  ** KEPT (pick-wt=31): 516 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 15.82/15.71  ** KEPT (pick-wt=35): 517 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C))),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(c_Nat_OSuc,C))))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 15.82/15.71  ** KEPT (pick-wt=36): 518 [] -class_Rings_Olinordered__semidom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C))!=hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(c_Nat_OSuc,C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|B=D.
% 15.82/15.71  ** KEPT (pick-wt=23): 519 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),A)).
% 15.82/15.71  ** KEPT (pick-wt=23): 520 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B)).
% 15.82/15.71  ** KEPT (pick-wt=32): 521 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B)).
% 15.82/15.71  ** KEPT (pick-wt=29): 522 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 15.82/15.71    Following clause subsumed by 430 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 15.82/15.71  ** KEPT (pick-wt=29): 523 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),C)).
% 15.82/15.71    Following clause subsumed by 429 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),C)).
% 15.82/15.71    Following clause subsumed by 522 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 15.82/15.71    Following clause subsumed by 430 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 15.82/15.71  ** KEPT (pick-wt=14): 524 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)).
% 15.82/15.71  ** KEPT (pick-wt=14): 525 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)).
% 15.82/15.71  ** KEPT (pick-wt=18): 526 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B)).
% 15.82/15.71  ** KEPT (pick-wt=18): 527 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint))))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B)).
% 15.82/15.71  ** KEPT (pick-wt=18): 528 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)).
% 15.82/15.71  ** KEPT (pick-wt=18): 529 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)).
% 15.82/15.71    Following clause subsumed by 529 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))),B)).
% 15.82/15.71  ** KEPT (pick-wt=23): 530 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))).
% 15.82/15.71  ** KEPT (pick-wt=58): 531 [] -class_Rings_Olinordered__semiring__1(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),F))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),E),F)!=c_Groups_Oone__class_Oone(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D))),C)).
% 15.82/15.71  ** KEPT (pick-wt=39): 532 [] -class_Rings_Olinordered__semidom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C))|B=D.
% 15.82/15.71  ** KEPT (pick-wt=21): 533 [] -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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 15.82/15.71  ** KEPT (pick-wt=25): 534 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osynthetic__div(A,hAPP(hAPP(c_Polynomial_OpCons(A),B),C),D)=hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(c_Polynomial_Opoly(A,C),D)),c_Polynomial_Osynthetic__div(A,C,D)).
% 15.82/15.71  ** KEPT (pick-wt=20): 535 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A))).
% 15.82/15.71  ** KEPT (pick-wt=22): 536 [] -class_Rings_Ocomm__semiring__0(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,hAPP(hAPP(c_Polynomial_OpCons(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)=hAPP(hAPP(c_Polynomial_OpCons(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).
% 15.82/15.71  ** KEPT (pick-wt=34): 538 [copy,537,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))!=A| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,C),c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 15.82/15.71  ** KEPT (pick-wt=33): 540 [copy,539,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))!=A| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),C)).
% 15.82/15.71  ** KEPT (pick-wt=29): 541 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Oone__class_Oone(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C))),B)).
% 15.82/15.71  ** KEPT (pick-wt=37): 542 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)).
% 15.82/15.71  ** KEPT (pick-wt=38): 543 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.82/15.71  ** KEPT (pick-wt=18): 544 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),C)).
% 15.82/15.71  ** KEPT (pick-wt=15): 545 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B),A))|A=B.
% 15.82/15.71    Following clause subsumed by 414 during input processing: 0 [] A!=B|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 15.82/15.71  ** KEPT (pick-wt=18): 546 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),C)).
% 15.82/15.71  ** KEPT (pick-wt=15): 547 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),A))|A=B.
% 15.82/15.71  ** KEPT (pick-wt=72): 548 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),E)),F)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),E)),F)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),F))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,D),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,E),B)).
% 15.82/15.71  ** KEPT (pick-wt=51): 549 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)),E)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,E),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,D),B)).
% 15.82/15.71  ** KEPT (pick-wt=72): 550 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),E)),F)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),E)),F)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,F),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,D),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B),E)).
