%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SWW267+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n015.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 13:22:20 EDT 2022

% Result   : Unknown 13.12s 13.04s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWW267+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n015.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 03:03:56 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 13.03/12.96  ----- Otter 3.3f, August 2004 -----
% 13.03/12.96  The process was started by sandbox2 on n015.cluster.edu,
% 13.03/12.96  Wed Jul 27 03:03:56 2022
% 13.03/12.96  The command was "./otter".  The process ID is 20664.
% 13.03/12.96  
% 13.03/12.96  set(prolog_style_variables).
% 13.03/12.96  set(auto).
% 13.03/12.96     dependent: set(auto1).
% 13.03/12.96     dependent: set(process_input).
% 13.03/12.96     dependent: clear(print_kept).
% 13.03/12.96     dependent: clear(print_new_demod).
% 13.03/12.96     dependent: clear(print_back_demod).
% 13.03/12.96     dependent: clear(print_back_sub).
% 13.03/12.96     dependent: set(control_memory).
% 13.03/12.96     dependent: assign(max_mem, 12000).
% 13.03/12.96     dependent: assign(pick_given_ratio, 4).
% 13.03/12.96     dependent: assign(stats_level, 1).
% 13.03/12.96     dependent: assign(max_seconds, 10800).
% 13.03/12.96  clear(print_given).
% 13.03/12.96  
% 13.03/12.96  formula_list(usable).
% 13.03/12.96  all A (A=A).
% 13.03/12.96  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).
% 13.03/12.96  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.03/12.96  -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)).
% 13.03/12.96  v_k____!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.03/12.96  v_a____!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.03/12.96  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____).
% 13.03/12.96  c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))=c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))).
% 13.03/12.96  c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____))=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.03/12.96  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)).
% 13.03/12.96  hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)=c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)).
% 13.03/12.96  c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)).
% 13.03/12.96  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 13.03/12.96  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 13.03/12.96  c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))))=c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))).
% 13.03/12.96  c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))=c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))).
% 13.03/12.96  c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))=c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))).
% 13.03/12.96  all T_a (class_RealVector_Oreal__algebra__1(T_a)->c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(T_a)).
% 13.03/12.96  all T_a (class_RealVector_Oreal__normed__algebra__1(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.03/12.96  all V_s V_y V_r V_x T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s))))).
% 13.03/12.96  all V_s V_y V_r V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s))))).
% 13.03/12.96  v_w____!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.03/12.96  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____).
% 13.03/12.96  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)).
% 13.03/12.96  c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.03/12.96  c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))).
% 13.03/12.96  c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_k____)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),v_k____))).
% 13.03/12.96  all B_z (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),B_z)),v_m____)).
% 13.03/12.96  c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))).
% 13.03/12.96  -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)).
% 13.03/12.96  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.03/12.96  c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))).
% 13.03/12.96  c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))).
% 13.03/12.96  all V_x T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x))).
% 13.03/12.96  all T_a (class_RealVector_Oreal__algebra__1(T_a)->c_RealVector_Oof__real(T_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(T_a)).
% 13.03/12.96  all T_a (class_RealVector_Oreal__algebra__1(T_a)&class_RealVector_Oreal__normed__vector(T_a)->c_RealVector_Oof__real(T_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(T_a)).
% 13.03/12.96  all T_a (class_RealVector_Oreal__normed__vector(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.03/12.96  all V_x T_a (class_RealVector_Oreal__algebra__1(T_a)->c_RealVector_Oof__real(T_a,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))=c_Groups_Ouminus__class_Ouminus(T_a,c_RealVector_Oof__real(T_a,V_x))).
% 13.03/12.96  all V_x T_a (class_RealVector_Oreal__algebra__1(T_a)&class_RealVector_Oreal__normed__vector(T_a)->c_RealVector_Oof__real(T_a,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))=c_Groups_Ouminus__class_Ouminus(T_a,c_RealVector_Oof__real(T_a,V_x))).
% 13.03/12.96  all V_y V_x T_a (class_RealVector_Oreal__algebra__1(T_a)->c_RealVector_Oof__real(T_a,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,c_RealVector_Oof__real(T_a,V_x),c_RealVector_Oof__real(T_a,V_y))).
% 13.03/12.96  all V_y V_x T_a (class_RealVector_Oreal__algebra__1(T_a)&class_RealVector_Oreal__normed__vector(T_a)->c_RealVector_Oof__real(T_a,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,c_RealVector_Oof__real(T_a,V_x),c_RealVector_Oof__real(T_a,V_y))).
% 13.03/12.96  all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)))).
% 13.03/12.96  all V_n_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.03/12.96  all V_x_2 T_a (class_RealVector_Oreal__algebra__1(T_a)-> (c_RealVector_Oof__real(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.03/12.96  all V_x_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_RealVector_Onorm__class_Onorm(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.96  all V_x_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->V_x_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.96  all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))).
% 13.03/12.96  all V_n_2 V_aa_2 T_a (class_Power_Opower(T_a)&class_Rings_Omult__zero(T_a)&class_Rings_Ono__zero__divisors(T_a)&class_Rings_Ozero__ne_q__one(T_a)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a)&V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.03/12.96  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))).
% 13.03/12.96  all V_n V_m V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 13.03/12.96  all V_n V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->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))))).
% 13.03/12.96  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)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->V_a=V_b))))).
% 13.03/12.96  all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->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)))))).
% 13.03/12.96  all V_n V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(T_a,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)))))).
% 13.03/12.96  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))).
% 13.03/12.96  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))).
% 13.03/12.96  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))).
% 13.03/12.96  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))).
% 13.03/12.96  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))).
% 13.03/12.96  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))).
% 13.03/12.96  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))).
% 13.03/12.96  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))).
% 13.03/12.96  all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))).
% 13.03/12.96  all V_x T_a (class_RealVector_Oreal__normed__vector(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x))=c_RealVector_Onorm__class_Onorm(T_a,V_x)).
% 13.03/12.96  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)).
% 13.03/12.96  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)).
% 13.03/12.96  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)).
% 13.03/12.96  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)).
% 13.03/12.96  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)).
% 13.03/12.96  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).
% 13.03/12.96  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))).
% 13.03/12.96  all V_d V_c V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))).
% 13.03/12.96  all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))).
% 13.03/12.96  all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->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))))).
% 13.03/12.96  all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 13.03/12.96  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))).
% 13.03/12.96  all V_x_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))<->V_x_2!=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.96  all V_f_2 T_b T_a (c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_a,T_b,V_f_2)<-> (all B_x B_y (hAPP(V_f_2,B_x)=hAPP(V_f_2,B_y)))).
% 13.03/12.96  all V_n V_m V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless__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))->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)))).
% 13.03/12.96  all V_y_2 V_x_2 V_b_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x_2,V_y_2)))).
% 13.03/12.96  all V_z V_w c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))).
% 13.03/12.96  all V_b V_a V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)))).
% 13.03/12.96  all V_n V_m V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 13.03/12.96  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->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)))).
% 13.03/12.96  all V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))).
% 13.03/12.96  all V_y V_x T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y)))).
% 13.03/12.96  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))).
% 13.03/12.96  all V_n V_x T_a (class_RealVector_Oreal__normed__algebra__1(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n))).
% 13.03/12.96  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)).
% 13.03/12.96  all V_x T_a (class_RealVector_Oreal__normed__vector(T_a)-> -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.03/12.96  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))).
% 13.03/12.96  all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))).
% 13.03/12.96  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 13.03/12.96  all V_n V_x (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_x)),V_n)=c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))).
% 13.03/12.96  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 13.03/12.96  all V_y_2 V_x_2 T_a (class_RealVector_Oreal__algebra__1(T_a)-> (c_RealVector_Oof__real(T_a,V_x_2)=c_RealVector_Oof__real(T_a,V_y_2)<->V_x_2=V_y_2)).
% 13.03/12.96  all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),V_ya)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya))).
% 13.03/12.96  all V_b V_a_H V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H)),V_b)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b))).
% 13.03/12.96  all V_y V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y))).
% 13.03/12.96  all V_b_H V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H))).
% 13.03/12.96  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))).
% 13.03/12.96  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))).
% 13.03/12.96  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)).
% 13.03/12.96  all V_y V_x T_a (class_RealVector_Oreal__normed__div__algebra(T_a)->c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))).
% 13.03/12.96  all V_n V_x T_a (class_RealVector_Oreal__normed__div__algebra(T_a)->c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n)).
% 13.03/12.96  all V_y V_x T_a (class_RealVector_Oreal__algebra__1(T_a)->c_RealVector_Oof__real(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_RealVector_Oof__real(T_a,V_x)),c_RealVector_Oof__real(T_a,V_y))).
% 13.03/12.96  all V_y V_x T_a (class_RealVector_Oreal__algebra__1(T_a)&class_RealVector_Oreal__normed__vector(T_a)->c_RealVector_Oof__real(T_a,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Oplus__class_Oplus(T_a,c_RealVector_Oof__real(T_a,V_x),c_RealVector_Oof__real(T_a,V_y))).
% 13.03/12.96  all V_y V_x T_a (class_RealVector_Oreal__algebra__1(T_a)->c_RealVector_Oof__real(T_a,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Oplus__class_Oplus(T_a,c_RealVector_Oof__real(T_a,V_x),c_RealVector_Oof__real(T_a,V_y))).
% 13.03/12.96  all V_n V_x T_a (class_RealVector_Oreal__algebra__1(T_a)->c_RealVector_Oof__real(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_RealVector_Oof__real(T_a,V_x)),V_n)).
% 13.03/12.96  all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))))).
% 13.03/12.96  all V_n V_m V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))).
% 13.03/12.96  all V_y_2 V_x_2 V_b_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2)))).
% 13.03/12.96  all V_n_2 V_ma_2 V_aa_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_aa_2)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_ma_2)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_n_2)<->V_ma_2=V_n_2))).
% 13.03/12.96  c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))).
% 13.03/12.96  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.03/12.96  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.03/12.96  -(all B_w (c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_w),v_k____)),v_a____))!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))).
% 13.03/12.96  exists B_m (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m)& (all B_z (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),B_z)),B_m)))).
% 13.03/12.96  c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))=c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)).
% 13.03/12.96  all V_v V_u V_y V_a V_x T_a (class_Rings_Olinordered__semiring__1__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)-> (c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)=c_Groups_Oone__class_Oone(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,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))))))).
% 13.03/12.96  all V_y V_x V_c T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y)))->V_x=c_Groups_Ozero__class_Ozero(T_a)))).
% 13.03/12.96  all V_v V_u V_y V_a V_x T_a (class_Rings_Olinordered__semiring__1(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)-> (c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)=c_Groups_Oone__class_Oone(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,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))))))).
% 13.03/12.96  all V_a V_b c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_b,V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a)).
% 13.03/12.96  all V_d2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2)-> (exists B_e (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,V_d2)))).
% 13.03/12.96  hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.03/12.96  all B_w c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_w))).
% 13.03/12.96  all V_t V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_t)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_t,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_t)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))).
% 13.03/12.96  c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.03/12.96  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))).
% 13.03/12.96  all V_r (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)).
% 13.03/12.96  all V_l_2 V_ka_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_l_2)<-> (exists B_n (V_l_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,B_n)))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))).
% 13.03/12.96  all V_a T_a (class_Rings_Olinordered__idom(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)).
% 13.03/12.96  all T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a)).
% 13.03/12.96  all V_n V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n)).
% 13.03/12.96  all V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a))=c_RealVector_Onorm__class_Onorm(T_a,V_a)).
% 13.03/12.96  all V_d V_b V_c V_a T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))))).
% 13.03/12.96  all V_b_2 V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),V_b_2)<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)&c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2))).
% 13.03/12.96  all V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)).
% 13.03/12.96  all V_y V_x (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)=c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_y))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Oordered__ring__abs(T_a)-> ((c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)))& (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)))->c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))).
% 13.03/12.96  all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x)=c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)))).
% 13.03/12.96  all V_n V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n))=c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 13.03/12.96  all V_y V_x V_c (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))->V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.03/12.96  all V_r T_a (class_RealVector_Oreal__normed__algebra__1(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)).
% 13.03/12.96  all V_n V_a T_a (class_Rings_Olinordered__idom(T_a)->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),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n))).
% 13.03/12.96  all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 13.03/12.96  c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)).
% 13.03/12.96  all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))).
% 13.03/12.96  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)).
% 13.03/12.96  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)).
% 13.03/12.96  all V_b_2 V_aa_2 T_a (class_Rings_Oring__no__zero__divisors(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.96  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)))).
% 13.03/12.96  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))).
% 13.03/12.96  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)).
% 13.03/12.96  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)).
% 13.03/12.96  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 13.03/12.96  all V_c V_b V_e V_a T_a (class_Rings_Osemiring(T_a)->c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c)).
% 13.03/12.96  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))).
% 13.03/12.96  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)).
% 13.03/12.96  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))).
% 13.03/12.96  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)).
% 13.03/12.96  all V_b_2 V_aa_2 T_a (class_Rings_Oidom(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_aa_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)<->V_aa_2=V_b_2|V_aa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)&c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))).
% 13.03/12.96  all V_d V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,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))))))).
% 13.03/12.96  all V_d V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,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))))))).
% 13.03/12.96  all V_c V_a V_b T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,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))))).
% 13.03/12.96  all V_c V_a V_b T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,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))))).
% 13.03/12.96  all V_c V_b V_a T_a (class_Rings_Oordered__comm__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,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))))).
% 13.03/12.96  all V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,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))))).
% 13.03/12.96  all V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,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))))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))).
% 13.03/12.96  all V_b_2 V_aa_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2))).
% 13.03/12.96  all V_b_2 V_aa_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 13.03/12.96  all V_a T_a (class_Rings_Olinordered__ring(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))).
% 13.03/12.96  all V_a T_a (class_Rings_Olinordered__ring(T_a)-> -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.96  all V_b_2 V_ca_2 V_aa_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)&c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2))).
% 13.03/12.96  all V_b_2 V_aa_2 V_ca_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)&c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2))).
% 13.03/12.96  all V_b_2 V_aa_2 V_ca_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)))).
% 13.03/12.96  all V_a V_b T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)))).
% 13.03/12.96  all V_b_2 V_aa_2 V_ca_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2)))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))).
% 13.03/12.96  all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))).
% 13.03/12.96  all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 13.03/12.96  all V_c V_b V_a T_a (class_Rings_Olinordered__comm__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 13.03/12.96  all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))).
% 13.03/12.96  all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 13.03/12.96  all V_c V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 13.03/12.96  all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))).
% 13.03/12.96  all T_a (class_Rings_Olinordered__semidom(T_a)-> -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.96  all T_a (class_Rings_Olinordered__semidom(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.96  all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))).
% 13.03/12.96  all V_n V_m T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))))).
% 13.03/12.96  all V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 13.03/12.96  all V_a T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)))).
% 13.03/12.96  all V_d_2 V_b_2 V_ca_2 V_e_2 V_aa_2 T_a (class_Rings_Oring(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)<->V_ca_2=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2))).
% 13.03/12.96  all V_d_2 V_b_2 V_ca_2 V_e_2 V_aa_2 T_a (class_Rings_Oring(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)<->c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_ca_2)=V_d_2)).
% 13.03/12.96  all V_x_2 T_a (class_Rings_Oring__1__no__zero__divisors(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)=c_Groups_Oone__class_Oone(T_a)<->V_x_2=c_Groups_Oone__class_Oone(T_a)|V_x_2=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)))).
% 13.03/12.96  all V_b_2 V_aa_2 V_ca_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2)))).
% 13.03/12.96  all V_b_2 V_aa_2 V_ca_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_aa_2)))).
% 13.03/12.96  all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))).
% 13.03/12.96  all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))).
% 13.03/12.96  all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))).
% 13.03/12.96  all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))).
% 13.03/12.96  all V_b V_c V_a T_a (class_Rings_Olinordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 13.03/12.96  all V_b V_c V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 13.03/12.96  all V_b V_a V_c T_a (class_Rings_Olinordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 13.03/12.96  all V_b V_a V_c T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 13.03/12.96  all V_b V_c V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)))).
% 13.03/12.96  all V_b V_a V_c T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)))).
% 13.03/12.96  all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x))))).
% 13.03/12.96  all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x))))).
% 13.03/12.96  all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))).
% 13.03/12.96  all V_d_2 V_b_2 V_ca_2 V_e_2 V_aa_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2)))).
% 13.03/12.96  all V_d_2 V_b_2 V_ca_2 V_e_2 V_aa_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_ca_2),V_d_2))).
% 13.03/12.96  all V_d_2 V_b_2 V_ca_2 V_e_2 V_aa_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))<->c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2)))).
% 13.03/12.96  all V_d_2 V_b_2 V_ca_2 V_e_2 V_aa_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_ca_2),V_d_2))).
% 13.03/12.96  c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)).
% 13.03/12.96  c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))).
% 13.03/12.96  all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))).
% 13.03/12.96  all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 13.03/12.96  all V_x V_n T_a (class_Groups_Omonoid__mult(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))).
% 13.03/12.96  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.03/12.96  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)))))).
% 13.03/12.96  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)))))).
% 13.03/12.96  all V_m V_l V_y V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m))))).
% 13.03/12.96  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)).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Oinverse(T_a,V_b)->V_a=V_b)).
% 13.03/12.96  all V_b_2 V_aa_2 T_a (class_Rings_Odivision__ring__inverse__zero(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2)=c_Rings_Oinverse__class_Oinverse(T_a,V_b_2)<->V_aa_2=V_b_2)).
% 13.03/12.96  all V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=V_a).
% 13.03/12.96  all V_a T_a (class_RealVector_Oreal__normed__div__algebra(T_a)&class_Rings_Odivision__ring__inverse__zero(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a))).
% 13.03/12.96  all V_x T_a (class_RealVector_Oreal__div__algebra(T_a)&class_Rings_Odivision__ring__inverse__zero(T_a)->c_RealVector_Oof__real(T_a,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x))=c_Rings_Oinverse__class_Oinverse(T_a,c_RealVector_Oof__real(T_a,V_x))).
% 13.03/12.96  c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.03/12.96  all V_a T_a (class_RealVector_Oreal__normed__div__algebra(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)))).
% 13.03/12.96  all V_x T_a (class_RealVector_Oreal__div__algebra(T_a)-> (V_x!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)->c_RealVector_Oof__real(T_a,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x))=c_Rings_Oinverse__class_Oinverse(T_a,c_RealVector_Oof__real(T_a,V_x)))).
% 13.03/12.96  all T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 13.03/12.96  all V_aa_2 T_a (class_Rings_Odivision__ring__inverse__zero(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.96  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,V_a)!=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.96  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=V_a)).
% 13.03/12.96  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Groups_Ozero__class_Ozero(T_a)->V_a=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Oinverse(T_a,V_b)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->V_a=V_b)))).
% 13.03/12.96  all T_a (class_Rings_Odivision__ring(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a)).
% 13.03/12.96  all V_n V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_n)).
% 13.03/12.96  all V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)=c_Groups_Oone__class_Oone(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,V_a)=V_b)).
% 13.03/12.96  all V_n V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_n))).
% 13.03/12.96  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)))).
% 13.03/12.96  all V_u V_y V_x1 V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x1),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_u))->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1)))))).
% 13.03/12.96  all V_u V_y V_x1 V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x1),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_u))->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1)),V_u))))).