% 15.82/15.71  ** KEPT (pick-wt=51): 551 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)),E)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,E),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B),D)).
% 15.82/15.71  ** KEPT (pick-wt=19): 552 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))).
% 15.82/15.71  ** KEPT (pick-wt=26): 553 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))).
% 15.82/15.71  ** KEPT (pick-wt=26): 554 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B))).
% 15.82/15.71  ** KEPT (pick-wt=8): 555 [] -class_Orderings_Opreorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),B)).
% 15.82/15.71  ** KEPT (pick-wt=46): 556 [] -class_Rings_Ocomm__ring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Ouminus__class_Ouminus(A,B)),hAPP(hAPP(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))),hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(c_Polynomial_Opoly(A,C),B)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))=C.
% 15.82/15.71  ** KEPT (pick-wt=16): 558 [copy,557,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),$f8(B,A))=B.
% 15.82/15.71    Following clause subsumed by 419 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|B!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C).
% 15.82/15.71  ** KEPT (pick-wt=14): 559 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 15.82/15.71  ** KEPT (pick-wt=14): 560 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 15.82/15.71  ** KEPT (pick-wt=23): 562 [copy,561,flip.2] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C))=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Polynomial_OpCons(A),B),C)).
% 15.82/15.71    Following clause subsumed by 562 during input processing: 0 [flip.2] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C))=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Polynomial_OpCons(A),B),C)).
% 15.82/15.71  ** KEPT (pick-wt=18): 563 [] -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)).
% 15.82/15.71  ** KEPT (pick-wt=12): 564 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=c_Groups_Ouminus__class_Ouminus(A,C)|B=C.
% 15.82/15.71  ** KEPT (pick-wt=12): 565 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=c_Groups_Ouminus__class_Ouminus(A,C)|B!=C.
% 15.82/15.71  ** KEPT (pick-wt=12): 566 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=C|c_Groups_Ouminus__class_Ouminus(A,C)=B.
% 15.82/15.71    Following clause subsumed by 566 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.
% 15.82/15.71  ** KEPT (pick-wt=12): 567 [] -class_Groups_Ogroup__add(A)|B!=c_Groups_Ouminus__class_Ouminus(A,C)|C=c_Groups_Ouminus__class_Ouminus(A,B).
% 15.82/15.71    Following clause subsumed by 567 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).
% 15.82/15.71  ** KEPT (pick-wt=9): 568 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ouminus__class_Ouminus(A,B))=B.
% 15.82/15.71  ** KEPT (pick-wt=16): 569 [] -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).
% 15.82/15.71  ** KEPT (pick-wt=20): 570 [] -class_Rings_Ocomm__ring(A)|hAPP(hAPP(c_Polynomial_Osmult(A),c_Groups_Ouminus__class_Ouminus(A,B)),C)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)).
% 15.82/15.71  ** KEPT (pick-wt=21): 571 [] -class_Rings_Ocomm__ring(A)|hAPP(hAPP(c_Polynomial_Osmult(A),B),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C))=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)).
% 15.82/15.71  ** KEPT (pick-wt=12): 572 [] -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)).
% 15.82/15.71  ** KEPT (pick-wt=17): 573 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ouminus__class_Ouminus(A,B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))=C.
% 15.82/15.71  ** KEPT (pick-wt=17): 574 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ouminus__class_Ouminus(A,B)),C))=C.
% 15.82/15.71  ** KEPT (pick-wt=21): 575 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ouminus__class_Ouminus(A,C)),c_Groups_Ouminus__class_Ouminus(A,B)).
% 15.82/15.71  ** KEPT (pick-wt=21): 577 [copy,576,flip.2] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C))=c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)).
% 15.82/15.71  ** KEPT (pick-wt=19): 579 [copy,578,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)).
% 15.82/15.71  ** KEPT (pick-wt=19): 581 [copy,580,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)).
% 15.82/15.71  ** KEPT (pick-wt=19): 582 [] -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)).
% 15.82/15.71  ** KEPT (pick-wt=19): 583 [] -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).
% 15.82/15.71  ** KEPT (pick-wt=23): 584 [] -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).
% 15.82/15.71  ** KEPT (pick-wt=18): 585 [] -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.
% 15.82/15.71  ** KEPT (pick-wt=20): 586 [] -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).
% 15.82/15.71  ** KEPT (pick-wt=19): 587 [] -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)).
% 15.82/15.71    Following clause subsumed by 587 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)).
% 15.82/15.71  ** KEPT (pick-wt=19): 588 [] -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)).
% 15.82/15.71    Following clause subsumed by 588 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)).
% 15.82/15.71  ** KEPT (pick-wt=18): 589 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.71  ** KEPT (pick-wt=18): 590 [] -class_Groups_Oordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.71  ** KEPT (pick-wt=18): 591 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,C)),B)).
% 15.82/15.71    Following clause subsumed by 591 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,C)),B)).
% 15.82/15.71  ** KEPT (pick-wt=18): 592 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ouminus__class_Ouminus(A,C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ouminus__class_Ouminus(A,B))).
% 15.82/15.71    Following clause subsumed by 592 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ouminus__class_Ouminus(A,C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ouminus__class_Ouminus(A,B))).
% 15.82/15.71  ** KEPT (pick-wt=18): 593 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ouminus__class_Ouminus(A,C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ouminus__class_Ouminus(A,B))).
% 15.82/15.71    Following clause subsumed by 593 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ouminus__class_Ouminus(A,C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ouminus__class_Ouminus(A,B))).
% 15.82/15.71  ** KEPT (pick-wt=18): 594 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,C)),B)).
% 15.82/15.71    Following clause subsumed by 594 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,C)),B)).
% 15.82/15.71  ** KEPT (pick-wt=18): 595 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 15.82/15.71  ** KEPT (pick-wt=18): 596 [] -class_Groups_Oordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 15.82/15.71    Following clause subsumed by 596 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,C)),c_Groups_Ouminus__class_Ouminus(A,B))).
% 15.82/15.71  ** KEPT (pick-wt=11): 597 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.71  ** KEPT (pick-wt=11): 598 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.71  ** KEPT (pick-wt=12): 599 [] -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).
% 15.82/15.72  ** KEPT (pick-wt=12): 600 [] -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).
% 15.82/15.72    Following clause subsumed by 597 during input processing: 0 [flip.2] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.72    Following clause subsumed by 598 during input processing: 0 [flip.2] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.72  ** KEPT (pick-wt=12): 601 [] -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.
% 15.82/15.72  ** KEPT (pick-wt=12): 602 [] -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.
% 15.82/15.72  ** KEPT (pick-wt=9): 603 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.72  ** KEPT (pick-wt=18): 604 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Ouminus__class_Ouminus(A,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.72  ** KEPT (pick-wt=18): 605 [] -class_Groups_Oordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Ouminus__class_Ouminus(A,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.72  ** KEPT (pick-wt=17): 606 [] -class_Groups_Olinordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ouminus__class_Ouminus(A,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.72  ** KEPT (pick-wt=17): 607 [] -class_Groups_Olinordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ouminus__class_Ouminus(A,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.72  ** KEPT (pick-wt=18): 608 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 15.82/15.72  ** KEPT (pick-wt=18): 609 [] -class_Groups_Oordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 15.82/15.72  ** KEPT (pick-wt=17): 610 [] -class_Groups_Olinordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 15.82/15.72  ** KEPT (pick-wt=17): 611 [] -class_Groups_Olinordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 15.82/15.72  ** KEPT (pick-wt=17): 612 [] -class_Groups_Olinordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 15.82/15.72  ** KEPT (pick-wt=17): 613 [] -class_Groups_Olinordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 15.82/15.72  ** KEPT (pick-wt=18): 614 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 15.82/15.72  ** KEPT (pick-wt=18): 615 [] -class_Groups_Oordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 15.82/15.72  ** KEPT (pick-wt=18): 616 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Ouminus__class_Ouminus(A,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.72  ** KEPT (pick-wt=18): 617 [] -class_Groups_Oordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Ouminus__class_Ouminus(A,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.72  ** KEPT (pick-wt=17): 618 [] -class_Rings_Olinordered__idom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ouminus__class_Ouminus(A,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.72  ** KEPT (pick-wt=17): 619 [] -class_Rings_Olinordered__idom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ouminus__class_Ouminus(A,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.72  ** KEPT (pick-wt=16): 620 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ouminus__class_Ouminus(A,B).