% 13.03/12.96  all V_x (V_x!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_x)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.03/12.96  all V_pb_2 T_a (class_Groups_Ozero(T_a)-> (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pb_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_pb_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))),c_Rings_Oinverse__class_Oinverse(T_a,V_b))))).
% 13.03/12.96  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a)=c_Groups_Oone__class_Oone(T_a))).
% 13.03/12.96  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Groups_Oone__class_Oone(T_a))).
% 13.03/12.96  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))),c_Rings_Oinverse__class_Oinverse(T_a,V_b))))).
% 13.03/12.96  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)).
% 13.03/12.96  all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 13.03/12.96  all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.03/12.96  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)).
% 13.03/12.96  all V_w c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_w).
% 13.03/12.96  all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z)).
% 13.03/12.96  all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_j,V_k)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_k))).
% 13.03/12.96  all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z)->V_z=V_w)).
% 13.03/12.96  all V_P_2 V_n_2 V_ma_2 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)))-> ((V_ma_2=V_n_2->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)))-> ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)))->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2))))).
% 13.03/12.96  all V_l V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)))).
% 13.03/12.96  all V_n V_k V_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k)).
% 13.03/12.96  all V_t V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)->V_s!=V_t).
% 13.03/12.96  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)->V_m!=V_n).
% 13.03/12.96  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 13.03/12.96  all V_y V_x (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x))).
% 13.03/12.96  all V_n_2 V_ma_2 (V_ma_2!=V_n_2<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)).
% 13.03/12.96  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 13.03/12.96  all V_n V_k V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 13.03/12.96  all V_n V_m V_k (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 13.03/12.96  all V_n_2 V_ka_2 V_ma_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_ka_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_ka_2)<->V_ma_2=V_n_2).
% 13.03/12.96  all V_n_2 V_ma_2 V_ka_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_ma_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_n_2)<->V_ma_2=V_n_2).
% 13.03/12.96  all V_k V_j V_i (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))).
% 13.03/12.96  all V_k V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))).
% 13.03/12.96  all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n)=V_m).
% 13.03/12.96  all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n)=V_m).
% 13.03/12.96  all V_z V_y V_x (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z))).
% 13.03/12.96  all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)).
% 13.03/12.96  all V_n_2 V_ma_2 V_ka_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_ma_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_n_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_ka_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ka_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)))).
% 13.03/12.96  all V_n V_m V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_m)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))).
% 13.03/12.96  all V_n_2 V_ma_2 V_ka_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_ma_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_n_2)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_ka_2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ka_2)<->V_ma_2=V_n_2))).
% 13.03/12.96  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->V_m=V_n)).
% 13.03/12.96  all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_k))).
% 13.03/12.96  all V_n V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i))=V_i).
% 13.03/12.96  all V_l V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l))).
% 13.03/12.96  all V_l V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))).
% 13.03/12.96  all V_n V_m (V_m=V_n->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 13.03/12.96  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)).
% 13.03/12.96  all V_n V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m).
% 13.03/12.96  all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n).
% 13.03/12.96  all V_w V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z)).
% 13.03/12.96  all V_z3 V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3))).
% 13.03/12.96  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))).
% 13.03/12.96  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))).
% 13.03/12.96  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))).
% 13.03/12.96  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)).
% 13.03/12.96  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.03/12.96  all V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 13.03/12.96  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.03/12.96  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.03/12.96  all V_n (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)).
% 13.03/12.96  all V_ma_2 V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ma_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)).
% 13.03/12.96  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m))).
% 13.03/12.96  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2=V_y_2).
% 13.03/12.96  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)&V_x_2!=V_y_2).
% 13.03/12.96  all V_n (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n).
% 13.03/12.96  all V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 13.03/12.96  all V_n_2 V_ma_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_ma_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.03/12.96  all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=V_m->V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.03/12.96  all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.03/12.96  all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 13.03/12.96  all V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.03/12.96  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.03/12.96  all V_n_2 V_ma_2 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)).
% 13.03/12.96  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)).
% 13.03/12.96  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)).
% 13.03/12.96  all V_n_2 V_ma_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_ma_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.03/12.96  all V_n_2 V_ma_2 V_ka_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2)<->V_ma_2=V_n_2|V_ka_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.03/12.96  all V_n_2 V_ka_2 V_ma_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_ka_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ka_2)<->V_ma_2=V_n_2|V_ka_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.03/12.96  all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k)).
% 13.03/12.96  all V_n V_m V_l V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)-> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 13.03/12.96  all V_l V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)))).
% 13.03/12.96  all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))).
% 13.03/12.96  all V_m V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))).
% 13.03/12.96  all V_m V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))).
% 13.03/12.96  all V_n V_m (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m).
% 13.03/12.96  all V_n_2 V_ma_2 V_ka_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)).
% 13.03/12.96  all V_ka_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_ka_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_ka_2),V_j_2)).
% 13.03/12.96  all V_i V_j (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i)).
% 13.03/12.96  all V_j V_i (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i)).
% 13.03/12.96  all V_b_2 V_aa_2 V_ca_2 (V_ca_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_aa_2),V_ca_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2)<->V_aa_2=V_b_2)).
% 13.03/12.96  all V_b_2 V_aa_2 V_ca_2 (V_ca_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_aa_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2)<->V_aa_2=V_b_2)).
% 13.03/12.96  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_m=V_n->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 13.03/12.96  all V_n_2 V_ma_2 V_ka_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_ma_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_n_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_ka_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ka_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)))).
% 13.03/12.96  all V_c V_b V_a (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_c,V_a)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)))).
% 13.03/12.96  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> (V_m!=V_n->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 13.03/12.96  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 13.03/12.96  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2=V_n_2).
% 13.03/12.96  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)&V_ma_2!=V_n_2).
% 13.03/12.96  all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)-> -(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n))).
% 13.03/12.96  all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 13.03/12.96  all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)).
% 13.03/12.96  all V_l V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)))).
% 13.03/12.96  all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)).
% 13.03/12.96  all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)).
% 13.03/12.96  all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))).
% 13.03/12.96  all V_ka_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_ka_2<->V_j_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_i_2))).
% 13.03/12.96  all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)=V_m).
% 13.03/12.96  all V_i_2 V_j_2 V_ka_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_j_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_ka_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_ka_2),V_j_2))).
% 13.03/12.96  all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)).
% 13.03/12.96  all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m).
% 13.03/12.96  all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))).
% 13.03/12.96  all V_m V_n V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k))).
% 13.03/12.96  all V_m V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))).
% 13.03/12.96  all V_m V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))).
% 13.03/12.96  all V_n_2 V_ma_2 V_ka_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)).
% 13.03/12.96  all V_i_2 V_ka_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_ka_2),V_i_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_ka_2))).
% 13.03/12.96  all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j)).
% 13.03/12.96  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)<-> (exists B_k (V_n_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k)))).
% 13.03/12.96  all V_m V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)).
% 13.03/12.96  all V_m V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 13.03/12.96  c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.03/12.96  all V_k V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))).
% 13.03/12.96  all V_n V_m V_k (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))).
% 13.03/12.96  all V_z V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y))).
% 13.03/12.96  all V_l V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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)))).
% 13.03/12.96  all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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))).
% 13.03/12.96  all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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))).
% 13.03/12.96  all V_m 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))).
% 13.03/12.96  all V_m 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)).
% 13.03/12.96  all V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z)=V_z).
% 13.03/12.96  all V_w V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2)),V_w)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w))).
% 13.03/12.96  all V_n_2 V_ma_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)<->V_ma_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)&V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.03/12.96  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).
% 13.03/12.96  all V_n_2 V_ma_2 (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)<->V_ma_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)&V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.03/12.96  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).
% 13.03/12.96  all V_y_2 V_x_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(T_a)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.96  all V_b V_a V_y V_x T_a (class_Rings_Oring(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b))).
% 13.03/12.96  all V_y_2 V_x_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_y_2=c_Groups_Ouminus__class_Ouminus(T_a,V_x_2))).
% 13.03/12.96  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 13.03/12.96  all V_b_2 V_aa_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))<-> -(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)& -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| (exists B_d (V_aa_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)& -hBOOL(hAPP(V_P_2,B_d)))))).
% 13.03/12.96  all V_b_2 V_aa_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))<-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)->hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))& (all B_d (V_aa_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)->hBOOL(hAPP(V_P_2,B_d))))).
% 13.03/12.96  all V_y_2 V_x_2 V_z_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2))).
% 13.03/12.97  all V_y V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)))).
% 13.03/12.97  all V_y V_x V_z (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y)))).
% 13.03/12.97  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 13.03/12.97  all V_n_2 V_ma_2 V_ka_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)).
% 13.03/12.97  all V_n_2 V_ka_2 V_ma_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_ka_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ka_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)).
% 13.03/12.97  all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))).
% 13.03/12.97  all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))).
% 13.03/12.97  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)).
% 13.03/12.97  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.03/12.97  all V_y_2 V_x_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)&V_y_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.03/12.97  all V_x V_u c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),V_u)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)).
% 13.03/12.97  all V_y_2 V_x_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_y_2=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)).
% 13.03/12.97  all V_aa_2 V_x_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_aa_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_x_2=V_aa_2).
% 13.03/12.97  all V_r_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_r_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r_2),V_x_2)&c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_r_2)).
% 13.03/12.97  all V_s V_r (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_s))).
% 13.03/12.97  all V_y V_x (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y))).
% 13.03/12.97  all V_y V_x (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y)))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)))).
% 13.03/12.97  all V_y_2 V_x_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))<->V_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  all V_y V_x T_a (class_Rings_Olinordered__ring(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))).
% 13.03/12.97  all V_y_2 V_x_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))<->V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  all V_y V_x T_a (class_Rings_Olinordered__ring(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  all V_x T_a (class_Rings_Oring__1(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)))).
% 13.03/12.97  all V_y_2 V_x_2 V_z_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2))).
% 13.03/12.97  all V_y_2 V_x_2 V_z_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2))).
% 13.03/12.97  all V_n_2 V_ma_2 V_ka_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))<-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2))).
% 13.03/12.97  all V_n_2 V_ka_2 V_ma_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_ka_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ka_2))<-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2))).
% 13.03/12.97  all V_n V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)))).
% 13.03/12.97  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.03/12.97  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2))).
% 13.03/12.97  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.03/12.97  all V_y_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2))).
% 13.03/12.97  all V_a ((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a))& (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a)=V_a)).
% 13.03/12.97  all V_r ((c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r))& (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)=V_r)).
% 13.03/12.97  all V_x (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)).
% 13.03/12.97  -(all B_t (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_t)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))-> -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))))).
% 13.03/12.97  all B_x (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),B_x)=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,B_x))).
% 13.03/12.97  all V_pb_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,V_pb_2),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____))-> (-c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,V_pb_2))-> (exists B_z (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_pb_2),B_z)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))).
% 13.03/12.97  exists B_q (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,B_q)=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)& (all B_x (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q),B_x)=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,B_x))))).
% 13.03/12.97  hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)-> (exists B_z (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_z)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))).
% 13.03/12.97  c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____)=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____).
% 13.03/12.97  all V_x V_r T_a (class_RealVector_Oreal__normed__div__algebra(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_r,c_RealVector_Onorm__class_Onorm(T_a,V_x))-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_r))))).
% 13.03/12.97  hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.03/12.97  -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)).
% 13.03/12.97  -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)).
% 13.03/12.97  all B_w c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_w))).
% 13.03/12.97  hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)).
% 13.03/12.97  c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)).
% 13.03/12.97  all V_n_2 V_ma_2 V_u_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2),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))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,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)))).
% 13.03/12.97  all V_n_2 V_ma_2 V_u_2 V_i_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2),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))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_ma_2),V_n_2))).
% 13.03/12.97  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))),c_Rings_Oinverse__class_Oinverse(T_a,V_b)))))).
% 13.03/12.97  all V_x_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)))).
% 13.03/12.97  hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))).
% 13.03/12.97  all B_z (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),B_z)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),B_z)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))).
% 13.03/12.97  hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex).
% 13.03/12.97  c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____)=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)).
% 13.03/12.97  -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))).
% 13.03/12.97  all V_wa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),V_wa_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),V_wa_2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))))).
% 13.03/12.97  all B_z (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),B_z)=c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),B_z)))).
% 13.03/12.97  all V_d V_b V_c V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d))).
% 13.03/12.97  all T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 13.03/12.97  all V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b))).
% 13.03/12.97  all V_n_2 V_ma_2 V_ka_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2)<->V_ka_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_ma_2=V_n_2).
% 13.03/12.97  all V_x_2 T_a (class_Fields_Ofield__inverse__zero(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)=c_Groups_Oone__class_Oone(T_a)<->V_x_2=c_Groups_Oone__class_Oone(T_a))).
% 13.03/12.97  all V_k V_j V_u V_i (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k)).
% 13.03/12.97  all V_a T_a (class_Fields_Olinordered__field__inverse__zero(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a))).
% 13.03/12.97  all V_aa_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 13.03/12.97  all V_aa_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 13.03/12.97  all V_aa_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 13.03/12.97  all V_aa_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 13.03/12.97  all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))).
% 13.03/12.97  all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)))).
% 13.03/12.97  all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))).
% 13.03/12.97  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 13.03/12.97  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 13.03/12.97  all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))))).
% 13.03/12.97  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 13.03/12.97  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 13.03/12.97  all V_a T_a (class_Fields_Olinordered__field(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)))).
% 13.03/12.97  all V_n_2 V_ma_2 V_ka_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2)<->V_ma_2=V_n_2)).
% 13.03/12.97  all V_n_2 V_ma_2 V_ka_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2))).
% 13.03/12.97  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 13.03/12.97  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 13.03/12.97  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)))).
% 13.03/12.97  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)))).
% 13.03/12.97  all V_x_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2))).
% 13.03/12.97  all V_b V_a T_a (class_Fields_Ofield(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a))),c_Rings_Oinverse__class_Oinverse(T_a,V_b))))).
% 13.03/12.97  all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 13.03/12.97  all V_x_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)&c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)))).
% 13.03/12.97  all V_a T_a (class_Fields_Ofield(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a)=c_Groups_Oone__class_Oone(T_a))).
% 13.03/12.97  all V_n_2 V_ma_2 V_ka_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2))).
% 13.03/12.97  all V_n_2 V_ma_2 V_u_2 V_i_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2),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))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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_ma_2),V_n_2))).
% 13.03/12.97  all V_n V_m V_u V_i V_j (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_i)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),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,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)).
% 13.03/12.97  all V_n_2 V_ma_2 V_u_2 V_i_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)-> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2)=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)<->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_ma_2)=V_n_2)).
% 13.03/12.97  all V_n_2 V_ma_2 V_u_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2),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))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,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)))).
% 13.03/12.97  all V_n V_m V_u V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),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,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))).
% 13.03/12.97  all V_n_2 V_ma_2 V_u_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2)=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_ma_2=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))).
% 13.03/12.97  all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 13.03/12.97  all V_x_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2))).
% 13.03/12.97  c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))-> (exists B_w c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),B_w)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.03/12.97  -(all B_x B_y (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),B_x)=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),B_y))).
% 13.03/12.97  all V_r_2 V_aa_2 V_x_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_aa_2)),V_r_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_r_2),V_x_2)&c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_r_2)))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))).
% 13.03/12.97  all V_a V_p V_c T_a (class_Rings_Ocomm__semiring__0(T_a)-> (c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 13.03/12.97  all V_x_2 T_a (class_Groups_Ozero(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=V_x_2<->V_x_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  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))).
% 13.03/12.97  all V_c V_b V_a T_a (class_Groups_Oab__semigroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))).
% 13.03/12.97  all V_ca_2 V_b_2 V_aa_2 T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2)=c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_ca_2)<->V_b_2=V_ca_2)).
% 13.03/12.97  all V_ca_2 V_aa_2 V_b_2 T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)=c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_aa_2)<->V_b_2=V_ca_2)).
% 13.03/12.97  all V_c V_b V_a T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)->V_b=V_c)).
% 13.03/12.97  all V_c V_b V_a T_a (class_Groups_Ocancel__ab__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)->V_b=V_c)).
% 13.03/12.97  all V_c V_a V_b T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_b,V_a)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)->V_b=V_c)).
% 13.03/12.97  all V_x_2 T_a (class_Groups_Oone(T_a)-> (c_Groups_Oone__class_Oone(T_a)=V_x_2<->V_x_2=c_Groups_Oone__class_Oone(T_a))).
% 13.03/12.97  all V_d_2 V_ca_2 V_b_2 V_aa_2 T_a (class_Groups_Oab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)-> (V_aa_2=V_b_2<->V_ca_2=V_d_2))).
% 13.03/12.97  all V_b_2 V_aa_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)<->V_aa_2=V_b_2)).
% 13.03/12.97  all V_b_2 V_aa_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)=V_b_2<->c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)=V_aa_2)).
% 13.03/12.97  all V_b_2 V_aa_2 T_a (class_Groups_Ogroup__add(T_a)-> (V_aa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)<->V_b_2=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))).
% 13.03/12.97  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).
% 13.03/12.97  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a))=c_Groups_Oabs__class_Oabs(T_a,V_a)).
% 13.03/12.97  all V_a T_a (class_Groups_Omonoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a).
% 13.03/12.97  all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  all V_a T_a (class_Groups_Omonoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 13.03/12.97  all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 13.03/12.97  all V_b_2 V_ca_2 V_aa_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2))).
% 13.03/12.97  all V_b_2 V_aa_2 V_ca_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2))).
% 13.03/12.97  all V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))).
% 13.03/12.97  all V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)))).
% 13.03/12.97  all V_d V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 13.03/12.97  all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b))).
% 13.03/12.97  all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b))).
% 13.03/12.97  all V_b_2 V_ca_2 V_aa_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2))).
% 13.03/12.97  all V_b_2 V_aa_2 V_ca_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2))).
% 13.03/12.97  all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))).
% 13.03/12.97  all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)))).
% 13.03/12.97  all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 13.03/12.97  all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 13.03/12.97  all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 13.03/12.97  all V_b_2 V_aa_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_aa_2=V_b_2)).
% 13.03/12.97  all V_b_2 V_aa_2 T_a (class_Groups_Oab__group__add(T_a)-> (V_aa_2=V_b_2<->c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  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)).
% 13.03/12.97  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).
% 13.03/12.97  all V_d_2 V_ca_2 V_b_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_ca_2,V_d_2)))).
% 13.03/12.97  all V_d_2 V_ca_2 V_b_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)-> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)<->c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_d_2)))).
% 13.03/12.97  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).
% 13.03/12.97  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).
% 13.03/12.97  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).
% 13.03/12.97  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).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)=V_aa_2<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (V_aa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)<->c_Groups_Ozero__class_Ozero(T_a)=V_aa_2)).
% 13.03/12.97  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)).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)))).
% 13.03/12.97  all V_aa_2 V_b_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2))).
% 13.03/12.97  all V_b_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2))).
% 13.03/12.97  all V_b_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b)=V_a).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=V_a).
% 13.03/12.97  all V_b_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)))).
% 13.03/12.97  all V_b_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2))).
% 13.03/12.97  all V_aa_2 V_b_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b))=V_b).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=V_b).
% 13.03/12.97  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)).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Groups_Oabs__class_Oabs(T_a,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  all T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b))).
% 13.03/12.97  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))).
% 13.03/12.97  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Oabs__class_Oabs(T_a,V_a)).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.03/12.97  all V_a V_b V_c T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 13.03/12.97  all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 13.03/12.97  all V_y_2 V_x_2 T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)-> (c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.03/12.97  all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 13.03/12.97  all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 13.03/12.97  all V_b_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))).