% 15.82/15.72  ** KEPT (pick-wt=16): 621 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ouminus__class_Ouminus(A,B).
% 15.82/15.72  ** KEPT (pick-wt=16): 622 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|c_Groups_Ouminus__class_Ouminus(A,B)=C.
% 15.82/15.72  ** KEPT (pick-wt=13): 623 [] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ouminus__class_Ouminus(A,B)),B)=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.72  ** KEPT (pick-wt=13): 624 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ouminus__class_Ouminus(A,B)),B)=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.72  ** KEPT (pick-wt=16): 625 [] -class_Groups_Ogroup__add(A)|B!=c_Groups_Ouminus__class_Ouminus(A,C)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.72  ** KEPT (pick-wt=16): 626 [] -class_Groups_Ogroup__add(A)|B=c_Groups_Ouminus__class_Ouminus(A,C)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.72  ** KEPT (pick-wt=13): 627 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ouminus__class_Ouminus(A,B))=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.72  ** KEPT (pick-wt=21): 628 [] -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)).
% 15.82/15.72  ** KEPT (pick-wt=15): 629 [] -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).
% 15.82/15.72  ** KEPT (pick-wt=17): 630 [] -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)).
% 15.82/15.72  ** KEPT (pick-wt=15): 632 [copy,631,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).
% 15.82/15.72  ** KEPT (pick-wt=16): 633 [] -class_Rings_Olinordered__idom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Opos__poly(A,B)|c_Polynomial_Opos__poly(A,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)).
% 15.82/15.72  ** KEPT (pick-wt=30): 634 [] -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)).
% 15.82/15.72  ** KEPT (pick-wt=33): 635 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))!=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|B=C|B=c_Groups_Ouminus__class_Ouminus(A,C).
% 15.82/15.72  ** KEPT (pick-wt=28): 636 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|B!=C.
% 15.82/15.72  ** KEPT (pick-wt=30): 637 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|B!=c_Groups_Ouminus__class_Ouminus(A,C).
% 15.82/15.72  ** KEPT (pick-wt=20): 638 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E)),hAPP(D,E))).
% 15.82/15.72  ** KEPT (pick-wt=28): 639 [] -class_Orderings_Oord(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,$f9(D,C,B,A))),hAPP(D,$f9(D,C,B,A)))).
% 15.82/15.72  ** KEPT (pick-wt=14): 640 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 15.82/15.72  ** KEPT (pick-wt=11): 641 [] -class_Orderings_Oorder(A)|B!=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C)).
% 15.82/15.72  ** KEPT (pick-wt=11): 642 [] -class_Orderings_Oorder(A)|B!=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 15.82/15.72  ** KEPT (pick-wt=17): 643 [] -class_Orderings_Oorder(A)|B=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 15.82/15.72  ** KEPT (pick-wt=11): 644 [] -class_Orderings_Opreorder(A)|B!=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C)).
% 15.82/15.72    Following clause subsumed by 638 during input processing: 0 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E)),hAPP(D,E))).
% 15.82/15.72    Following clause subsumed by 643 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B))|C=B.
% 15.82/15.72    Following clause subsumed by 641 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B))|C!=B.
% 15.82/15.72  ** KEPT (pick-wt=17): 645 [] -class_Orderings_Oord(A)|B!=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 15.82/15.72  ** KEPT (pick-wt=17): 646 [] -class_Orderings_Oorder(A)|B!=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),B)).
% 15.82/15.72  ** KEPT (pick-wt=17): 647 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|C!=D|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 15.82/15.72  ** KEPT (pick-wt=17): 648 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|B!=D|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),C)).
% 15.82/15.72    Following clause subsumed by 643 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B))|B=C.
% 15.82/15.72  ** KEPT (pick-wt=20): 649 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 15.82/15.72    Following clause subsumed by 643 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B))|C=B.
% 15.82/15.72  ** KEPT (pick-wt=20): 650 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),C)).
% 15.82/15.72    Following clause subsumed by 638 during input processing: 0 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E)),hAPP(D,E))).
% 15.82/15.72    Following clause subsumed by 640 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 15.82/15.72  ** KEPT (pick-wt=17): 651 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.72  ** KEPT (pick-wt=14): 652 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.72  ** KEPT (pick-wt=20): 653 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 15.82/15.72  ** KEPT (pick-wt=20): 654 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 15.82/15.72  ** KEPT (pick-wt=17): 655 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B!=D|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 15.82/15.72  ** KEPT (pick-wt=17): 656 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|C!=D|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 15.82/15.72  ** KEPT (pick-wt=17): 657 [] -class_Orderings_Oorder(A)|B!=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),B)).
% 15.82/15.72  ** KEPT (pick-wt=17): 658 [] -class_Orderings_Oord(A)|B!=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 15.82/15.72  ** KEPT (pick-wt=14): 659 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.72    Following clause subsumed by 652 during input processing: 0 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.72  ** KEPT (pick-wt=11): 660 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|C!=B.
% 15.82/15.72  ** KEPT (pick-wt=11): 661 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B!=C.
% 15.82/15.72    Following clause subsumed by 652 during input processing: 0 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.72    Following clause subsumed by 652 during input processing: 0 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.72    Following clause subsumed by 661 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B!=C.
% 15.82/15.72    Following clause subsumed by 651 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.72    Following clause subsumed by 651 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B))|C=B.
% 15.82/15.72  ** KEPT (pick-wt=17): 662 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B))|C!=B.
% 15.82/15.72    Following clause subsumed by 651 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.72    Following clause subsumed by 651 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B))|B=C.
% 15.82/15.72  ** KEPT (pick-wt=14): 663 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.72  ** KEPT (pick-wt=11): 664 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B!=C.
% 15.82/15.72    Following clause subsumed by 651 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.72    Following clause subsumed by 664 during input processing: 0 [] -class_Orderings_Olinorder(A)|B!=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)).
% 15.82/15.72  ** KEPT (pick-wt=11): 665 [] -class_Orderings_Olinorder(A)|B!=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.72  ** KEPT (pick-wt=8): 666 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),B)).
% 15.82/15.72  ** KEPT (pick-wt=20): 667 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 15.82/15.72  ** KEPT (pick-wt=20): 668 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 15.82/15.72  ** KEPT (pick-wt=20): 669 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 15.82/15.72  ** KEPT (pick-wt=20): 670 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 15.82/15.72  ** KEPT (pick-wt=17): 671 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|C=B|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)).
% 15.82/15.72  ** KEPT (pick-wt=17): 672 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|B=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)).
% 15.82/15.72    Following clause subsumed by 672 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B=C.
% 15.82/15.72  ** KEPT (pick-wt=17): 673 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B=C.
% 15.82/15.72    Following clause subsumed by 664 during input processing: 0 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B!=C.
% 15.82/15.72  ** KEPT (pick-wt=14): 674 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C)).
% 15.82/15.72    Following clause subsumed by 560 during input processing: 0 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.72    Following clause subsumed by 671 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.72    Following clause subsumed by 672 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)).
% 15.82/15.72    Following clause subsumed by 673 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|B=C.
% 15.82/15.72  ** KEPT (pick-wt=17): 675 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|B!=C.
% 15.82/15.72    Following clause subsumed by 559 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.72    Following clause subsumed by 559 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 15.82/15.72    Following clause subsumed by 672 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B=C.
% 15.82/15.72  ** KEPT (pick-wt=14): 676 [] -class_Orderings_Oorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)).
% 15.82/15.72    Following clause subsumed by 641 during input processing: 0 [] -class_Orderings_Oorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|B!=C.
% 15.82/15.72    Following clause subsumed by 674 during input processing: 0 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C)).