% 13.03/12.97  all V_b_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,V_a)=V_b)).
% 13.03/12.97  all V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 13.03/12.97  all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 13.03/12.97  all V_b_2 V_aa_2 T_a (class_Groups_Ogroup__add(T_a)-> (V_aa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)<->c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 13.03/12.97  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)).
% 13.03/12.97  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a)).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a))).
% 13.03/12.97  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a)).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_aa_2))<->V_aa_2!=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)))).
% 13.03/12.97  all V_b_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2)&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2))).
% 13.03/12.97  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 13.03/12.97  all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 13.03/12.97  all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.03/12.97  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.03/12.97  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Oabs__class_Oabs(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a))).
% 13.03/12.97  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Oabs__class_Oabs(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a))).
% 13.03/12.97  all V_a T_a (class_Groups_Oabs__if(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Oabs__class_Oabs(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a))& (-c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a)).
% 13.03/12.97  all V_d V_c V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))).
% 13.03/12.97  -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))).
% 13.03/12.97  c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))).
% 13.03/12.97  all V_x V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x)=c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)))).
% 13.03/12.97  all V_n V_b (V_b!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)-> (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (exists B_z c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),V_n)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))).
% 13.03/12.97  all V_r V_q V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_r)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r))).
% 13.03/12.97  all V_b_2 V_n_2 V_aa_2 T_a (class_Groups_Ozero(T_a)-> (c_Polynomial_Omonom(T_a,V_aa_2,V_n_2)=c_Polynomial_Omonom(T_a,V_b_2,V_n_2)<->V_aa_2=V_b_2)).
% 13.03/12.97  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)).
% 13.03/12.97  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)).
% 13.03/12.97  all V_b V_n V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_n)).
% 13.03/12.97  all V_n V_b V_m V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_m)),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))).
% 13.03/12.97  all V_n_2 V_aa_2 T_a (class_Groups_Ozero(T_a)-> (c_Polynomial_Omonom(T_a,V_aa_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  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))).
% 13.03/12.97  all V_n V_b V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_n)).
% 13.03/12.97  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))).
% 13.03/12.97  all V_a T_a (class_Groups_Ozero(T_a)->c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 13.03/12.97  all V_qa_2 V_pb_2 T_a (class_Int_Oring__char__0(T_a)&class_Rings_Oidom(T_a)-> (c_Polynomial_Opoly(T_a,V_pb_2)=c_Polynomial_Opoly(T_a,V_qa_2)<->V_pb_2=V_qa_2)).
% 13.03/12.97  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))).
% 13.03/12.97  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))).
% 13.03/12.97  all V_q T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q)=V_q).
% 13.03/12.97  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))).
% 13.03/12.97  all V_p T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=V_p).
% 13.03/12.97  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).
% 13.03/12.97  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)).
% 13.03/12.97  all V_x T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))->c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x))& (-c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))->c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x)=V_x)).
% 13.03/12.97  all V_qa_2 V_b_2 V_pb_2 V_aa_2 T_a (class_Groups_Ozero(T_a)-> (c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2)=c_Polynomial_OpCons(T_a,V_b_2,V_qa_2)<->V_aa_2=V_b_2&V_pb_2=V_qa_2)).
% 13.03/12.97  all V_p V_a T_a (class_Rings_Ocomm__ring(T_a)->c_Polynomial_Osmult(T_a,V_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p))).
% 13.03/12.97  all V_q V_a V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_Osmult(T_a,V_a,V_q))=c_Polynomial_Osmult(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))).
% 13.03/12.97  all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osmult(T_a,V_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q))).
% 13.03/12.97  all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Osmult(T_a,V_a,V_p)),V_q)=c_Polynomial_Osmult(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))).
% 13.03/12.97  all V_q V_p V_a T_a (class_Rings_Ocomm__ring(T_a)->c_Polynomial_Osmult(T_a,V_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q))=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q))).
% 13.03/12.97  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))).
% 13.03/12.97  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))).
% 13.03/12.97  all V_x V_q V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x)=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))).
% 13.03/12.97  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)).
% 13.03/12.97  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))).
% 13.03/12.97  all V_q V_b V_p V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q))=c_Polynomial_OpCons(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))).
% 13.03/12.97  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)).
% 13.03/12.97  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))).
% 13.03/12.97  all V_q V_b V_p V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q))=c_Polynomial_OpCons(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q))).
% 13.03/12.97  all V_p V_b V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Osmult(T_a,V_b,V_p))=c_Polynomial_Osmult(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_p)).
% 13.03/12.97  all V_p V_b V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osmult(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_p)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p))).
% 13.03/12.97  all V_p T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Polynomial_Osmult(T_a,c_Groups_Oone__class_Oone(T_a),V_p)=V_p).
% 13.03/12.97  all V_p V_a T_b (class_Groups_Oab__group__add(T_b)->c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_a,V_p))=c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),V_p))).
% 13.03/12.97  all V_p V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p))=c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))).
% 13.03/12.97  all V_p V_b V_a T_a (class_Rings_Ocomm__ring(T_a)->c_Polynomial_Osmult(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_p)=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p))).
% 13.03/12.97  all V_p V_a T_a (class_Rings_Ocomm__ring(T_a)->c_Polynomial_Osmult(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_p)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p))).
% 13.03/12.97  all V_pb_2 T_a (class_Int_Oring__char__0(T_a)&class_Rings_Oidom(T_a)-> (c_Polynomial_Opoly(T_a,V_pb_2)=c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))<->V_pb_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 13.03/12.97  all V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 13.03/12.97  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)).
% 13.03/12.97  all T_a (class_Groups_Ozero(T_a)->c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 13.03/12.97  all V_pb_2 V_aa_2 T_a (class_Groups_Ozero(T_a)-> (c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a)&V_pb_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 13.03/12.97  all V_pb_2 V_aa_2 T_a (class_Rings_Oidom(T_a)-> (c_Polynomial_Osmult(T_a,V_aa_2,V_pb_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a)|V_pb_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 13.03/12.97  all V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osmult(T_a,c_Groups_Ozero__class_Ozero(T_a),V_p)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 13.03/12.97  all T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))=c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 13.03/12.97  all V_x V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))).
% 13.03/12.97  all V_q V_a V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q))=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)))).
% 13.03/12.97  all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,V_p)),V_q)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_q),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)))).
% 13.03/12.97  all V_p V_b V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osmult(T_a,V_a,c_Polynomial_OpCons(T_a,V_b,V_p))=c_Polynomial_OpCons(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Polynomial_Osmult(T_a,V_a,V_p))).
% 13.03/12.97  all V_a V_p V_c T_a (class_Rings_Ocomm__semiring__0(T_a)-> (c_Polynomial_Osmult(T_a,V_c,V_p)=c_Polynomial_OpCons(T_a,V_a,V_p)->V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 13.03/12.97  exists B_z (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),B_z)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)).
% 13.03/12.97  all V_p V_c T_a (class_Rings_Ocomm__ring__1(T_a)->c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)),c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))=V_p).
% 13.03/12.97  all V_n_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)).
% 13.03/12.97  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))).
% 13.03/12.97  all V_c V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osynthetic__div(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_c)=c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c))).
% 13.03/12.97  all V_c V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,c_Polynomial_Osynthetic__div(T_a,V_p,V_c)))=c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c))).
% 13.03/12.97  all V_r V_q V_c V_p T_a (class_Rings_Ocomm__semiring__0(T_a)-> (c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,V_q))=c_Polynomial_OpCons(T_a,V_r,V_q)->V_r=hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)&V_q=c_Polynomial_Osynthetic__div(T_a,V_p,V_c))).
% 13.03/12.97  all V_x_2 (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))<->V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.03/12.97  all V_q V_p V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q))).
% 13.03/12.97  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)).
% 13.03/12.97  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))).
% 13.03/12.97  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))).
% 13.03/12.97  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)))).
% 13.03/12.97  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)).
% 13.03/12.97  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))).
% 13.03/12.97  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)).
% 13.03/12.97  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))).
% 13.03/12.97  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)).
% 13.03/12.97  all V_d V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))).
% 13.03/12.97  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b)).
% 13.03/12.97  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))).
% 13.03/12.97  all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d)).
% 13.03/12.97  all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d))).
% 13.03/12.97  all V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)).
% 13.03/12.97  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)).
% 13.03/12.97  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)).
% 13.03/12.97  all V_aa_2 V_b_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_b_2=c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 13.03/12.97  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a).
% 13.03/12.97  all V_z_2 V_x_2 V_y_2 V_wa_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_wa_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_wa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))<->V_wa_2=V_x_2|V_y_2=V_z_2)).
% 13.03/12.97  all V_b V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m)).
% 13.03/12.97  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 13.03/12.97  all V_d_2 V_ca_2 V_b_2 V_aa_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_aa_2!=V_b_2&V_ca_2!=V_d_2<->c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2))!=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)))).
% 13.03/12.97  all V_z V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z))).
% 13.03/12.97  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).
% 13.03/12.97  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).
% 13.03/12.97  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))).
% 13.03/12.97  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))).
% 13.03/12.97  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).
% 13.03/12.97  all V_d V_c V_b V_a V_r T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_r!=c_Groups_Ozero__class_Ozero(T_a)-> (V_a=V_b&V_c!=V_d->c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c))!=c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d))))).
% 13.03/12.97  all V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m)).
% 13.03/12.97  all V_a V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m)).
% 13.03/12.97  all V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_m,V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_m)).
% 13.03/12.97  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)).
% 13.03/12.97  all V_y V_x T_a (class_Rings_Ocomm__ring__1(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)=c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y))).
% 13.03/12.97  all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Opcompose(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_q)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q)))).
% 13.03/12.97  all V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 13.03/12.97  all T_a (class_RealVector_Oreal__algebra__1(T_a)&class_RealVector_Oreal__normed__vector(T_a)-> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B_x)),B_K)))))).
% 13.03/12.97  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))).
% 13.03/12.97  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))).
% 13.03/12.97  all V_n_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))<->V_x_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.03/12.97  all V_z V_y V_x (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z))).
% 13.03/12.97  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))).
% 13.03/12.97  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.03/12.97  all V_z (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.03/12.97  all V_aa_2 V_pb_2 T_a (class_Rings_Oidom(T_a)-> (hAPP(c_Polynomial_Opoly(T_a,V_pb_2),V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_pb_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Oorder(T_a,V_aa_2,V_pb_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.03/12.97  all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z).
% 13.03/12.97  all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)=V_z).
% 13.03/12.97  all V_n V_x 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n)).
% 13.03/12.97  all V_i ((c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))->c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_i))& (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))->c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)=V_i)).
% 13.03/12.97  all V_l_2 V_ka_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_ka_2,V_l_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_ka_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.03/12.97  all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))<->V_z_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 13.03/12.97  all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)->c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)))).
% 13.03/12.97  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint)<->V_ma_2=c_Groups_Oone__class_Oone(tc_Int_Oint)&V_n_2=c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 13.03/12.97  all V_z_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)).
% 13.03/12.97  c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 13.03/12.97  c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 13.03/12.97  c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.03/12.97  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).
% 13.03/12.97  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).
% 13.03/12.97  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)).
% 13.03/12.97  all V_wa_2 V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_wa_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_wa_2)&V_z_2!=V_wa_2).
% 13.03/12.97  all V_y V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x)).
% 13.03/12.97  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))).
% 13.03/12.97  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))).
% 13.03/12.97  all V_n V_m (c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n))=c_Groups_Oone__class_Oone(tc_Int_Oint)->c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m)=c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 13.03/12.97  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))).
% 13.03/12.97  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))).
% 13.03/12.97  all V_z_2 V_wa_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_wa_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2)).
% 13.03/12.97  all V_z V_z_H V_w V_w_H (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_H,V_z)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)))).
% 13.03/12.97  all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k))).
% 13.03/12.97  all V_z V_w (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)).
% 13.03/12.97  all V_w V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))).
% 13.03/12.97  all V_z_2 V_wa_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2)).
% 13.03/12.97  all V_z2 V_z1 V_w (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))).
% 13.03/12.97  all V_z_2 V_wa_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2)|V_wa_2=V_z_2).
% 13.03/12.97  all V_z_2 V_wa_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_wa_2,V_z_2)).
% 13.03/12.97  all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 13.03/12.97  all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 13.03/12.97  all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.03/12.97  all V_z (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z))).
% 13.03/12.97  c_Complex_Oii!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex).
% 13.03/12.97  c_Complex_Oii!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.03/12.97  all V_x (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),V_x))=c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_x)).
% 13.03/12.97  c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii)=c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii).
% 13.03/12.97  hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii)=c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)).
% 13.03/12.97  all V_x V_z V_d (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))).
% 13.03/12.97  all V_z V_x V_d (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)),V_z)).
% 13.03/12.97  all V_w V_z (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))).
% 13.03/12.97  all V_w V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w)).
% 13.03/12.97  all V_w V_z (c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))).
% 13.03/12.97  all V_z (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z))=V_z).
% 13.03/12.97  all V_w c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_w).
% 13.03/12.97  all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z)).
% 13.03/12.97  all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_j,V_k)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_k))).
% 13.03/12.97  all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z)->V_z=V_w)).
% 13.03/12.97  all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j))).
% 13.03/12.97  all V_z3 V_z2 V_z1 (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3))).
% 13.03/12.97  all V_z V_y V_x (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z))).
% 13.03/12.97  all V_w V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)).
% 13.03/12.97  all V_q V_r V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)-> (V_a=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint))))).
% 13.03/12.97  all V_q V_r V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)-> (V_a=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q)))).
% 13.03/12.97  all V_r_H V_q_H V_b_H V_r V_q V_b (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)=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_Orderings_Oord__class_Oless(tc_Int_Oint,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))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H,V_b)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,V_q))))))).
% 13.03/12.97  all V_r V_q V_r_H V_q_H V_b (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,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),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,V_q_H))))).
% 13.03/12.97  all V_r_H V_q_H V_b_H V_r V_q V_b (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)=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_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),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_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H,V_b)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,V_q_H))))))).
% 13.03/12.97  all V_r V_q V_r_H V_q_H V_b (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,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),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,V_q))))).
% 13.03/12.97  all V_r_H V_q_H V_b_H (c_Orderings_Oord__class_Oless(tc_Int_Oint,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))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))).
% 13.03/12.97  all V_r_H V_q_H V_b_H (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),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_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H)))).
% 13.03/12.97  all V_n V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))).
% 13.03/12.97  all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)))).
% 13.03/12.97  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)).
% 13.03/12.97  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)).
% 13.03/12.97  all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)))).
% 13.03/12.97  -(all B_m (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m)-> -(all B_z (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),B_z)),B_m))))).
% 13.03/12.97  all V_x T_a (class_Orderings_Opreorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x)).
% 13.03/12.97  all V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)<-> (all B_x c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x))))).
% 13.03/12.97  all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)).
% 13.03/12.97  all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (V_x_2=V_y_2<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 13.03/12.97  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (V_x=V_y->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y))).
% 13.03/12.97  all V_x_2 V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)->c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)))).
% 13.03/12.97  all V_x_2 V_y_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 13.03/12.97  all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)))).
% 13.03/12.97  all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a)))).
% 13.03/12.97  all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (V_b=V_c->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)))).
% 13.03/12.97  all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (V_b=V_c->c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a)))).
% 13.03/12.97  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)->V_x=V_y))).
% 13.03/12.97  all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_z)))).
% 13.03/12.97  all V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->V_x=V_y))).
% 13.03/12.97  all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x)))).
% 13.03/12.97  all V_x_2 V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)->c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)))).
% 13.03/12.97  all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x))).
% 13.03/12.97  all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (V_x!=V_y->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 13.03/12.97  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 13.03/12.97  all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 13.03/12.97  all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 13.03/12.97  all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))).
% 13.03/12.97  all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))).
% 13.03/12.97  all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_b)->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))).
% 13.03/12.97  all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))).
% 13.03/12.97  all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> -c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 13.03/12.97  all V_b V_a T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> -c_Orderings_Oord__class_Oless(T_a,V_b,V_a))).
% 13.03/12.97  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_y!=V_x)).
% 13.03/12.97  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)).
% 13.03/12.97  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 13.03/12.97  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 13.03/12.97  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)).
% 13.03/12.97  all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 13.03/12.97  all V_x_2 V_y_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 13.03/12.97  all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x)).
% 13.03/12.97  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|V_x_2=V_y_2)).
% 13.03/12.97  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (V_x_2!=V_y_2<->c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2))).
% 13.03/12.97  all V_x T_a (class_Orderings_Opreorder(T_a)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_x)).
% 13.03/12.97  all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 13.03/12.97  all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 13.03/12.97  all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 13.03/12.97  all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 13.03/12.97  all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (V_a!=V_b->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 13.03/12.97  all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (V_a!=V_b->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 13.03/12.97  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y)).
% 13.03/12.97  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 13.03/12.97  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y))).
% 13.03/12.97  all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_y))).
% 13.03/12.97  all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 13.03/12.97  all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 13.03/12.97  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 13.03/12.97  all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y))).
% 13.03/12.97  all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x))).
% 13.03/12.97  all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2)).
% 13.03/12.97  all V_y_2 V_x_2 T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)& -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 13.03/12.97  all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)&V_x_2!=V_y_2)).
% 13.03/12.97  all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x)).
% 13.03/12.97  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2))).
% 13.03/12.97  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 13.03/12.97  exists B_k B_a (B_a!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)&B_k!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)& (exists B_q (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,B_q),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))& (all B_z (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),B_z)=c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),B_k)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,B_a,B_q)),B_z)))))))).
% 13.03/12.97  all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 13.03/12.97  all V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)& -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2))).
% 13.03/12.97  c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.03/12.97  all V_x c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)).
% 13.03/12.97  all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y))).
% 13.03/12.97  c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.03/12.97  all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_RComplete_Onatceiling(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.03/12.97  all V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.03/12.97  all T_a (class_Power_Opower(T_a)->c_Power_Opower__class_Opower(T_a)=c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a))).
% 13.03/12.97  all T_a (class_RealVector_Oreal__algebra__1(T_a)&class_RealVector_Oreal__normed__vector(T_a)-> (exists B_K (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B_x)),B_K)))))).
% 13.03/12.97  all V_aa_2 V_times_2 V_one_2 T_a (hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_aa_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_one_2).
% 13.03/12.97  all V_X_2 V_M_2 T_a T_b (class_RealVector_Oreal__normed__vector(T_b)&class_Orderings_Oord(T_a)-> ((all B_n (c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2,B_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,B_n))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))-> (all B_n (c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2,B_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2)))))))).
% 13.03/12.97  all V_y T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)))))).
% 13.03/12.97  all T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_a B_b c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K)))))).
% 13.03/12.97  all V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)))))).
% 13.03/12.97  -(all B_q (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,B_q)=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)-> -(all B_x (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q),B_x)=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,B_x)))))).
% 13.03/12.97  all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 13.03/12.97  c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.03/12.97  c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.03/12.97  all V_x c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)).
% 13.03/12.97  all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y))).
% 13.03/12.97  all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_RComplete_Onatfloor(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.03/12.97  all V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2)).
% 13.03/12.97  all V_b V_a (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b))))).
% 13.03/12.97  all V_x V_y ((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))& (-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))).
% 13.03/12.97  all V_z V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 13.03/12.97  all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y)))).
% 13.03/12.97  all V_x V_y (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)).