% 15.82/15.72  ** KEPT (pick-wt=14): 677 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 15.82/15.72  ** KEPT (pick-wt=20): 678 [] -class_Orderings_Opreorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 15.82/15.72    Following clause subsumed by 676 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C)).
% 15.82/15.72    Following clause subsumed by 661 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B!=C.
% 15.82/15.72    Following clause subsumed by 672 during input processing: 0 [] -class_Orderings_Oorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|B=C.
% 15.82/15.72    Following clause subsumed by 559 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.72    Following clause subsumed by 559 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.72    Following clause subsumed by 560 during input processing: 0 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 15.82/15.72  ** KEPT (pick-wt=39): 679 [] -class_Rings_Oidom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Ouminus__class_Ouminus(A,C)),hAPP(hAPP(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)).
% 15.82/15.72  ** KEPT (pick-wt=41): 680 [] -class_Rings_Oidom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Ouminus__class_Ouminus(A,C)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(A,C,B)))),B)).
% 15.82/15.72    Following clause subsumed by 680 during input processing: 0 [] -class_Rings_Oidom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Ouminus__class_Ouminus(A,C)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(A,C,B)))),B)).
% 15.82/15.72  ** KEPT (pick-wt=18): 681 [] -class_Lattices_Oboolean__algebra(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 15.82/15.72  ** KEPT (pick-wt=18): 682 [] -class_Lattices_Oboolean__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 15.82/15.72    Following clause subsumed by 682 during input processing: 0 [] -class_Lattices_Oboolean__algebra(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,C)),c_Groups_Ouminus__class_Ouminus(A,B))).
% 15.82/15.72  ** KEPT (pick-wt=10): 683 [] -class_Rings_Ocomm__semiring__1(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),c_Groups_Ozero__class_Ozero(A))).
% 15.82/15.72  ** KEPT (pick-wt=18): 684 [] -class_Rings_Ocomm__ring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),c_Groups_Ouminus__class_Ouminus(A,B)),C))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)).
% 15.82/15.72  ** KEPT (pick-wt=18): 685 [] -class_Rings_Ocomm__ring__1(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),c_Groups_Ouminus__class_Ouminus(A,B)),C))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)).
% 15.82/15.72  ** KEPT (pick-wt=18): 686 [] -class_Rings_Ocomm__ring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),c_Groups_Ouminus__class_Ouminus(A,C)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)).
% 15.82/15.72  ** KEPT (pick-wt=18): 687 [] -class_Rings_Ocomm__ring__1(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),c_Groups_Ouminus__class_Ouminus(A,C)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)).
% 15.82/15.72  ** KEPT (pick-wt=18): 688 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(B,A),C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C),D)).
% 15.82/15.72  ** KEPT (pick-wt=18): 689 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(B,A),C),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D),C)).
% 15.82/15.72  ** KEPT (pick-wt=26): 690 [] -class_Orderings_Oord(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(B,A),C),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D),C)).
% 15.82/15.72  ** KEPT (pick-wt=23): 691 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),D))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),D)).
% 15.82/15.72  ** KEPT (pick-wt=23): 692 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),C))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Polynomial_Osmult(A),D),C))).
% 15.82/15.72  ** KEPT (pick-wt=9): 693 [] -class_Rings_Ocomm__semiring__1(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),B)).
% 15.82/15.72  ** KEPT (pick-wt=23): 694 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),D))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)).
% 15.82/15.72  ** KEPT (pick-wt=26): 695 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))|hBOOL(hAPP(hAPP(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))).
% 15.82/15.72  ** KEPT (pick-wt=10): 696 [] -class_Rings_Ocomm__semiring__1(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),c_Groups_Oone__class_Oone(A)),B)).
% 15.82/15.72  ** KEPT (pick-wt=28): 697 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D))).
% 15.82/15.72  ** KEPT (pick-wt=21): 698 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),D)).
% 15.82/15.72  ** KEPT (pick-wt=21): 699 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)).
% 15.82/15.72  ** KEPT (pick-wt=17): 700 [] -class_Rings_Odvd(A)|B!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),B)).
% 15.82/15.72  ** KEPT (pick-wt=33): 701 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),D),E))|hBOOL(hAPP(hAPP(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))).
% 15.82/15.72  ** KEPT (pick-wt=21): 702 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))).
% 15.82/15.72  ** KEPT (pick-wt=21): 703 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))).
% 15.82/15.72  ** KEPT (pick-wt=14): 704 [] -class_Rings_Ocomm__semiring__1(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B))).
% 15.82/15.72  ** KEPT (pick-wt=14): 705 [] -class_Rings_Ocomm__semiring__1(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))).
% 15.82/15.72  ** KEPT (pick-wt=14): 706 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),c_Groups_Ozero__class_Ozero(A)),B))|B=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.72  ** KEPT (pick-wt=30): 707 [] -class_Rings_Oidom(A)| -hBOOL(hAPP(hAPP(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)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)).
% 15.82/15.72  ** KEPT (pick-wt=23): 708 [] -class_Rings_Oidom(A)|hBOOL(hAPP(hAPP(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).
% 15.82/15.72  ** KEPT (pick-wt=26): 709 [] -class_Rings_Oidom(A)|hBOOL(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)).
% 15.82/15.72  ** KEPT (pick-wt=30): 710 [] -class_Rings_Oidom(A)| -hBOOL(hAPP(hAPP(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)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),D)).
% 15.82/15.72  ** KEPT (pick-wt=23): 711 [] -class_Rings_Oidom(A)|hBOOL(hAPP(hAPP(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).
% 15.82/15.72  ** KEPT (pick-wt=26): 712 [] -class_Rings_Oidom(A)|hBOOL(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),D)).
% 15.82/15.72  ** KEPT (pick-wt=25): 713 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))).
% 15.82/15.72  ** KEPT (pick-wt=32): 714 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,D),E))|hBOOL(hAPP(hAPP(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),E))).
% 15.82/15.72  ** KEPT (pick-wt=32): 715 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,E),C))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),E)),D)).
% 15.82/15.72  ** KEPT (pick-wt=27): 716 [] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),hAPP(hAPP(c_Polynomial_Osmult(A),B),D)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),D)).
% 15.82/15.72  ** KEPT (pick-wt=27): 717 [] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),hAPP(hAPP(c_Polynomial_Osmult(A),B),D)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),D)).
% 15.82/15.72  ** KEPT (pick-wt=27): 718 [] -class_Fields_Ofield(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),C))|D=c_Groups_Ozero__class_Ozero(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),D),B)),C)).
% 15.82/15.72    Following clause subsumed by 716 during input processing: 0 [] -class_Fields_Ofield(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Polynomial_Osmult(A),C),D)))|C=c_Groups_Ozero__class_Ozero(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),D)).
% 15.82/15.72  ** KEPT (pick-wt=24): 719 [] -class_Fields_Ofield(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),D))|B!=c_Groups_Ozero__class_Ozero(A)|D=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.82/15.72  ** KEPT (pick-wt=27): 720 [] -class_Fields_Ofield(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),D))|B=c_Groups_Ozero__class_Ozero(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),D)).
% 15.82/15.72    Following clause subsumed by 718 during input processing: 0 [] -class_Fields_Ofield(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),D))|B=c_Groups_Ozero__class_Ozero(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),D)).
% 15.82/15.72  ** KEPT (pick-wt=24): 721 [] -class_Fields_Ofield(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),D))|D!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B!=c_Groups_Ozero__class_Ozero(A).
% 15.82/15.72  ** KEPT (pick-wt=28): 722 [] -class_Fields_Ofield(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),D))|D!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),D)).
% 15.82/15.72  ** KEPT (pick-wt=10): 723 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=B.
% 15.82/15.72    Following clause subsumed by 723 during input processing: 0 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=B.
% 15.82/15.72  ** KEPT (pick-wt=20): 724 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C).
% 15.82/15.72  ** KEPT (pick-wt=12): 725 [] -class_Lattices_Oboolean__algebra(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=c_Groups_Ouminus__class_Ouminus(A,C)|B=C.