% 13.03/12.97  all V_y V_z V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 13.03/12.97  all V_z V_y V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 13.03/12.97  all V_y V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)).
% 13.03/12.97  all V_y V_z V_x (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_z)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 13.03/12.97  all V_x V_n (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))->c_RComplete_Onatceiling(V_x)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 13.03/12.97  all V_pb_2 V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2))<->c_Polynomial_Opos__poly(T_a,V_pb_2)|V_pb_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))&c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 13.03/12.97  all V_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 13.03/12.97  all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 13.03/12.97  all V_ma_2 V_n_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)).
% 13.03/12.97  all V_n (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.03/12.97  all V_n V_m (hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n)=c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))).
% 13.03/12.97  all V_n V_m (c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n)).
% 13.12/12.97  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))))).
% 13.12/12.97  all V_x (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x))=c_RealDef_Oreal(tc_Nat_Onat,V_x)).
% 13.12/12.97  all V_n_2 (c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.12/12.97  c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/12.97  all V_n V_m (c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 13.12/12.97  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)))).
% 13.12/12.97  all V_ma_2 V_n_2 (c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)<->V_n_2=V_ma_2).
% 13.12/12.97  all V_q V_p T_a (class_Rings_Olinordered__idom(T_a)-> (c_Polynomial_Opos__poly(T_a,V_p)-> (c_Polynomial_Opos__poly(T_a,V_q)->c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))))).
% 13.12/12.97  all V_n V_m (c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 13.12/12.97  c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.12/12.97  all V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.12/12.97  all V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))).
% 13.12/12.97  all V_ma_2 V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_ma_2)).
% 13.12/12.97  all V_y_2 V_x_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)<->V_x_2=V_y_2|c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)))).
% 13.12/12.97  all V_n (c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n).
% 13.12/12.97  all V_n (c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n).
% 13.12/12.97  all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x)).
% 13.12/12.97  all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a))).
% 13.12/12.97  all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)).
% 13.12/12.97  all V_n V_x (V_x=c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))->c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n)).
% 13.12/12.97  all V_n_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 13.12/12.97  all V_ma_2 V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))).
% 13.12/12.97  all V_ma_2 V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_ma_2)<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_ma_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))).
% 13.12/12.97  all V_aa_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_aa_2,c_RComplete_Onatfloor(V_x_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_aa_2),V_x_2))).
% 13.12/12.97  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))).
% 13.12/12.97  all V_aa_2 V_x_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_aa_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_aa_2)))).
% 13.12/12.97  all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.12/12.97  all V_x V_a (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)->c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)).
% 13.12/12.97  all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))).
% 13.12/12.97  all V_x V_a (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)->c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)).
% 13.12/12.97  all V_n V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n))).
% 13.12/12.97  all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)).
% 13.12/12.97  all V_n V_z (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 13.12/12.97  all V_x V_n (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))->c_RComplete_Onatfloor(V_x)=V_n)).
% 13.12/12.97  all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)).
% 13.12/12.97  all V_y_2 V_x_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)<->c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)))).
% 13.12/12.97  all V_n V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n))).
% 13.12/12.97  all V_r (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)-> (exists B_n (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_r)&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,B_n))))).
% 13.12/12.97  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))).
% 13.12/12.97  all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Odecse_q(T_a,V_X_2)<-> (all B_m B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)))))).
% 13.12/12.97  all V_p V_z V_e (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_e)-> (exists B_d (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)& (all B_w (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,V_z)))&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,V_z)),B_d)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),B_w),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),V_z))),V_e)))))).
% 13.12/12.97  all V_y V_x T_a (class_Lattices_Oboolean__algebra(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x)))).
% 13.12/12.97  all V_y_2 V_x_2 T_a (class_Lattices_Oboolean__algebra(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 13.12/12.97  all V_y_2 V_x_2 T_a (class_Lattices_Oboolean__algebra(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)<->V_x_2=V_y_2)).
% 13.12/12.97  all V_x_2 V_A_2 T_b T_a (class_Groups_Ouminus(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2))).
% 13.12/12.97  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).
% 13.12/12.97  all V_x_2 V_B_2 V_A_2 T_b T_a (class_Groups_Ominus(T_a)->hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2)=c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2))).
% 13.12/12.97  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).
% 13.12/12.97  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).
% 13.12/12.97  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)).
% 13.12/12.97  all T_a (class_RealVector_Oreal__algebra__1(T_a)&class_RealVector_Oreal__normed__vector(T_a)-> (exists B_K all B_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B_x)),B_K)))).
% 13.12/12.97  all V_x T_a (class_Rings_Olinordered__idom(T_a)-> (V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))& (V_x!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))-> (c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)->c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x)=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))& (-c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)->c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))))).
% 13.12/12.97  all V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 13.12/12.97  all V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 13.12/12.97  all V_x T_a (class_Rings_Olinordered__idom(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x))=V_x).
% 13.12/12.97  all V_k T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,V_k)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k))).
% 13.12/12.97  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))).
% 13.12/12.97  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))).
% 13.12/12.97  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)).
% 13.12/12.97  all V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.12/12.97  all V_x_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.12/12.97  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)).
% 13.12/12.97  all V_r T_a (class_RealVector_Oreal__normed__algebra__1(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r))=c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r))).
% 13.12/12.97  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)).
% 13.12/12.97  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))).
% 13.12/12.97  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)).
% 13.12/12.97  all V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_aa_2)=c_Groups_Oone__class_Oone(T_a)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 13.12/12.97  all V_a T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Groups_Osgn__class_Osgn(T_a,V_a)=c_Groups_Oone__class_Oone(T_a))).
% 13.12/12.97  all V_x T_a (class_Groups_Osgn__if(T_a)-> (V_x=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Ozero__class_Ozero(T_a))& (V_x!=c_Groups_Ozero__class_Ozero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)->c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Oone__class_Oone(T_a))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)->c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))))).
% 13.12/12.97  all V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_aa_2)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 13.12/12.97  all V_a T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Osgn__class_Osgn(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)))).
% 13.12/12.97  all V_x T_a (class_RealVector_Oreal__normed__vector(T_a)-> (V_x=c_Groups_Ozero__class_Ozero(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))& (V_x!=c_Groups_Ozero__class_Ozero(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.12/12.97  all V_p V_a T_a (class_Rings_Oidom(T_a)->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p)).
% 13.12/12.97  all V_h V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)))).
% 13.12/12.97  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))).
% 13.12/12.97  all V_y_2 V_x_2 T_a (class_Rings_Ocomm__ring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))<->c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2))).
% 13.12/12.97  all V_y_2 V_x_2 T_a (class_Rings_Ocomm__ring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2)<->c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2))).
% 13.12/12.97  all V_z V_y V_x T_a (class_Rings_Ocomm__ring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)-> (c_Rings_Odvd__class_Odvd(T_a,V_x,V_z)->c_Rings_Odvd__class_Odvd(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_z))))).
% 13.12/12.97  all V_ta_2 V_D_2 V_d_2 T_a (class_Rings_Ocomm__ring(T_a)&class_Rings_Odvd(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)-> (all B_x B_k (c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_ta_2))<->c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_ta_2)))))).
% 13.12/12.97  all V_ta_2 V_D_2 V_d_2 T_a (class_Rings_Ocomm__ring(T_a)&class_Rings_Odvd(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)-> (all B_x B_k (c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_ta_2))<->c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_ta_2)))))).
% 13.12/12.97  all V_l_2 V_P_2 T_a (class_Rings_Odvd(T_a)&class_Rings_Osemiring__0(T_a)-> ((exists B_x hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x))))<-> (exists B_x (c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a)))&hBOOL(hAPP(V_P_2,B_x)))))).
% 13.12/12.97  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)-> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)->c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))))).
% 13.12/12.97  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oone__class_Oone(T_a),V_a)).
% 13.12/12.97  all V_h_2 V_pb_2 T_a (class_Rings_Ocomm__semiring__0(T_a)-> (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_pb_2,V_h_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))<->V_pb_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 13.12/12.97  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))).
% 13.12/12.97  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)-> (c_Rings_Odvd__class_Odvd(T_a,V_b,V_c)->c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)))).
% 13.12/12.97  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Rings_Odvd__class_Odvd(T_a,V_a,V_a)).
% 13.12/12.97  all V_a V_q V_p T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q)))).
% 13.12/12.97  all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q)->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q))).
% 13.12/12.97  all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 13.12/12.97  class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex).
% 13.12/12.97  class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat).
% 13.12/12.97  class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint).
% 13.12/12.97  all T_2 T_1 (class_Lattices_Oboolean__algebra(T_1)->class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))).
% 13.12/12.97  all T_2 T_1 (class_Orderings_Opreorder(T_1)->class_Orderings_Opreorder(tc_fun(T_2,T_1))).
% 13.12/12.97  all T_2 T_1 (class_Orderings_Oorder(T_1)->class_Orderings_Oorder(tc_fun(T_2,T_1))).
% 13.12/12.97  all T_2 T_1 (class_Orderings_Oord(T_1)->class_Orderings_Oord(tc_fun(T_2,T_1))).
% 13.12/12.97  all T_2 T_1 (class_Groups_Ouminus(T_1)->class_Groups_Ouminus(tc_fun(T_2,T_1))).
% 13.12/12.97  all T_2 T_1 (class_Groups_Ominus(T_1)->class_Groups_Ominus(tc_fun(T_2,T_1))).
% 13.12/12.97  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 13.12/12.97  class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 13.12/12.97  class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 13.12/12.97  class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 13.12/12.97  class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint).
% 13.12/12.97  class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 13.12/12.97  class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint).
% 13.12/12.97  class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint).
% 13.12/12.97  class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 13.12/12.97  class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 13.12/12.97  class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 13.12/12.97  class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 13.12/12.97  class_Rings_Oordered__cancel__semiring(tc_Int_Oint).
% 13.12/12.97  class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 13.12/12.97  class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 13.12/12.97  class_Rings_Oordered__comm__semiring(tc_Int_Oint).
% 13.12/12.97  class_Rings_Olinordered__semiring__1(tc_Int_Oint).
% 13.12/12.97  class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 13.12/12.97  class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 13.12/12.97  class_Rings_Olinordered__semiring(tc_Int_Oint).
% 13.12/12.97  class_Rings_Olinordered__semidom(tc_Int_Oint).
% 13.12/12.97  class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 13.12/12.97  class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 13.12/12.97  class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 13.12/12.97  class_Rings_Oordered__semiring(tc_Int_Oint).
% 13.12/12.97  class_Rings_Oordered__ring__abs(tc_Int_Oint).
% 13.12/12.97  class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 13.12/12.97  class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 13.12/12.97  class_Rings_Olinordered__ring(tc_Int_Oint).
% 13.12/12.97  class_Rings_Olinordered__idom(tc_Int_Oint).
% 13.12/12.97  class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 13.12/12.97  class_Rings_Ocomm__semiring__0(tc_Int_Oint).
% 13.12/12.97  class_Rings_Ocomm__semiring(tc_Int_Oint).
% 13.12/12.97  class_Groups_Oab__group__add(tc_Int_Oint).
% 13.12/12.97  class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 13.12/12.97  class_Rings_Oordered__ring(tc_Int_Oint).
% 13.12/12.97  class_Orderings_Opreorder(tc_Int_Oint).
% 13.12/12.97  class_Orderings_Olinorder(tc_Int_Oint).
% 13.12/12.97  class_Groups_Omonoid__mult(tc_Int_Oint).
% 13.12/12.97  class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 13.12/12.97  class_Groups_Omonoid__add(tc_Int_Oint).
% 13.12/12.97  class_Rings_Osemiring__0(tc_Int_Oint).
% 13.12/12.97  class_Groups_Ogroup__add(tc_Int_Oint).
% 13.12/12.97  class_Rings_Omult__zero(tc_Int_Oint).
% 13.12/12.97  class_Rings_Ocomm__ring(tc_Int_Oint).
% 13.12/12.97  class_Orderings_Oorder(tc_Int_Oint).
% 13.12/12.97  class_Int_Oring__char__0(tc_Int_Oint).
% 13.12/12.97  class_Rings_Osemiring(tc_Int_Oint).
% 13.12/12.97  class_Orderings_Oord(tc_Int_Oint).
% 13.12/12.97  class_Groups_Ouminus(tc_Int_Oint).
% 13.12/12.97  class_Groups_Osgn__if(tc_Int_Oint).
% 13.12/12.97  class_Groups_Oabs__if(tc_Int_Oint).
% 13.12/12.97  class_Rings_Oring__1(tc_Int_Oint).
% 13.12/12.97  class_Groups_Ominus(tc_Int_Oint).
% 13.12/12.97  class_Power_Opower(tc_Int_Oint).
% 13.12/12.97  class_Groups_Ozero(tc_Int_Oint).
% 13.12/12.97  class_Rings_Oring(tc_Int_Oint).
% 13.12/12.97  class_Rings_Oidom(tc_Int_Oint).
% 13.12/12.97  class_Groups_Oone(tc_Int_Oint).
% 13.12/12.97  class_Rings_Odvd(tc_Int_Oint).
% 13.12/12.97  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 13.12/12.97  class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 13.12/12.97  class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 13.12/12.97  class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 13.12/12.97  class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 13.12/12.97  class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 13.12/12.97  class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 13.12/12.97  class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 13.12/12.97  class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 13.12/12.97  class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 13.12/12.97  class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 13.12/12.97  class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 13.12/12.97  class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 13.12/12.97  class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 13.12/12.97  class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 13.12/12.97  class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 13.12/12.97  class_Rings_Oordered__semiring(tc_Nat_Onat).
% 13.12/12.97  class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 13.12/12.97  class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 13.12/12.97  class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 13.12/12.97  class_Rings_Ocomm__semiring__0(tc_Nat_Onat).
% 13.12/12.97  class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 13.12/12.97  class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 13.12/12.97  class_Orderings_Opreorder(tc_Nat_Onat).
% 13.12/12.97  class_Orderings_Olinorder(tc_Nat_Onat).
% 13.12/12.97  class_Groups_Omonoid__mult(tc_Nat_Onat).
% 13.12/12.97  class_Groups_Omonoid__add(tc_Nat_Onat).
% 13.12/12.97  class_Rings_Osemiring__0(tc_Nat_Onat).
% 13.12/12.97  class_Rings_Omult__zero(tc_Nat_Onat).
% 13.12/12.97  class_Orderings_Oorder(tc_Nat_Onat).
% 13.12/12.97  class_Rings_Osemiring(tc_Nat_Onat).
% 13.12/12.97  class_Orderings_Oord(tc_Nat_Onat).
% 13.12/12.97  class_Groups_Ominus(tc_Nat_Onat).
% 13.12/12.97  class_Power_Opower(tc_Nat_Onat).
% 13.12/12.97  class_Groups_Ozero(tc_Nat_Onat).
% 13.12/12.97  class_Groups_Oone(tc_Nat_Onat).
% 13.12/12.97  class_Rings_Odvd(tc_Nat_Onat).
% 13.12/12.97  class_Lattices_Oboolean__algebra(tc_HOL_Obool).
% 13.12/12.97  class_Orderings_Opreorder(tc_HOL_Obool).
% 13.12/12.97  class_Orderings_Oorder(tc_HOL_Obool).
% 13.12/12.97  class_Orderings_Oord(tc_HOL_Obool).
% 13.12/12.97  class_Groups_Ouminus(tc_HOL_Obool).
% 13.12/12.97  class_Groups_Ominus(tc_HOL_Obool).
% 13.12/12.97  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal).
% 13.12/12.97  class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal).
% 13.12/12.97  class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal).
% 13.12/12.97  class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal).
% 13.12/12.97  class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal).
% 13.12/12.97  class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal).
% 13.12/12.97  class_RealVector_Oreal__div__algebra(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Olinordered__semiring(tc_RealDef_Oreal).
% 13.12/12.97  class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal).
% 13.12/12.97  class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Olinordered__semidom(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Oab__semigroup__add(tc_RealDef_Oreal).
% 13.12/12.97  class_Fields_Olinordered__field(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Oordered__semiring(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Oordered__ring__abs(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Ono__zero__divisors(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Olinordered__ring(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Olinordered__idom(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Odivision__ring(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Ocomm__semiring(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Oab__group__add(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Oordered__ring(tc_RealDef_Oreal).
% 13.12/12.97  class_Orderings_Opreorder(tc_RealDef_Oreal).
% 13.12/12.97  class_Orderings_Olinorder(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Omonoid__mult(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Ocomm__ring__1(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Omonoid__add(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Osemiring__0(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Ogroup__add(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Omult__zero(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Ocomm__ring(tc_RealDef_Oreal).
% 13.12/12.97  class_Orderings_Oorder(tc_RealDef_Oreal).
% 13.12/12.97  class_Int_Oring__char__0(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Osemiring(tc_RealDef_Oreal).
% 13.12/12.97  class_Orderings_Oord(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Ouminus(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Osgn__if(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Oabs__if(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Oring__1(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Ominus(tc_RealDef_Oreal).
% 13.12/12.97  class_Fields_Ofield(tc_RealDef_Oreal).
% 13.12/12.97  class_Power_Opower(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Ozero(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Oring(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Oidom(tc_RealDef_Oreal).
% 13.12/12.97  class_Groups_Oone(tc_RealDef_Oreal).
% 13.12/12.97  class_Rings_Odvd(tc_RealDef_Oreal).
% 13.12/12.97  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex).
% 13.12/12.97  class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex).
% 13.12/12.97  class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex).
% 13.12/12.97  class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex).
% 13.12/12.97  class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex).
% 13.12/12.97  class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex).
% 13.12/12.97  class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex).
% 13.12/12.97  class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex).
% 13.12/12.97  class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex).
% 13.12/12.97  class_RealVector_Oreal__div__algebra(tc_Complex_Ocomplex).
% 13.12/12.97  class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex).
% 13.12/12.97  class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex).
% 13.12/12.97  class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex).
% 13.12/12.97  class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex).
% 13.12/12.97  class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex).
% 13.12/12.97  class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex).
% 13.12/12.97  class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex).
% 13.12/12.97  class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex).
% 13.12/12.97  class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex).
% 13.12/12.97  class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex).
% 13.12/12.97  class_Rings_Odivision__ring(tc_Complex_Ocomplex).
% 13.12/12.97  class_Rings_Ocomm__semiring(tc_Complex_Ocomplex).
% 13.12/12.97  class_Groups_Oab__group__add(tc_Complex_Ocomplex).
% 13.12/12.97  class_Rings_Ozero__ne_q__one(tc_Complex_Ocomplex).
% 13.12/12.97  class_Groups_Omonoid__mult(tc_Complex_Ocomplex).
% 13.12/12.97  class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex).
% 13.12/12.97  class_Groups_Omonoid__add(tc_Complex_Ocomplex).
% 13.12/12.97  class_Rings_Osemiring__0(tc_Complex_Ocomplex).
% 13.12/12.97  class_Groups_Ogroup__add(tc_Complex_Ocomplex).
% 13.12/12.97  class_Rings_Omult__zero(tc_Complex_Ocomplex).
% 13.12/12.97  class_Rings_Ocomm__ring(tc_Complex_Ocomplex).
% 13.12/12.97  class_Int_Oring__char__0(tc_Complex_Ocomplex).
% 13.12/12.97  class_Rings_Osemiring(tc_Complex_Ocomplex).
% 13.12/12.97  class_Groups_Ouminus(tc_Complex_Ocomplex).
% 13.12/12.97  class_Rings_Oring__1(tc_Complex_Ocomplex).
% 13.12/12.97  class_Groups_Ominus(tc_Complex_Ocomplex).
% 13.12/12.97  class_Fields_Ofield(tc_Complex_Ocomplex).
% 13.12/12.97  class_Power_Opower(tc_Complex_Ocomplex).
% 13.12/12.98  class_Groups_Ozero(tc_Complex_Ocomplex).
% 13.12/12.98  class_Rings_Oring(tc_Complex_Ocomplex).
% 13.12/12.98  class_Rings_Oidom(tc_Complex_Ocomplex).
% 13.12/12.98  class_Groups_Oone(tc_Complex_Ocomplex).
% 13.12/12.98  class_Rings_Odvd(tc_Complex_Ocomplex).
% 13.12/12.98  all T_1 (class_Rings_Oidom(T_1)->class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Oorder(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Osemiring(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Oord(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ouminus(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Oring__1(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ominus(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Power_Opower(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Groups_Ozero(T_1)->class_Groups_Ozero(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Oring(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oidom(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Oone(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Odvd(tc_Polynomial_Opoly(T_1))).
% 13.12/12.98  -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.12/12.98  end_of_list.
% 13.12/12.98  
% 13.12/12.98  -------> usable clausifies to:
% 13.12/12.98  
% 13.12/12.98  list(usable).
% 13.12/12.98  0 [] A=A.
% 13.12/12.98  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.
% 13.12/12.98  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.12/12.98  0 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)).
% 13.12/12.98  0 [] v_k____!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.98  0 [] v_a____!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.12/12.98  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____).
% 13.12/12.98  0 [] c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))=c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))).
% 13.12/12.98  0 [] c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____))=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.12/12.98  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)).
% 13.12/12.98  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)=c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)).
% 13.12/12.98  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)).
% 13.12/12.98  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 13.12/12.98  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 13.12/12.98  0 [] c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))))=c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))).
% 13.12/12.98  0 [] c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))=c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))).
% 13.12/12.98  0 [] c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))=c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))).
% 13.12/12.98  0 [] -class_RealVector_Oreal__algebra__1(T_a)|c_RealVector_Oof__real(T_a,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(T_a).
% 13.12/12.98  0 [] -class_RealVector_Oreal__normed__algebra__1(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.12/12.98  0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s)).
% 13.12/12.98  0 [] -class_RealVector_Oreal__normed__algebra(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s)).
% 13.12/12.98  0 [] v_w____!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.12/12.98  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____).
% 13.12/12.98  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)).
% 13.12/12.98  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.12/12.98  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))).
% 13.12/12.98  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_k____)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),v_k____)).
% 13.12/12.98  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),B_z)),v_m____).
% 13.12/12.98  0 [] c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))).
% 13.12/12.98  0 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)).
% 13.12/12.98  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.12/12.98  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))).
% 13.12/12.98  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))).
% 13.12/12.98  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)).
% 13.12/12.98  0 [] -class_RealVector_Oreal__algebra__1(T_a)|c_RealVector_Oof__real(T_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.98  0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Oof__real(T_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.98  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/12.98  0 [] -class_RealVector_Oreal__algebra__1(T_a)|c_RealVector_Oof__real(T_a,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))=c_Groups_Ouminus__class_Ouminus(T_a,c_RealVector_Oof__real(T_a,V_x)).
% 13.12/12.98  0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Oof__real(T_a,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))=c_Groups_Ouminus__class_Ouminus(T_a,c_RealVector_Oof__real(T_a,V_x)).
% 13.12/12.98  0 [] -class_RealVector_Oreal__algebra__1(T_a)|c_RealVector_Oof__real(T_a,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,c_RealVector_Oof__real(T_a,V_x),c_RealVector_Oof__real(T_a,V_y)).
% 13.12/12.98  0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Oof__real(T_a,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,c_RealVector_Oof__real(T_a,V_x),c_RealVector_Oof__real(T_a,V_y)).
% 13.12/12.98  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] -class_RealVector_Oreal__algebra__1(T_a)|c_RealVector_Oof__real(T_a,V_x_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/12.99  0 [] -class_RealVector_Oreal__algebra__1(T_a)|c_RealVector_Oof__real(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(T_a)|V_x_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,V_x_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|V_x_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))).
% 13.12/12.99  0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_n_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_n_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|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)).
% 13.12/12.99  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)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|V_a=V_b.
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|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)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(T_a,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)).
% 13.12/12.99  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)).
% 13.12/12.99  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)).
% 13.12/12.99  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)).
% 13.12/12.99  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)).
% 13.12/12.99  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)).
% 13.12/12.99  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)).
% 13.12/12.99  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)).
% 13.12/12.99  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)).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x))=c_RealVector_Onorm__class_Onorm(T_a,V_x).
% 13.12/12.99  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).
% 13.12/12.99  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).
% 13.12/12.99  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).
% 13.12/12.99  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).
% 13.12/12.99  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).
% 13.12/12.99  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.
% 13.12/12.99  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).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|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)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.12/12.99  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).
% 13.12/12.99  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).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))|V_x_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_a,T_b,V_f_2)|hAPP(V_f_2,B_x)=hAPP(V_f_2,B_y).
% 13.12/12.99  0 [] c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_a,T_b,V_f_2)|hAPP(V_f_2,$f3(V_f_2,T_b,T_a))!=hAPP(V_f_2,$f2(V_f_2,T_b,T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless__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))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x_2,V_y_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x_2,V_y_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))).
% 13.12/12.99  0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|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)).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__algebra__1(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n)).
% 13.12/12.99  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).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.12/12.99  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)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.12/12.99  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,V_x)),V_n)=c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.12/12.99  0 [] -class_RealVector_Oreal__algebra__1(T_a)|c_RealVector_Oof__real(T_a,V_x_2)!=c_RealVector_Oof__real(T_a,V_y_2)|V_x_2=V_y_2.
% 13.12/12.99  0 [] -class_RealVector_Oreal__algebra__1(T_a)|c_RealVector_Oof__real(T_a,V_x_2)=c_RealVector_Oof__real(T_a,V_y_2)|V_x_2!=V_y_2.
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),V_ya)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H)),V_b)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)).
% 13.12/12.99  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)).
% 13.12/12.99  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)).
% 13.12/12.99  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).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__div__algebra(T_a)|c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__div__algebra(T_a)|c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n).
% 13.12/12.99  0 [] -class_RealVector_Oreal__algebra__1(T_a)|c_RealVector_Oof__real(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_RealVector_Oof__real(T_a,V_x)),c_RealVector_Oof__real(T_a,V_y)).
% 13.12/12.99  0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Oof__real(T_a,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Oplus__class_Oplus(T_a,c_RealVector_Oof__real(T_a,V_x),c_RealVector_Oof__real(T_a,V_y)).
% 13.12/12.99  0 [] -class_RealVector_Oreal__algebra__1(T_a)|c_RealVector_Oof__real(T_a,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Oplus__class_Oplus(T_a,c_RealVector_Oof__real(T_a,V_x),c_RealVector_Oof__real(T_a,V_y)).
% 13.12/12.99  0 [] -class_RealVector_Oreal__algebra__1(T_a)|c_RealVector_Oof__real(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_RealVector_Oof__real(T_a,V_x)),V_n).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_aa_2)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_ma_2)!=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_n_2)|V_ma_2=V_n_2.
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_aa_2)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_ma_2)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_n_2)|V_ma_2!=V_n_2.
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)))).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),$c1),v_k____)),v_a____))=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$c2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),B_z)),$c2).
% 13.12/12.99  0 [] c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))=c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__1__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)|c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)!=c_Groups_Oone__class_Oone(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,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).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y)))|V_x=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__1(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)|c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)!=c_Groups_Oone__class_Oone(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,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).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_b,V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f4(V_d2)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,$f4(V_d2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,$f4(V_d2),V_d2).
% 13.12/12.99  0 [] hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_w))).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_t)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_t,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_t)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.12/12.99  0 [] c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))).
% 13.12/12.99  0 [] c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_l_2)|V_l_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,$f5(V_l_2,V_ka_2)).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_l_2)|V_l_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,B_n).
% 13.12/12.99  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__idom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a).
% 13.12/12.99  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a).
% 13.12/12.99  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a))=c_RealVector_Onorm__class_Onorm(T_a,V_a).
% 13.12/12.99  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)).
% 13.12/12.99  0 [] c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)=c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_y)).
% 13.12/12.99  0 [] -class_Rings_Oordered__ring__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)).
% 13.12/12.99  0 [] -class_Rings_Oordered__ring__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)).
% 13.12/12.99  0 [] -class_Rings_Oordered__ring__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)).
% 13.12/12.99  0 [] -class_Rings_Oordered__ring__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x)=c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n))=c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))|V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__algebra__1(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,V_r))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r).
% 13.12/12.99  0 [] -class_Rings_Olinordered__idom(T_a)|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),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__idom(T_a)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 13.12/12.99  0 [] c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))).
% 13.12/12.99  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).
% 13.12/12.99  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).
% 13.12/12.99  0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_b_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  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).
% 13.12/12.99  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).
% 13.12/12.99  0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a).
% 13.12/12.99  0 [] -class_Rings_Ocomm__semiring(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 13.12/12.99  0 [] -class_Rings_Osemiring(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c).
% 13.12/12.99  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)).
% 13.12/12.99  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).
% 13.12/12.99  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)).
% 13.12/12.99  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).
% 13.12/12.99  0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_aa_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)|V_aa_2=V_b_2|V_aa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2).
% 13.12/12.99  0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_aa_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)|V_aa_2!=V_b_2.
% 13.12/12.99  0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_aa_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)|V_aa_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2).
% 13.12/12.99  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 13.12/12.99  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 13.12/12.99  0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,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)).
% 13.12/12.99  0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,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)).
% 13.12/12.99  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,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)).
% 13.12/12.99  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,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)).
% 13.12/12.99  0 [] -class_Rings_Oordered__comm__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,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)).
% 13.12/12.99  0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,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)).
% 13.12/12.99  0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,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)).
% 13.12/12.99  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 13.12/12.99  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -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_aa_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -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_aa_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -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_aa_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -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_aa_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)|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_aa_2),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)|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_aa_2),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring(T_a)|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)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__comm__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))).
% 13.12/12.99  0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2)!=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)|V_ca_2=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2).
% 13.12/12.99  0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)|V_ca_2!=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2).
% 13.12/12.99  0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2)!=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_ca_2)=V_d_2.
% 13.12/12.99  0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_ca_2)!=V_d_2.
% 13.12/12.99  0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)!=c_Groups_Oone__class_Oone(T_a)|V_x_2=c_Groups_Oone__class_Oone(T_a)|V_x_2=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)).
% 13.12/12.99  0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)=c_Groups_Oone__class_Oone(T_a)|V_x_2!=c_Groups_Oone__class_Oone(T_a).
% 13.12/12.99  0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)=c_Groups_Oone__class_Oone(T_a)|V_x_2!=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_aa_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_aa_2).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b).
% 13.12/12.99  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x).
% 13.12/12.99  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x).
% 13.12/12.99  0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))).
% 13.12/12.99  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2)).
% 13.12/12.99  0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2)).
% 13.12/12.99  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_ca_2),V_d_2).
% 13.12/12.99  0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_ca_2),V_d_2).
% 13.12/12.99  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2)).
% 13.12/12.99  0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2)).
% 13.12/12.99  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_ca_2),V_d_2).
% 13.12/12.99  0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_ca_2),V_d_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 13.12/12.99  0 [] -class_Groups_Omonoid__mult(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.12/12.99  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).
% 13.12/12.99  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)))).
% 13.12/12.99  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).
% 13.12/12.99  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)))).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m))))).
% 13.12/12.99  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).
% 13.12/12.99  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)!=c_Rings_Oinverse__class_Oinverse(T_a,V_b)|V_a=V_b.
% 13.12/12.99  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2)!=c_Rings_Oinverse__class_Oinverse(T_a,V_b_2)|V_aa_2=V_b_2.
% 13.12/12.99  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2)=c_Rings_Oinverse__class_Oinverse(T_a,V_b_2)|V_aa_2!=V_b_2.
% 13.12/12.99  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=V_a.
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__div__algebra(T_a)| -class_Rings_Odivision__ring__inverse__zero(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)).
% 13.12/12.99  0 [] -class_RealVector_Oreal__div__algebra(T_a)| -class_Rings_Odivision__ring__inverse__zero(T_a)|c_RealVector_Oof__real(T_a,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x))=c_Rings_Oinverse__class_Oinverse(T_a,c_RealVector_Oof__real(T_a,V_x)).
% 13.12/12.99  0 [] c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/12.99  0 [] -class_RealVector_Oreal__normed__div__algebra(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)).
% 13.12/12.99  0 [] -class_RealVector_Oreal__div__algebra(T_a)|V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_RealVector_Oof__real(T_a,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x))=c_Rings_Oinverse__class_Oinverse(T_a,c_RealVector_Oof__real(T_a,V_x)).
% 13.12/12.99  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=V_a.
% 13.12/12.99  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)!=c_Groups_Ozero__class_Ozero(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)!=c_Rings_Oinverse__class_Oinverse(T_a,V_b)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|V_a=V_b.
% 13.12/12.99  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a).
% 13.12/12.99  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_n).
% 13.12/12.99  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 13.12/12.99  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 13.12/12.99  0 [] -class_Rings_Odivision__ring(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)!=c_Groups_Oone__class_Oone(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)=V_b.
% 13.12/12.99  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_n).
% 13.12/12.99  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x1),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_u))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1))).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x1),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_u))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1)),V_u)).
% 13.12/12.99  0 [] V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_x)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.12/12.99  0 [] -class_Groups_Ozero(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pb_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_pb_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.12/12.99  0 [] -class_Groups_Ozero(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pb_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_pb_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.12/12.99  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))),c_Rings_Oinverse__class_Oinverse(T_a,V_b)).
% 13.12/12.99  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a)=c_Groups_Oone__class_Oone(T_a).
% 13.12/12.99  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Groups_Oone__class_Oone(T_a).
% 13.12/12.99  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))),c_Rings_Oinverse__class_Oinverse(T_a,V_b)).
% 13.12/12.99  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).
% 13.12/12.99  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 13.12/12.99  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  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.
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_w).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_j,V_k)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_k).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z)|V_z=V_w.
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2=V_n_2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)|hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)|V_s!=V_t.
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)|V_m!=V_n.
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 13.12/12.99  0 [] V_x=V_y|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x).
% 13.12/12.99  0 [] V_ma_2=V_n_2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2).
% 13.12/12.99  0 [] V_ma_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] V_ma_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 13.12/12.99  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 13.12/12.99  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_ka_2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_ka_2)|V_ma_2=V_n_2.
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_ka_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_ka_2)|V_ma_2!=V_n_2.
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_ma_2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_n_2)|V_ma_2=V_n_2.
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_ma_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_n_2)|V_ma_2!=V_n_2.
% 13.12/12.99  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)).
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)).
% 13.12/12.99  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n)=V_m.
% 13.12/12.99  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n)=V_m.
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)).
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_ma_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_ka_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ka_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_ma_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_n_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_ka_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ka_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_m)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_ma_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_n_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_ka_2)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ka_2)|V_ma_2=V_n_2.
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_ma_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_n_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_ka_2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ka_2)|V_ma_2!=V_n_2.
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|V_m=V_n.
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_k).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i))=V_i.
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)).
% 13.12/12.99  0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n).
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z).
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3)).
% 13.12/12.99  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)).
% 13.12/12.99  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)).
% 13.12/12.99  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)).
% 13.12/12.99  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).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.12/12.99  0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 13.12/12.99  0 [] V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ma_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ma_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2=V_y_2.
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2=V_y_2.
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n.
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_ma_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_ma_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)!=V_m|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  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).
% 13.12/12.99  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).
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_ma_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_ma_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2)|V_ma_2=V_n_2|V_ka_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2)|V_ma_2!=V_n_2.
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2)|V_ka_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_ka_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ka_2)|V_ma_2=V_n_2|V_ka_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_ka_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ka_2)|V_ma_2!=V_n_2.
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_ka_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ka_2)|V_ka_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m.
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_ka_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_ka_2),V_j_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_ka_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_ka_2),V_j_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i).
% 13.12/12.99  0 [] V_ca_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_aa_2),V_ca_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2)|V_aa_2=V_b_2.
% 13.12/12.99  0 [] V_ca_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_aa_2),V_ca_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2)|V_aa_2!=V_b_2.
% 13.12/12.99  0 [] V_ca_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_aa_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2)|V_aa_2=V_b_2.
% 13.12/12.99  0 [] V_ca_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_aa_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2)|V_aa_2!=V_b_2.
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 13.12/12.99  0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_ma_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_ka_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ka_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_ma_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_ka_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ka_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_c,V_a)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|V_m=V_n|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2=V_n_2.
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2!=V_n_2.
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2!=V_n_2.
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2=V_n_2.
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)!=V_ka_2|V_j_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_i_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_ka_2|V_j_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_i_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)=V_m.
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_j_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_ka_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_ka_2),V_j_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ka_2,V_j_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_ka_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_ka_2),V_j_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m.
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ka_2,V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_ka_2),V_i_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_ka_2)).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_ka_2),V_i_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_ka_2)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)|V_n_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,$f6(V_n_2,V_ma_2)).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)|V_n_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 13.12/12.99  0 [] c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)).
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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)).
% 13.12/12.99  0 [] 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))).
% 13.12/12.99  0 [] 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)).
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z)=V_z.
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2)),V_w)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)).
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_ma_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_ma_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 13.12/12.99  0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)|V_ma_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.12/12.99  0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.12/12.99  0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)|V_ma_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.12/12.99  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)=V_n.
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(T_a)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Oring(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)).
% 13.12/12.99  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2=c_Groups_Ouminus__class_Ouminus(T_a,V_x_2).
% 13.12/12.99  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_x_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 13.12/12.99  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.12/12.99  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))|V_aa_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 13.12/12.99  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)|V_aa_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f7(V_b_2,V_aa_2,V_P_2)).
% 13.12/12.99  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)| -hBOOL(hAPP(V_P_2,$f7(V_b_2,V_aa_2,V_P_2))).
% 13.12/12.99  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_aa_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f7(V_b_2,V_aa_2,V_P_2)).
% 13.12/12.99  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f7(V_b_2,V_aa_2,V_P_2))).
% 13.12/12.99  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.12/12.99  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))|V_aa_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 13.12/12.99  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)|V_aa_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f8(V_b_2,V_aa_2,V_P_2)).
% 13.12/12.99  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)| -hBOOL(hAPP(V_P_2,$f8(V_b_2,V_aa_2,V_P_2))).
% 13.12/12.99  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_aa_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f8(V_b_2,V_aa_2,V_P_2)).
% 13.12/12.99  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f8(V_b_2,V_aa_2,V_P_2))).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_ka_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ka_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_ka_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ka_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_ka_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ka_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)).
% 13.12/12.99  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).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),V_u)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)).
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2).
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2!=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2).
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_aa_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=V_aa_2.
% 13.12/12.99  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_aa_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2!=V_aa_2.
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_r_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r_2),V_x_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_r_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_r_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_r_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r_2),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_r_2).
% 13.12/12.99  0 [] c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_s)).
% 13.12/12.99  0 [] c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y)).
% 13.12/12.99  0 [] c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y)))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/12.99  0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/12.99  0 [] -class_Rings_Oring__1(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2).
% 13.12/12.99  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2).