% 15.82/15.72  ** KEPT (pick-wt=12): 726 [] -class_Lattices_Oboolean__algebra(A)|c_Groups_Ouminus__class_Ouminus(A,B)=c_Groups_Ouminus__class_Ouminus(A,C)|B!=C.
% 15.82/15.72  ** KEPT (pick-wt=15): 727 [] -class_Groups_Ouminus(A)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(B,A),C),D)=c_Groups_Ouminus__class_Ouminus(A,hAPP(C,D)).
% 15.82/15.72  ** KEPT (pick-wt=9): 728 [] -class_Lattices_Oboolean__algebra(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ouminus__class_Ouminus(A,B))=B.
% 15.82/15.72  ** KEPT (pick-wt=21): 729 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B))).
% 15.82/15.72  ** KEPT (pick-wt=18): 730 [] -class_Rings_Ocomm__semiring__1(A)|B!=c_Groups_Oone__class_Oone(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))).
% 15.82/15.72    Following clause subsumed by 727 during input processing: 0 [] -class_Groups_Ouminus(A)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(B,A),C),D)=c_Groups_Ouminus__class_Ouminus(A,hAPP(C,D)).
% 15.82/15.72  ** KEPT (pick-wt=33): 731 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Opoly(A,B),C)!=c_Groups_Ozero__class_Ozero(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_O
% 15.82/15.72  Search stopped in tp_alloc by max_mem option.
% 15.82/15.72  poly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Ouminus__class_Ouminus(A,C)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),B)).
% 15.82/15.72  ** KEPT (pick-wt=33): 732 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Opoly(A,B),C)=c_Groups_Ozero__class_Ozero(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Ouminus__class_Ouminus(A,C)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),B)).
% 15.82/15.72  ** KEPT (pick-wt=33): 733 [] -class_Rings_Oidom(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),B),hAPP(hAPP(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).
% 15.82/15.72  ** KEPT (pick-wt=33): 734 [] -class_Rings_Oidom(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),B),hAPP(hAPP(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).
% 15.82/15.72  ** KEPT (pick-wt=34): 735 [] -class_Rings_Oidom(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Ouminus__class_Ouminus(A,B)),hAPP(hAPP(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)).
% 15.82/15.72  ** KEPT (pick-wt=29): 736 [] -class_Rings_Odvd(A)| -class_Rings_Osemiring__0(A)| -hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),$f10(C,B,A)),c_Groups_Ozero__class_Ozero(A)))).
% 15.82/15.72  ** KEPT (pick-wt=20): 737 [] -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,$f10(C,B,A))).
% 15.82/15.72  ** KEPT (pick-wt=33): 738 [] -class_Rings_Odvd(A)| -class_Rings_Osemiring__0(A)|hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),$f11(C,B,A))))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),c_Groups_Ozero__class_Ozero(A))))| -hBOOL(hAPP(B,D)).
% 15.82/15.72  
% 15.82/15.72  Search stopped in tp_alloc by max_mem option.
% 15.82/15.72  
% 15.82/15.72  ============ end of search ============
% 15.82/15.72  
% 15.82/15.72  -------------- statistics -------------
% 15.82/15.72  clauses given                  0
% 15.82/15.72  clauses generated              0
% 15.82/15.72  clauses kept                 697
% 15.82/15.72  clauses forward subsumed     150
% 15.82/15.72  clauses back subsumed          0
% 15.82/15.72  Kbytes malloced            11718
% 15.82/15.72  
% 15.82/15.72  ----------- times (seconds) -----------
% 15.82/15.72  user CPU time          0.20          (0 hr, 0 min, 0 sec)
% 15.82/15.72  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 15.82/15.72  wall-clock time       15             (0 hr, 0 min, 15 sec)
% 15.82/15.72  
% 15.82/15.72  Process 14801 finished Wed Jul 27 03:20:48 2022
% 15.82/15.72  Otter interrupted
% 15.82/15.72  PROOF NOT FOUND
%------------------------------------------------------------------------------