% 13.12/12.99  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_ka_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ka_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_ka_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ka_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_ka_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ka_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/13.00  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).
% 13.12/13.00  0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a)=V_a.
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)=V_r.
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$c3).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,$c3,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,$c3,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))).
% 13.12/13.00  0 [] hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),B_x)=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,B_x)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,V_pb_2),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____))|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,V_pb_2))|hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_pb_2),$f9(V_pb_2))=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.12/13.00  0 [] c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,$c4)=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____).
% 13.12/13.00  0 [] hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,$c4),B_x)=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,B_x)).
% 13.12/13.00  0 [] hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),$c5)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.12/13.00  0 [] c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____)=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____).
% 13.12/13.00  0 [] -class_RealVector_Oreal__normed__div__algebra(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_r,c_RealVector_Onorm__class_Onorm(T_a,V_x))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_r)).
% 13.12/13.00  0 [] hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.12/13.00  0 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)).
% 13.12/13.00  0 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_w))).
% 13.12/13.00  0 [] hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)).
% 13.12/13.00  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2),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))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,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)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2),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))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,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)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2),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))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_ma_2),V_n_2).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2),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))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_ma_2),V_n_2).
% 13.12/13.00  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))),c_Rings_Oinverse__class_Oinverse(T_a,V_b))).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)).
% 13.12/13.00  0 [] hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))).
% 13.12/13.00  0 [] hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),B_z)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),B_z)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))).
% 13.12/13.00  0 [] hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex).
% 13.12/13.00  0 [] c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____)=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)).
% 13.12/13.00  0 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),V_wa_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),V_wa_2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),V_wa_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),V_wa_2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))).
% 13.12/13.00  0 [] hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),B_z)=c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),B_z))).
% 13.12/13.00  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)).
% 13.12/13.00  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)).
% 13.12/13.00  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2)|V_ka_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_ma_2=V_n_2.
% 13.12/13.00  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2)|V_ka_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.00  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2)|V_ma_2!=V_n_2.
% 13.12/13.00  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)!=c_Groups_Oone__class_Oone(T_a)|V_x_2=c_Groups_Oone__class_Oone(T_a).
% 13.12/13.00  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)=c_Groups_Oone__class_Oone(T_a)|V_x_2!=c_Groups_Oone__class_Oone(T_a).
% 13.12/13.00  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2)|V_ma_2=V_n_2.
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2)|V_ma_2!=V_n_2.
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2).
% 13.12/13.00  0 [] -class_Fields_Ofield(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a))),c_Rings_Oinverse__class_Oinverse(T_a,V_b)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))|c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)).
% 13.12/13.00  0 [] -class_Fields_Ofield(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a)=c_Groups_Oone__class_Oone(T_a).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ka_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ka_2),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2),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))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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_ma_2),V_n_2).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2),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))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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_ma_2),V_n_2).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_i)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),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,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).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2)!=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)|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_ma_2)=V_n_2.
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2)=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)|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_ma_2)!=V_n_2.
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2),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))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,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)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2),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))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,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)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),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,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)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2)!=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_ma_2=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).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_ma_2)=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_ma_2!=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).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2).
% 13.12/13.00  0 [] c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),$c6)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.12/13.00  0 [] hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),$c8)!=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),$c7).
% 13.12/13.00  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_aa_2)),V_r_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_r_2),V_x_2).
% 13.12/13.00  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_aa_2)),V_r_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_r_2)).
% 13.12/13.00  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_aa_2)),V_r_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_r_2),V_x_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_r_2)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p))!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.12/13.00  0 [] -class_Groups_Ozero(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=V_x_2|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Ozero(T_a)|c_Groups_Ozero__class_Ozero(T_a)=V_x_2|V_x_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  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)).
% 13.12/13.00  0 [] -class_Groups_Oab__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 13.12/13.00  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2)!=c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_ca_2)|V_b_2=V_ca_2.
% 13.12/13.00  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2)=c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_ca_2)|V_b_2!=V_ca_2.
% 13.12/13.00  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)!=c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_aa_2)|V_b_2=V_ca_2.
% 13.12/13.00  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)=c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_aa_2)|V_b_2!=V_ca_2.
% 13.12/13.00  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)!=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)|V_b=V_c.
% 13.12/13.00  0 [] -class_Groups_Ocancel__ab__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)!=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)|V_b=V_c.
% 13.12/13.00  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_b,V_a)!=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)|V_b=V_c.
% 13.12/13.00  0 [] -class_Groups_Oone(T_a)|c_Groups_Oone__class_Oone(T_a)!=V_x_2|V_x_2=c_Groups_Oone__class_Oone(T_a).
% 13.12/13.00  0 [] -class_Groups_Oone(T_a)|c_Groups_Oone__class_Oone(T_a)=V_x_2|V_x_2!=c_Groups_Oone__class_Oone(T_a).
% 13.12/13.00  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)|V_aa_2!=V_b_2|V_ca_2=V_d_2.
% 13.12/13.00  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)|V_aa_2=V_b_2|V_ca_2!=V_d_2.
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_aa_2=V_b_2.
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_aa_2!=V_b_2.
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)!=V_b_2|c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)=V_aa_2.
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)=V_b_2|c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)!=V_aa_2.
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|V_aa_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_b_2=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2).
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|V_aa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_b_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2).
% 13.12/13.00  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.
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a))=c_Groups_Oabs__class_Oabs(T_a,V_a).
% 13.12/13.00  0 [] -class_Groups_Omonoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a.
% 13.12/13.00  0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a.
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Omonoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 13.12/13.00  0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 13.12/13.00  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)).
% 13.12/13.00  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=V_b_2.
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=V_b_2.
% 13.12/13.00  0 [] -class_Groups_Oab__group__add(T_a)|V_aa_2!=V_b_2|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Oab__group__add(T_a)|V_aa_2=V_b_2|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  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).
% 13.12/13.00  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.
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_ca_2,V_d_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_ca_2,V_d_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_d_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_d_2).
% 13.12/13.00  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.
% 13.12/13.00  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.
% 13.12/13.00  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.
% 13.12/13.00  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.
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)!=V_aa_2|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)=V_aa_2|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|V_aa_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|V_aa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)|c_Groups_Ozero__class_Ozero(T_a)=V_aa_2.
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)|c_Groups_Ozero__class_Ozero(T_a)!=V_aa_2.
% 13.12/13.00  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).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)).
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b)=V_a.
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=V_a.
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 13.12/13.00  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)).
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b))=V_b.
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=V_b.
% 13.12/13.00  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).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,V_aa_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Oabs__class_Oabs(T_a,V_a).
% 13.12/13.00  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 13.12/13.00  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 13.12/13.00  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_a)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 13.12/13.00  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 13.12/13.00  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)!=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a)=V_b.
% 13.12/13.00  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|V_aa_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|V_aa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  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).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a.
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a.
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_aa_2))|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_aa_2))|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,V_a,V_b).
% 13.12/13.00  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 13.12/13.00  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_aa_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a)).
% 13.12/13.00  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 13.12/13.00  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 13.12/13.00  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 13.12/13.00  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 13.12/13.00  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a).
% 13.12/13.00  0 [] -class_Groups_Oabs__if(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a).
% 13.12/13.00  0 [] -class_Groups_Oabs__if(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a.
% 13.12/13.00  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))).
% 13.12/13.00  0 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))).
% 13.12/13.00  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x)=c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))).
% 13.12/13.00  0 [] V_b=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),$f10(V_n,V_b)),V_n)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_r)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r)).
% 13.12/13.00  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,V_aa_2,V_n_2)!=c_Polynomial_Omonom(T_a,V_b_2,V_n_2)|V_aa_2=V_b_2.
% 13.12/13.00  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,V_aa_2,V_n_2)=c_Polynomial_Omonom(T_a,V_b_2,V_n_2)|V_aa_2!=V_b_2.
% 13.12/13.00  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).
% 13.12/13.00  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).
% 13.12/13.00  0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_n).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_m)),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 13.12/13.00  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,V_aa_2,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,V_aa_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  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)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_n).
% 13.12/13.00  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)).
% 13.12/13.00  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 13.12/13.00  0 [] -class_Int_Oring__char__0(T_a)| -class_Rings_Oidom(T_a)|c_Polynomial_Opoly(T_a,V_pb_2)!=c_Polynomial_Opoly(T_a,V_qa_2)|V_pb_2=V_qa_2.
% 13.12/13.00  0 [] -class_Int_Oring__char__0(T_a)| -class_Rings_Oidom(T_a)|c_Polynomial_Opoly(T_a,V_pb_2)=c_Polynomial_Opoly(T_a,V_qa_2)|V_pb_2!=V_qa_2.
% 13.12/13.00  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)).
% 13.12/13.00  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)).
% 13.12/13.00  0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q)=V_q.
% 13.12/13.00  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)).
% 13.12/13.00  0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=V_p.
% 13.12/13.00  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.
% 13.12/13.00  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).
% 13.12/13.00  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))|c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x).
% 13.12/13.00  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))|c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x)=V_x.
% 13.12/13.00  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2)!=c_Polynomial_OpCons(T_a,V_b_2,V_qa_2)|V_aa_2=V_b_2.
% 13.12/13.00  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2)!=c_Polynomial_OpCons(T_a,V_b_2,V_qa_2)|V_pb_2=V_qa_2.
% 13.12/13.00  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2)=c_Polynomial_OpCons(T_a,V_b_2,V_qa_2)|V_aa_2!=V_b_2|V_pb_2!=V_qa_2.
% 13.12/13.00  0 [] -class_Rings_Ocomm__ring(T_a)|c_Polynomial_Osmult(T_a,V_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_Osmult(T_a,V_a,V_q))=c_Polynomial_Osmult(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,V_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Osmult(T_a,V_a,V_p)),V_q)=c_Polynomial_Osmult(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__ring(T_a)|c_Polynomial_Osmult(T_a,V_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q))=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q)).
% 13.12/13.00  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)).
% 13.12/13.00  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)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x)=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)).
% 13.12/13.00  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).
% 13.12/13.00  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)).
% 13.12/13.00  0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q))=c_Polynomial_OpCons(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)).
% 13.12/13.00  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).
% 13.12/13.00  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)).
% 13.12/13.00  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q))=c_Polynomial_OpCons(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Osmult(T_a,V_b,V_p))=c_Polynomial_Osmult(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_p).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_p)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Polynomial_Osmult(T_a,c_Groups_Oone__class_Oone(T_a),V_p)=V_p.
% 13.12/13.00  0 [] -class_Groups_Oab__group__add(T_b)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_a,V_p))=c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),V_p)).
% 13.12/13.00  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p))=c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__ring(T_a)|c_Polynomial_Osmult(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_p)=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__ring(T_a)|c_Polynomial_Osmult(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_p)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p)).
% 13.12/13.00  0 [] -class_Int_Oring__char__0(T_a)| -class_Rings_Oidom(T_a)|c_Polynomial_Opoly(T_a,V_pb_2)!=c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))|V_pb_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.12/13.00  0 [] -class_Int_Oring__char__0(T_a)| -class_Rings_Oidom(T_a)|c_Polynomial_Opoly(T_a,V_pb_2)=c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))|V_pb_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.12/13.00  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).
% 13.12/13.00  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.12/13.00  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_pb_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.12/13.00  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_pb_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.12/13.00  0 [] -class_Rings_Oidom(T_a)|c_Polynomial_Osmult(T_a,V_aa_2,V_pb_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_aa_2=c_Groups_Ozero__class_Ozero(T_a)|V_pb_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.12/13.00  0 [] -class_Rings_Oidom(T_a)|c_Polynomial_Osmult(T_a,V_aa_2,V_pb_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Rings_Oidom(T_a)|c_Polynomial_Osmult(T_a,V_aa_2,V_pb_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_pb_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,c_Groups_Ozero__class_Ozero(T_a),V_p)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))=c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q))=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,V_p)),V_q)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_q),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,V_a,c_Polynomial_OpCons(T_a,V_b,V_p))=c_Polynomial_OpCons(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Polynomial_Osmult(T_a,V_a,V_p)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,V_c,V_p)!=c_Polynomial_OpCons(T_a,V_a,V_p)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.12/13.00  0 [] hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),$c9)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.12/13.00  0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)),c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))=V_p.
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2).
% 13.12/13.00  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)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osynthetic__div(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_c)=c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,c_Polynomial_Osynthetic__div(T_a,V_p,V_c)))=c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,V_q))!=c_Polynomial_OpCons(T_a,V_r,V_q)|V_r=hAPP(c_Polynomial_Opoly(T_a,V_p),V_c).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,V_q))!=c_Polynomial_OpCons(T_a,V_r,V_q)|V_q=c_Polynomial_Osynthetic__div(T_a,V_p,V_c).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))|V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))|V_x_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)).
% 13.12/13.00  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).
% 13.12/13.00  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)).
% 13.12/13.00  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)).
% 13.12/13.00  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))).
% 13.12/13.00  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).
% 13.12/13.00  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)).
% 13.12/13.00  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).
% 13.12/13.00  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)).
% 13.12/13.00  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).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a).
% 13.12/13.00  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).
% 13.12/13.00  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).
% 13.12/13.00  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_b_2!=c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_b_2=c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a.
% 13.12/13.00  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_wa_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2))!=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_wa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))|V_wa_2=V_x_2|V_y_2=V_z_2.
% 13.12/13.00  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_wa_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_wa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))|V_wa_2!=V_x_2.
% 13.12/13.00  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_wa_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_wa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))|V_y_2!=V_z_2.
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 13.12/13.00  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_aa_2=V_b_2|V_ca_2=V_d_2|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2))!=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)).
% 13.12/13.00  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_aa_2!=V_b_2|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)).
% 13.12/13.00  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_ca_2!=V_d_2|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)).
% 13.12/13.00  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.
% 13.12/13.00  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.
% 13.12/13.00  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)).
% 13.12/13.00  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)).
% 13.12/13.00  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.
% 13.12/13.00  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_r=c_Groups_Ozero__class_Ozero(T_a)|V_a!=V_b|V_c=V_d|c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c))!=c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_m,V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_m).
% 13.12/13.00  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).
% 13.12/13.00  0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)=c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)).
% 13.12/13.00  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Opcompose(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_q)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q))).
% 13.12/13.00  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.00  0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f11(T_a)).
% 13.12/13.00  0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B_x)),$f11(T_a))).
% 13.12/13.00  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)).
% 13.12/13.00  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)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))|V_x_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))|V_x_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.00  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)).
% 13.12/13.00  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)).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.00  0 [] c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.12/13.00  0 [] -class_Rings_Oidom(T_a)|hAPP(c_Polynomial_Opoly(T_a,V_pb_2),V_aa_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_pb_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Oorder(T_a,V_aa_2,V_pb_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.00  0 [] -class_Rings_Oidom(T_a)|hAPP(c_Polynomial_Opoly(T_a,V_pb_2),V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)|V_pb_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.12/13.00  0 [] -class_Rings_Oidom(T_a)|hAPP(c_Polynomial_Opoly(T_a,V_pb_2),V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)|c_Polynomial_Oorder(T_a,V_aa_2,V_pb_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.00  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z.
% 13.12/13.00  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)=V_z.
% 13.12/13.00  0 [] 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_i).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)=V_i.
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_ka_2,V_l_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_ka_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_ka_2,V_l_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_ka_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))|V_z_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))|V_z_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_ma_2=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_n_2=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_ma_2!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_n_2!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2).
% 13.12/13.00  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).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 13.12/13.00  0 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.12/13.00  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)=V_z.
% 13.12/13.00  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z.
% 13.12/13.00  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).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_wa_2)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_wa_2).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_wa_2)|V_z_2!=V_wa_2.
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_wa_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_wa_2)|V_z_2=V_wa_2.
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x).
% 13.12/13.00  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)).
% 13.12/13.00  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)).
% 13.12/13.00  0 [] c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n))!=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m)=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.12/13.00  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)).
% 13.12/13.00  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)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_wa_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_wa_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_H,V_z)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z).
% 13.12/13.00  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2).
% 13.12/13.00  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2)|V_wa_2=V_z_2.
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_z_2).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|V_wa_2!=V_z_2.
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_wa_2,V_z_2).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_wa_2,V_z_2).
% 13.12/13.00  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 13.12/13.00  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)).
% 13.12/13.00  0 [] c_Complex_Oii!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex).
% 13.12/13.00  0 [] c_Complex_Oii!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.12/13.00  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),V_x))=c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_x).
% 13.12/13.00  0 [] c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii)=c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii).
% 13.12/13.00  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii)=c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)),V_z).
% 13.12/13.00  0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)).
% 13.12/13.00  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w).
% 13.12/13.00  0 [] c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)).
% 13.12/13.00  0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z))=V_z.
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_w).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_j,V_k)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_k).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z)|V_z=V_w.
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j)).
% 13.12/13.00  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)).
% 13.12/13.00  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)).
% 13.12/13.00  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)|V_a!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)|V_a!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q).
% 13.12/13.00  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)!=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_Orderings_Oord__class_Oless(tc_Int_Oint,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))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H,V_b)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,V_q).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,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),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,V_q_H).
% 13.12/13.00  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)!=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_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),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_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H,V_b)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,V_q_H).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,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),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,V_q).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,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))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),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_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)).
% 13.12/13.00  0 [] 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)).
% 13.12/13.00  0 [] 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)).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)).
% 13.12/13.00  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$c10).
% 13.12/13.00  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),B_z)),$c10).
% 13.12/13.00  0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x).
% 13.12/13.00  0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)).
% 13.12/13.00  0 [] -class_Orderings_Oord(T_b)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,$f12(V_g_2,V_f_2,T_a,T_b)),hAPP(V_g_2,$f12(V_g_2,V_f_2,T_a,T_b))).
% 13.12/13.00  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x).
% 13.12/13.00  0 [] -class_Orderings_Oorder(T_a)|V_x_2!=V_y_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2).
% 13.12/13.00  0 [] -class_Orderings_Oorder(T_a)|V_x_2!=V_y_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 13.12/13.00  0 [] -class_Orderings_Oorder(T_a)|V_x_2=V_y_2| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 13.12/13.00  0 [] -class_Orderings_Opreorder(T_a)|V_x!=V_y|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 13.12/13.00  0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)).
% 13.12/13.00  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 13.12/13.00  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 13.12/13.00  0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c).
% 13.12/13.00  0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a).
% 13.12/13.00  0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|V_b!=V_c|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c).
% 13.12/13.00  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|V_b!=V_c|c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a).
% 13.12/13.00  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)|V_x=V_y.
% 13.12/13.00  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_z).
% 13.12/13.00  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|V_x=V_y.
% 13.12/13.00  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x).
% 13.12/13.00  0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)).
% 13.12/13.00  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x).
% 13.12/13.00  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 13.12/13.00  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 13.12/13.00  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 13.12/13.00  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_c,V_a).
% 13.12/13.01  0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_a,V_c).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_c,V_b)|c_Orderings_Oord__class_Oless(T_a,V_c,V_a).
% 13.12/13.01  0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_c).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.12/13.01  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_y!=V_x.
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 13.12/13.01  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 13.12/13.01  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|V_x_2=V_y_2.
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)|V_x_2=V_y_2|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)|V_x_2!=V_y_2| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2).
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)|V_x_2!=V_y_2| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 13.12/13.01  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_x).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 13.12/13.01  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 13.12/13.01  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|V_a=V_b|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|V_a=V_b|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y.
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 13.12/13.01  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y).
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 13.12/13.01  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2).
% 13.12/13.01  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 13.12/13.01  0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 13.12/13.01  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 13.12/13.01  0 [] $c12!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] $c13!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.01  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,$c11),$c13),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)).
% 13.12/13.01  0 [] hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),B_z)=c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),$c13)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,$c12,$c11)),B_z))).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.12/13.01  0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2).
% 13.12/13.01  0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2).
% 13.12/13.01  0 [] -class_Orderings_Oord(T_b)|c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2).
% 13.12/13.01  0 [] c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.01  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)).
% 13.12/13.01  0 [] c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatceiling(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.12/13.01  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.12/13.01  0 [] -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(T_a)=c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)).
% 13.12/13.01  0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f13(T_a)).
% 13.12/13.01  0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B_x)),$f13(T_a))).
% 13.12/13.01  0 [] hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_aa_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_one_2.
% 13.12/13.01  0 [] -class_RealVector_Oreal__normed__vector(T_b)| -class_Orderings_Oord(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2,$f14(V_X_2,V_M_2,T_a,T_b))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2,B_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2)))).
% 13.12/13.01  0 [] -class_RealVector_Oreal__normed__vector(T_b)| -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,$f14(V_X_2,V_M_2,T_a,T_b)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2,B_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2)))).
% 13.12/13.01  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f15(V_y,T_a)).
% 13.12/13.01  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),$f15(V_y,T_a))).
% 13.12/13.01  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f16(T_a)).
% 13.12/13.01  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),$f16(T_a))).
% 13.12/13.01  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f17(V_x,T_a)).
% 13.12/13.01  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),$f17(V_x,T_a))).
% 13.12/13.01  0 [] c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,$c14)=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____).
% 13.12/13.01  0 [] hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,$c14),B_x)=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,B_x)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.12/13.01  0 [] c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.01  0 [] c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.12/13.01  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatfloor(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2).
% 13.12/13.01  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b))).
% 13.12/13.01  0 [] -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).
% 13.12/13.01  0 [] 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).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y)).
% 13.12/13.01  0 [] -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).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_z)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatceiling(V_x)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2))|c_Polynomial_Opos__poly(T_a,V_pb_2)|V_pb_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2))|c_Polynomial_Opos__poly(T_a,V_pb_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)|c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2))| -c_Polynomial_Opos__poly(T_a,V_pb_2).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)|c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2))|V_pb_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.01  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2).
% 13.12/13.01  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.12/13.01  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n)=c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)).
% 13.12/13.01  0 [] c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n).
% 13.12/13.01  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)).
% 13.12/13.01  0 [] c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x))=c_RealDef_Oreal(tc_Nat_Onat,V_x).
% 13.12/13.01  0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.01  0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.01  0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/13.01  0 [] c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 13.12/13.01  0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)!=c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)|V_n_2=V_ma_2.
% 13.12/13.01  0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)|V_n_2!=V_ma_2.
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,V_p)| -c_Polynomial_Opos__poly(T_a,V_q)|c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)).
% 13.12/13.01  0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 13.12/13.01  0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.01  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.01  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_ma_2).
% 13.12/13.01  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_ma_2).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)|V_x_2=V_y_2|c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)|V_x_2!=V_y_2.
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)| -c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)).
% 13.12/13.01  0 [] c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n.
% 13.12/13.01  0 [] c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n.
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a).
% 13.12/13.01  0 [] V_x!=c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))|c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 13.12/13.01  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)).
% 13.12/13.01  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_ma_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_ma_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.12/13.01  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_ma_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_ma_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_aa_2,c_RComplete_Onatfloor(V_x_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_aa_2),V_x_2).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_aa_2,c_RComplete_Onatfloor(V_x_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_aa_2),V_x_2).
% 13.12/13.01  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)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_aa_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_aa_2)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_aa_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_aa_2)).
% 13.12/13.01  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)|c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a).
% 13.12/13.01  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)|c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatfloor(V_x)=V_n.
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)|c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)| -c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,$f18(V_r),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_r).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,$f18(V_r))).
% 13.12/13.01  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)).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Odecse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Odecse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f20(V_X_2,T_a),$f19(V_X_2,T_a)).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Odecse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f19(V_X_2,T_a)),hAPP(V_X_2,$f20(V_X_2,T_a))).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_e)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f21(V_p,V_z,V_e)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_e)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,V_z)))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,V_z)),$f21(V_p,V_z,V_e))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),B_w),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),V_z))),V_e).
% 13.12/13.01  0 [] -class_Lattices_Oboolean__algebra(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x)).
% 13.12/13.01  0 [] -class_Lattices_Oboolean__algebra(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 13.12/13.01  0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 13.12/13.01  0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)!=c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)|V_x_2=V_y_2.
% 13.12/13.01  0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)|V_x_2!=V_y_2.
% 13.12/13.01  0 [] -class_Groups_Ouminus(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2)).
% 13.12/13.01  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.
% 13.12/13.01  0 [] -class_Groups_Ominus(T_a)|hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2)=c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)).
% 13.12/13.01  0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)=V_a.
% 13.12/13.01  0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)=V_x.
% 13.12/13.01  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).
% 13.12/13.01  0 [] -class_RealVector_Oreal__algebra__1(T_a)| -class_RealVector_Oreal__normed__vector(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_RealVector_Oof__real(T_a,B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,B_x)),$f22(T_a))).
% 13.12/13.01  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)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)|V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))| -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)|c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x)=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)|V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)|c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_aa_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x))=V_x.
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,V_k)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)).
% 13.12/13.01  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)).
% 13.12/13.01  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)).
% 13.12/13.01  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).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_aa_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.01  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_x_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.01  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(T_a)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.12/13.01  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).
% 13.12/13.01  0 [] -class_RealVector_Oreal__normed__algebra__1(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_RealVector_Oof__real(T_a,V_r))=c_RealVector_Oof__real(T_a,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_r)).
% 13.12/13.01  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).
% 13.12/13.01  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)).
% 13.12/13.01  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).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_aa_2)!=c_Groups_Oone__class_Oone(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_aa_2)=c_Groups_Oone__class_Oone(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Groups_Osgn__class_Osgn(T_a,V_a)=c_Groups_Oone__class_Oone(T_a).
% 13.12/13.01  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).
% 13.12/13.01  0 [] -class_Groups_Osgn__if(T_a)|V_x=c_Groups_Ozero__class_Ozero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)|c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Oone__class_Oone(T_a).
% 13.12/13.01  0 [] -class_Groups_Osgn__if(T_a)|V_x=c_Groups_Ozero__class_Ozero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)|c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_aa_2)!=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_aa_2)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Osgn__class_Osgn(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)).
% 13.12/13.01  0 [] -class_RealVector_Oreal__normed__vector(T_a)|V_x!=c_Groups_Ozero__class_Ozero(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/13.01  0 [] -class_RealVector_Oreal__normed__vector(T_a)|V_x=c_Groups_Ozero__class_Ozero(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.12/13.01  0 [] -class_Rings_Oidom(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__ring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))|c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2).
% 13.12/13.01  0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))| -c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2).
% 13.12/13.01  0 [] -class_Rings_Ocomm__ring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2)|c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2).
% 13.12/13.01  0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2)| -c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2).
% 13.12/13.01  0 [] -class_Rings_Ocomm__ring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)| -c_Rings_Odvd__class_Odvd(T_a,V_x,V_z)|c_Rings_Odvd__class_Odvd(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_z)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__ring(T_a)| -class_Rings_Odvd(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_ta_2))|c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_ta_2)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__ring(T_a)| -class_Rings_Odvd(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)|c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_ta_2))| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_ta_2)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__ring(T_a)| -class_Rings_Odvd(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_ta_2))|c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_ta_2)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__ring(T_a)| -class_Rings_Odvd(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)|c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_ta_2))| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_ta_2)).
% 13.12/13.01  0 [] -class_Rings_Odvd(T_a)| -class_Rings_Osemiring__0(T_a)| -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x)))|c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,$f23(V_l_2,V_P_2,T_a),c_Groups_Ozero__class_Ozero(T_a))).
% 13.12/13.01  0 [] -class_Rings_Odvd(T_a)| -class_Rings_Osemiring__0(T_a)| -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x)))|hBOOL(hAPP(V_P_2,$f23(V_l_2,V_P_2,T_a))).
% 13.12/13.01  0 [] -class_Rings_Odvd(T_a)| -class_Rings_Osemiring__0(T_a)|hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),$f24(V_l_2,V_P_2,T_a))))| -c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,X1,c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(V_P_2,X1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)| -c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)|c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oone__class_Oone(T_a),V_a).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_pb_2,V_h_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_pb_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_pb_2,V_h_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_pb_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.12/13.01  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)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)| -c_Rings_Odvd__class_Odvd(T_a,V_b,V_c)|c_Rings_Odvd__class_Odvd(T_a,V_a,V_c).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a,V_a).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q).
% 13.12/13.01  0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint).
% 13.12/13.01  0 [] -class_Lattices_Oboolean__algebra(T_1)|class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)).
% 13.12/13.01  0 [] -class_Orderings_Opreorder(T_1)|class_Orderings_Opreorder(tc_fun(T_2,T_1)).
% 13.12/13.01  0 [] -class_Orderings_Oorder(T_1)|class_Orderings_Oorder(tc_fun(T_2,T_1)).
% 13.12/13.01  0 [] -class_Orderings_Oord(T_1)|class_Orderings_Oord(tc_fun(T_2,T_1)).
% 13.12/13.01  0 [] -class_Groups_Ouminus(T_1)|class_Groups_Ouminus(tc_fun(T_2,T_1)).
% 13.12/13.01  0 [] -class_Groups_Ominus(T_1)|class_Groups_Ominus(tc_fun(T_2,T_1)).
% 13.12/13.01  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Oordered__cancel__semiring(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Oordered__comm__semiring(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Olinordered__semiring__1(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Olinordered__semiring(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Olinordered__semidom(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Oordered__semiring(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Oordered__ring__abs(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Olinordered__ring(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Olinordered__idom(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Ocomm__semiring__0(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Ocomm__semiring(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Oab__group__add(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Oordered__ring(tc_Int_Oint).
% 13.12/13.01  0 [] class_Orderings_Opreorder(tc_Int_Oint).
% 13.12/13.01  0 [] class_Orderings_Olinorder(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Omonoid__mult(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Omonoid__add(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Osemiring__0(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Ogroup__add(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Omult__zero(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Ocomm__ring(tc_Int_Oint).
% 13.12/13.01  0 [] class_Orderings_Oorder(tc_Int_Oint).
% 13.12/13.01  0 [] class_Int_Oring__char__0(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Osemiring(tc_Int_Oint).
% 13.12/13.01  0 [] class_Orderings_Oord(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Ouminus(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Osgn__if(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Oabs__if(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Oring__1(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Ominus(tc_Int_Oint).
% 13.12/13.01  0 [] class_Power_Opower(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Ozero(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Oring(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Oidom(tc_Int_Oint).
% 13.12/13.01  0 [] class_Groups_Oone(tc_Int_Oint).
% 13.12/13.01  0 [] class_Rings_Odvd(tc_Int_Oint).
% 13.12/13.01  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Rings_Oordered__semiring(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Rings_Ocomm__semiring__0(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Orderings_Opreorder(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Orderings_Olinorder(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Groups_Omonoid__mult(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Groups_Omonoid__add(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Rings_Osemiring__0(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Rings_Omult__zero(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Orderings_Oorder(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Rings_Osemiring(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Orderings_Oord(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Groups_Ominus(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Power_Opower(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Groups_Ozero(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Groups_Oone(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Rings_Odvd(tc_Nat_Onat).
% 13.12/13.01  0 [] class_Lattices_Oboolean__algebra(tc_HOL_Obool).
% 13.12/13.01  0 [] class_Orderings_Opreorder(tc_HOL_Obool).
% 13.12/13.01  0 [] class_Orderings_Oorder(tc_HOL_Obool).
% 13.12/13.01  0 [] class_Orderings_Oord(tc_HOL_Obool).
% 13.12/13.01  0 [] class_Groups_Ouminus(tc_HOL_Obool).
% 13.12/13.01  0 [] class_Groups_Ominus(tc_HOL_Obool).
% 13.12/13.01  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_RealVector_Oreal__div__algebra(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Olinordered__semiring(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Olinordered__semidom(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Oab__semigroup__add(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Fields_Olinordered__field(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Oordered__semiring(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Oordered__ring__abs(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Ono__zero__divisors(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Olinordered__ring(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Olinordered__idom(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Odivision__ring(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Ocomm__semiring(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Oab__group__add(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Oordered__ring(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Orderings_Opreorder(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Orderings_Olinorder(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Omonoid__mult(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Ocomm__ring__1(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Omonoid__add(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Osemiring__0(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Ogroup__add(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Omult__zero(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Ocomm__ring(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Orderings_Oorder(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Int_Oring__char__0(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Osemiring(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Orderings_Oord(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Ouminus(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Osgn__if(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Oabs__if(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Oring__1(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Ominus(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Fields_Ofield(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Power_Opower(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Ozero(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Oring(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Oidom(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Groups_Oone(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Rings_Odvd(tc_RealDef_Oreal).
% 13.12/13.01  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_RealVector_Oreal__div__algebra(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Odivision__ring(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Ocomm__semiring(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Groups_Oab__group__add(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Ozero__ne_q__one(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Groups_Omonoid__mult(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Groups_Omonoid__add(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Osemiring__0(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Groups_Ogroup__add(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Omult__zero(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Ocomm__ring(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Int_Oring__char__0(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Osemiring(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Groups_Ouminus(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Oring__1(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Groups_Ominus(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Fields_Ofield(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Power_Opower(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Groups_Ozero(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Oring(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Oidom(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Groups_Oone(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] class_Rings_Odvd(tc_Complex_Ocomplex).
% 13.12/13.01  0 [] -class_Rings_Oidom(T_1)|class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Oidom(T_1)|class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Oidom(T_1)|class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Oidom(T_1)|class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Oord(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ominus(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Power_Opower(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Groups_Ozero(T_1)|class_Groups_Ozero(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Oring(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Oidom(T_1)|class_Rings_Oidom(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Oone(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Odvd(tc_Polynomial_Opoly(T_1)).
% 13.12/13.01  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.12/13.01  end_of_list.
% 13.12/13.01  
% 13.12/13.01  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 13.12/13.01  
% 13.12/13.01  This ia a non-Horn set with equality.  The strategy will be
% 13.12/13.01  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 13.12/13.01  deletion, with positive clauses in sos and nonpositive
% 13.12/13.01  clauses in usable.
% 13.12/13.01  
% 13.12/13.01     dependent: set(knuth_bendix).
% 13.12/13.01     dependent: set(anl_eq).
% 13.12/13.01     dependent: set(para_from).
% 13.12/13.01     dependent: set(para_into).
% 13.12/13.01     dependent: clear(para_from_right).
% 13.12/13.01     dependent: clear(para_into_right).
% 13.12/13.01     dependent: set(para_from_vars).
% 13.12/13.01     dependent: set(eq_units_both_ways).
% 13.12/13.01     dependent: set(dynamic_demod_all).
% 13.12/13.01     dependent: set(dynamic_demod).
% 13.12/13.01     dependent: set(order_eq).
% 13.12/13.01     dependent: set(back_demod).
% 13.12/13.01     dependent: set(lrpo).
% 13.12/13.01     dependent: set(hyper_res).
% 13.12/13.01     dependent: set(unit_deletion).
% 13.12/13.01     dependent: set(factor).
% 13.12/13.01  
% 13.12/13.01  ------------> process usable:
% 13.12/13.01  ** KEPT (pick-wt=14): 1 [] hAPP(A,$f1(B,A))!=hAPP(B,$f1(B,A))|A=B.
% 13.12/13.01  ** KEPT (pick-wt=6): 2 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)).
% 13.12/13.01  ** KEPT (pick-wt=4): 4 [copy,3,flip.1] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=v_k____.
% 13.12/13.01  ** KEPT (pick-wt=4): 6 [copy,5,flip.1] c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)!=v_a____.
% 13.12/13.01  ** KEPT (pick-wt=22): 7 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))).
% 13.12/13.01  ** KEPT (pick-wt=26): 8 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|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))).
% 13.12/13.01  ** KEPT (pick-wt=9): 9 [] -class_RealVector_Oreal__algebra__1(A)|c_RealVector_Oof__real(A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(A).
% 13.12/13.01  ** KEPT (pick-wt=9): 10 [] -class_RealVector_Oreal__normed__algebra__1(A)|c_RealVector_Onorm__class_Onorm(A,c_Groups_Oone__class_Oone(A))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.12/13.01  ** KEPT (pick-wt=26): 11 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),C)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,D),E)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Oplus__class_Oplus(A,B,D)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,E)).
% 13.12/13.01  ** KEPT (pick-wt=30): 12 [] -class_RealVector_Oreal__normed__algebra(A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),C)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,D),E)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),E)).
% 13.12/13.01  ** KEPT (pick-wt=4): 14 [copy,13,flip.1] c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)!=v_w____.
% 13.12/13.01  ** KEPT (pick-wt=25): 15 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),v_k____)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),v_k____)).
% 13.12/13.01  ** KEPT (pick-wt=18): 16 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),A)),v_m____).
% 13.12/13.01  ** KEPT (pick-wt=6): 17 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)).
% 13.12/13.01  ** KEPT (pick-wt=9): 18 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)).
% 13.12/13.01  ** KEPT (pick-wt=9): 19 [] -class_RealVector_Oreal__algebra__1(A)|c_RealVector_Oof__real(A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.01    Following clause subsumed by 19 during input processing: 0 [] -class_RealVector_Oreal__algebra__1(A)| -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Oof__real(A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.01  ** KEPT (pick-wt=9): 20 [] -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Onorm__class_Onorm(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/13.01  ** KEPT (pick-wt=13): 21 [] -class_RealVector_Oreal__algebra__1(A)|c_RealVector_Oof__real(A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B))=c_Groups_Ouminus__class_Ouminus(A,c_RealVector_Oof__real(A,B)).
% 13.12/13.01    Following clause subsumed by 21 during input processing: 0 [] -class_RealVector_Oreal__algebra__1(A)| -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Oof__real(A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B))=c_Groups_Ouminus__class_Ouminus(A,c_RealVector_Oof__real(A,B)).
% 13.12/13.01  ** KEPT (pick-wt=17): 22 [] -class_RealVector_Oreal__algebra__1(A)|c_RealVector_Oof__real(A,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,C))=c_Groups_Ominus__class_Ominus(A,c_RealVector_Oof__real(A,B),c_RealVector_Oof__real(A,C)).
% 13.12/13.01    Following clause subsumed by 22 during input processing: 0 [] -class_RealVector_Oreal__algebra__1(A)| -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Oof__real(A,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,C))=c_Groups_Ominus__class_Ominus(A,c_RealVector_Oof__real(A,B),c_RealVector_Oof__real(A,C)).
% 13.12/13.01  ** KEPT (pick-wt=18): 23 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C))).
% 13.12/13.01  ** KEPT (pick-wt=19): 24 [] -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))|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).
% 13.12/13.01  ** KEPT (pick-wt=15): 25 [] 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))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 13.12/13.01  ** KEPT (pick-wt=14): 26 [] 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).
% 13.12/13.01  ** KEPT (pick-wt=12): 27 [] -class_RealVector_Oreal__algebra__1(A)|c_RealVector_Oof__real(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/13.01  ** KEPT (pick-wt=12): 28 [] -class_RealVector_Oreal__algebra__1(A)|c_RealVector_Oof__real(A,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/13.01  ** KEPT (pick-wt=12): 29 [] -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Onorm__class_Onorm(A,B)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.01  ** KEPT (pick-wt=12): 30 [] -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Onorm__class_Onorm(A,B)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.01  ** KEPT (pick-wt=13): 31 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|B=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.01  ** KEPT (pick-wt=13): 32 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|B!=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.01  ** KEPT (pick-wt=18): 33 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C)),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C))).
% 13.12/13.01  ** KEPT (pick-wt=21): 34 [] -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).
% 13.12/13.01  ** KEPT (pick-wt=21): 35 [] -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).
% 13.12/13.01  ** KEPT (pick-wt=25): 36 [] -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).
% 13.12/13.01  ** KEPT (pick-wt=17): 37 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 13.12/13.01  ** KEPT (pick-wt=23): 38 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 13.12/13.01  ** KEPT (pick-wt=25): 39 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|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)).
% 13.12/13.01  ** KEPT (pick-wt=33): 40 [] -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)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|B=D.
% 13.12/13.01  ** KEPT (pick-wt=30): 41 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Oone__class_Oone(A))|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)).
% 13.12/13.01  ** KEPT (pick-wt=30): 42 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),D)|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)).
% 13.12/13.01  ** KEPT (pick-wt=26): 43 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,C)),D)=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 13.12/13.01    Following clause subsumed by 43 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,C)),D)=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 13.12/13.01  ** KEPT (pick-wt=26): 44 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ominus__class_Ominus(A,C,D))=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 13.12/13.01    Following clause subsumed by 44 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ominus__class_Ominus(A,C,D))=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 13.12/13.01  ** KEPT (pick-wt=19): 45 [] -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)).
% 13.12/13.01    Following clause subsumed by 45 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)).
% 13.12/13.01  ** KEPT (pick-wt=19): 46 [] -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)).
% 13.12/13.01    Following clause subsumed by 46 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)).
% 13.12/13.01  ** KEPT (pick-wt=15): 47 [] -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C))=c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,C,B)).
% 13.12/13.01  ** KEPT (pick-wt=11): 48 [] -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Onorm__class_Onorm(A,c_Groups_Ouminus__class_Ouminus(A,B))=c_RealVector_Onorm__class_Onorm(A,B).
% 13.12/13.01  ** KEPT (pick-wt=25): 50 [copy,49,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)).
% 13.12/13.01  ** KEPT (pick-wt=12): 51 [] -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).
% 13.12/13.01    Following clause subsumed by 51 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).
% 13.12/13.01  ** KEPT (pick-wt=12): 52 [] -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).
% 13.12/13.01    Following clause subsumed by 52 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).
% 13.12/13.01  ** KEPT (pick-wt=11): 53 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat))=B.
% 13.12/13.01  ** KEPT (pick-wt=15): 54 [] -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).
% 13.12/13.01  ** KEPT (pick-wt=30): 55 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,E))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,D)),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,C,E)))).
% 13.12/13.01  ** KEPT (pick-wt=18): 56 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C)),c_RealVector_Onorm__class_Onorm(A,c_Groups_Oplus__class_Oplus(A,B,C))).
% 13.12/13.01  ** KEPT (pick-wt=25): 57 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),D)|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)).
% 13.12/13.02  ** KEPT (pick-wt=25): 58 [] -class_Rings_Olinordered__semidom(A)| -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))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,B,D).
% 13.12/13.02  ** KEPT (pick-wt=18): 59 [] -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).
% 13.12/13.02  ** KEPT (pick-wt=18): 60 [] -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).
% 13.12/13.02  ** KEPT (pick-wt=13): 61 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B))|B!=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.02  ** KEPT (pick-wt=13): 62 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B))|B=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.02  ** KEPT (pick-wt=11): 63 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(A,B,C)|hAPP(C,D)=hAPP(C,E).
% 13.12/13.02  ** KEPT (pick-wt=17): 64 [] c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(A,B,C)|hAPP(C,$f3(C,B,A))!=hAPP(C,$f2(C,B,A)).
% 13.12/13.02  ** KEPT (pick-wt=25): 65 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -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))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D).
% 13.12/13.02    Following clause subsumed by 65 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -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))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D).
% 13.12/13.02  ** KEPT (pick-wt=25): 66 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|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))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D).
% 13.12/13.02  ** KEPT (pick-wt=51): 68 [copy,67,flip.2] -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,C)),c_Groups_Ominus__class_Ominus(A,D,E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,C)),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),c_Groups_Ominus__class_Ominus(A,D,E)))=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 13.12/13.02  ** KEPT (pick-wt=28): 70 [copy,69,flip.2] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)).
% 13.12/13.02  ** KEPT (pick-wt=17): 71 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=22): 72 [] -class_RealVector_Oreal__normed__algebra(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))).
% 13.12/13.02  ** KEPT (pick-wt=18): 73 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C))).
% 13.12/13.02  ** KEPT (pick-wt=17): 74 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=20): 75 [] -class_RealVector_Oreal__normed__algebra__1(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),C)).
% 13.12/13.02  ** KEPT (pick-wt=12): 76 [] -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).
% 13.12/13.02  ** KEPT (pick-wt=9): 77 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.12/13.02  ** KEPT (pick-wt=30): 78 [] -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)).
% 13.12/13.02  ** KEPT (pick-wt=30): 79 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Oone__class_Oone(A))|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)).
% 13.12/13.02  ** KEPT (pick-wt=22): 80 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=31): 81 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Oone__class_Oone(A))|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)).
% 13.12/13.02  ** KEPT (pick-wt=12): 82 [] -class_RealVector_Oreal__algebra__1(A)|c_RealVector_Oof__real(A,B)!=c_RealVector_Oof__real(A,C)|B=C.
% 13.12/13.02  ** KEPT (pick-wt=12): 83 [] -class_RealVector_Oreal__algebra__1(A)|c_RealVector_Oof__real(A,B)=c_RealVector_Oof__real(A,C)|B!=C.
% 13.12/13.02  ** KEPT (pick-wt=26): 84 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 13.12/13.02    Following clause subsumed by 84 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 13.12/13.02  ** KEPT (pick-wt=26): 85 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 13.12/13.02    Following clause subsumed by 85 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 13.12/13.02  ** KEPT (pick-wt=30): 86 [] -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)).
% 13.12/13.02  ** KEPT (pick-wt=25): 87 [] -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)).
% 13.12/13.02  ** KEPT (pick-wt=12): 88 [] -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).
% 13.12/13.02  ** KEPT (pick-wt=21): 89 [] -class_RealVector_Oreal__normed__div__algebra(A)|c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C)).
% 13.12/13.02  ** KEPT (pick-wt=19): 90 [] -class_RealVector_Oreal__normed__div__algebra(A)|c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),C).
% 13.12/13.02  ** KEPT (pick-wt=21): 91 [] -class_RealVector_Oreal__algebra__1(A)|c_RealVector_Oof__real(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_RealVector_Oof__real(A,B)),c_RealVector_Oof__real(A,C)).
% 13.12/13.02  ** KEPT (pick-wt=19): 92 [] -class_RealVector_Oreal__algebra__1(A)| -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Oof__real(A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,C))=c_Groups_Oplus__class_Oplus(A,c_RealVector_Oof__real(A,B),c_RealVector_Oof__real(A,C)).
% 13.12/13.02  ** KEPT (pick-wt=17): 93 [] -class_RealVector_Oreal__algebra__1(A)|c_RealVector_Oof__real(A,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,B,C))=c_Groups_Oplus__class_Oplus(A,c_RealVector_Oof__real(A,B),c_RealVector_Oof__real(A,C)).
% 13.12/13.02  ** KEPT (pick-wt=19): 94 [] -class_RealVector_Oreal__algebra__1(A)|c_RealVector_Oof__real(A,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),C))=hAPP(hAPP(c_Power_Opower__class_Opower(A),c_RealVector_Oof__real(A,B)),C).
% 13.12/13.02  ** KEPT (pick-wt=25): 95 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),D)|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)).
% 13.12/13.02  ** KEPT (pick-wt=25): 96 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -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))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D).
% 13.12/13.02    Following clause subsumed by 96 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -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))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D).
% 13.12/13.02    Following clause subsumed by 95 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|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))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D).
% 13.12/13.02  ** KEPT (pick-wt=23): 97 [] -class_Rings_Olinordered__semidom(A)| -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.
% 13.12/13.02  ** KEPT (pick-wt=23): 98 [] -class_Rings_Olinordered__semidom(A)| -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.
% 13.12/13.02  ** KEPT (pick-wt=18): 99 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),A)),$c2).
% 13.12/13.02  ** KEPT (pick-wt=44): 100 [] -class_Rings_Olinordered__semiring__1__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),F)|c_Groups_Oplus__class_Oplus(A,E,F)!=c_Groups_Oone__class_Oone(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D)),C).
% 13.12/13.02  ** KEPT (pick-wt=24): 101 [] -class_RealVector_Oreal__normed__vector(A)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),c_RealVector_Onorm__class_Onorm(A,D)))|C=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.02  ** KEPT (pick-wt=44): 102 [] -class_Rings_Olinordered__semiring__1(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),F)|c_Groups_Oplus__class_Oplus(A,E,F)!=c_Groups_Oone__class_Oone(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D)),C).
% 13.12/13.02  ** KEPT (pick-wt=11): 103 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f4(A)).
% 13.12/13.02  ** KEPT (pick-wt=11): 104 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,$f4(A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.12/13.02  ** KEPT (pick-wt=10): 105 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,$f4(A),A).
% 13.12/13.02  ** KEPT (pick-wt=8): 107 [copy,106,flip.1] c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)!=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____).
% 13.12/13.02  ** KEPT (pick-wt=28): 108 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),B)),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.12/13.02  ** KEPT (pick-wt=9): 110 [copy,109,flip.1] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____).
% 13.12/13.02  ** KEPT (pick-wt=12): 112 [copy,111,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,$f5(B,A))=B.
% 13.12/13.02  ** KEPT (pick-wt=10): 113 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C).
% 13.12/13.02  ** KEPT (pick-wt=21): 115 [copy,114,flip.2] -class_Rings_Olinordered__idom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C))=c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=19): 116 [] -class_Rings_Olinordered__idom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,B))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B).
% 13.12/13.02  ** KEPT (pick-wt=9): 117 [] -class_Rings_Olinordered__idom(A)|c_Groups_Oabs__class_Oabs(A,c_Groups_Oone__class_Oone(A))=c_Groups_Oone__class_Oone(A).
% 13.12/13.02  ** KEPT (pick-wt=19): 119 [copy,118,flip.2] -class_Rings_Olinordered__idom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Oabs__class_Oabs(A,B)),C)=c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=11): 120 [] -class_RealVector_Oreal__normed__vector(A)|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B))=c_RealVector_Onorm__class_Onorm(A,B).
% 13.12/13.02  ** KEPT (pick-wt=32): 121 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,D),E)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 13.12/13.02  ** KEPT (pick-wt=12): 122 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),C)|c_Orderings_Oord__class_Oless(A,B,C).
% 13.12/13.02  ** KEPT (pick-wt=14): 123 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),C).
% 13.12/13.02  ** KEPT (pick-wt=18): 124 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),C)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),C).
% 13.12/13.02  ** KEPT (pick-wt=31): 126 [copy,125,flip.4] -class_Rings_Oordered__ring__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C))=c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=31): 128 [copy,127,flip.4] -class_Rings_Oordered__ring__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C))=c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=31): 130 [copy,129,flip.4] -class_Rings_Oordered__ring__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C))=c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=31): 132 [copy,131,flip.4] -class_Rings_Oordered__ring__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Oabs__class_Oabs(A,C))=c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=24): 133 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oabs__class_Oabs(A,C)),B)=c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)).
% 13.12/13.02  ** KEPT (pick-wt=21): 134 [] -class_Rings_Olinordered__idom(A)|c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ouminus__class_Ouminus(A,B)),C))=c_Groups_Oabs__class_Oabs(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=22): 135 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,C)))|B=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/13.02  ** KEPT (pick-wt=11): 136 [] -class_RealVector_Oreal__normed__algebra__1(A)|c_RealVector_Onorm__class_Onorm(A,c_RealVector_Oof__real(A,B))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,B).
% 13.12/13.02  ** KEPT (pick-wt=14): 137 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Oabs__class_Oabs(A,B)),C)).
% 13.12/13.02  ** KEPT (pick-wt=13): 138 [] -class_Rings_Olinordered__idom(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 13.12/13.02  ** KEPT (pick-wt=20): 139 [] -class_RealVector_Oreal__normed__vector(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B),c_RealVector_Onorm__class_Onorm(A,C))),c_RealVector_Onorm__class_Onorm(A,c_Groups_Ominus__class_Ominus(A,B,C))).
% 13.12/13.02  ** KEPT (pick-wt=12): 140 [] -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).
% 13.12/13.02  ** KEPT (pick-wt=12): 141 [] -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).
% 13.12/13.02  ** KEPT (pick-wt=19): 142 [] -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).
% 13.12/13.02  ** KEPT (pick-wt=15): 143 [] -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).
% 13.12/13.02  ** KEPT (pick-wt=15): 144 [] -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).
% 13.12/13.02  ** KEPT (pick-wt=19): 145 [] -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).
% 13.12/13.02    Following clause subsumed by 145 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).
% 13.12/13.02  ** KEPT (pick-wt=7): 147 [copy,146,flip.2] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 13.12/13.02    Following clause subsumed by 147 during input processing: 0 [] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 13.12/13.02  ** KEPT (pick-wt=26): 148 [] -class_Rings_Ocomm__semiring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 13.12/13.02  ** KEPT (pick-wt=32): 150 [copy,149,flip.2] -class_Rings_Osemiring(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D),E)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),E)).
% 13.12/13.02  ** KEPT (pick-wt=19): 152 [copy,151,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)).
% 13.12/13.02  ** KEPT (pick-wt=19): 154 [copy,153,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)).
% 13.12/13.02  ** KEPT (pick-wt=19): 155 [] -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)).
% 13.12/13.02  ** KEPT (pick-wt=19): 156 [] -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).
% 13.12/13.02  ** KEPT (pick-wt=23): 157 [] -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).
% 13.12/13.02  ** KEPT (pick-wt=18): 158 [] -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.
% 13.12/13.02  ** KEPT (pick-wt=20): 159 [] -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).
% 13.12/13.02  ** KEPT (pick-wt=22): 160 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=22): 161 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=22): 162 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=22): 163 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=34): 164 [] -class_Rings_Oordered__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 13.12/13.02  ** KEPT (pick-wt=34): 165 [] -class_Rings_Oordered__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 13.12/13.02  ** KEPT (pick-wt=25): 166 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)).
% 13.12/13.02  ** KEPT (pick-wt=25): 167 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 13.12/13.02  ** KEPT (pick-wt=25): 168 [] -class_Rings_Oordered__comm__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)).
% 13.12/13.02  ** KEPT (pick-wt=25): 169 [] -class_Rings_Oordered__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)).
% 13.12/13.02  ** KEPT (pick-wt=25): 170 [] -class_Rings_Oordered__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 13.12/13.02    Following clause subsumed by 163 during input processing: 0 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.12/13.02    Following clause subsumed by 161 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02    Following clause subsumed by 161 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02    Following clause subsumed by 160 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=22): 171 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=22): 172 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=22): 173 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C).
% 13.12/13.02  ** KEPT (pick-wt=22): 174 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=22): 175 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C).
% 13.12/13.02  ** KEPT (pick-wt=22): 176 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=22): 177 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C).
% 13.12/13.02  ** KEPT (pick-wt=22): 178 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=22): 179 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=22): 180 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=22): 181 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=22): 182 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C).
% 13.12/13.02  ** KEPT (pick-wt=22): 183 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=12): 184 [] -class_Rings_Olinordered__ring(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)).
% 13.12/13.02  ** KEPT (pick-wt=12): 185 [] -class_Rings_Olinordered__ring(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=26): 186 [] -class_Rings_Olinordered__ring__strict(A)| -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))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=25): 187 [] -class_Rings_Olinordered__ring__strict(A)| -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))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,D,B).
% 13.12/13.02  ** KEPT (pick-wt=25): 188 [] -class_Rings_Olinordered__ring__strict(A)| -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))|c_Orderings_Oord__class_Oless(A,B,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=24): 189 [] -class_Rings_Olinordered__ring__strict(A)| -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))|c_Orderings_Oord__class_Oless(A,B,D)|c_Orderings_Oord__class_Oless(A,D,B).
% 13.12/13.02  ** KEPT (pick-wt=25): 190 [] -class_Rings_Olinordered__ring__strict(A)|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))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless(A,B,D).
% 13.12/13.02  ** KEPT (pick-wt=25): 191 [] -class_Rings_Olinordered__ring__strict(A)|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))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,D,B).
% 13.12/13.02  ** KEPT (pick-wt=26): 192 [] -class_Rings_Olinordered__ring__strict(A)| -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))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=25): 193 [] -class_Rings_Olinordered__ring__strict(A)| -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))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,D,C).
% 13.12/13.02  ** KEPT (pick-wt=25): 194 [] -class_Rings_Olinordered__ring__strict(A)| -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))|c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=24): 195 [] -class_Rings_Olinordered__ring__strict(A)| -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))|c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,D,C).
% 13.12/13.02  ** KEPT (pick-wt=25): 196 [] -class_Rings_Olinordered__ring__strict(A)|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))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D).
% 13.12/13.02  ** KEPT (pick-wt=25): 197 [] -class_Rings_Olinordered__ring__strict(A)|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))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,D,C).
% 13.12/13.02  ** KEPT (pick-wt=25): 198 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,C,D).
% 13.12/13.02    Following clause subsumed by 196 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -c_Orderings_Oord__class_Oless(A,C,D).
% 13.12/13.02  ** KEPT (pick-wt=22): 199 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=22): 200 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=22): 201 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=22): 202 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C).
% 13.12/13.02  ** KEPT (pick-wt=22): 203 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.02  ** KEPT (pick-wt=25): 204 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,D,C).
% 13.12/13.02    Following clause subsumed by 197 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -c_Orderings_Oord__class_Oless(A,D,C).
% 13.12/13.02    Following clause subsumed by 201 during input processing: 0 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=22): 205 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=25): 206 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 13.12/13.02  ** KEPT (pick-wt=25): 207 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)).
% 13.12/13.02  ** KEPT (pick-wt=25): 208 [] -class_Rings_Olinordered__comm__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)).
% 13.12/13.02    Following clause subsumed by 191 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 13.12/13.02    Following clause subsumed by 197 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)).
% 13.12/13.02  ** KEPT (pick-wt=18): 209 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 13.12/13.02  ** KEPT (pick-wt=8): 210 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)).
% 13.12/13.02  ** KEPT (pick-wt=8): 211 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=8): 212 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=8): 213 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)).
% 13.12/13.02  ** KEPT (pick-wt=22): 214 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=13): 215 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,B))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=13): 216 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,B))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.02  ** KEPT (pick-wt=10): 217 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))).
% 13.12/13.02  ** KEPT (pick-wt=35): 218 [] -class_Rings_Oring(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D)!=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F)|D=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F).
% 13.12/13.02  ** KEPT (pick-wt=35): 219 [] -class_Rings_Oring(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F)|D!=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F).
% 13.12/13.02  ** KEPT (pick-wt=35): 220 [] -class_Rings_Oring(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D)!=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D)=F.
% 13.12/13.02  ** KEPT (pick-wt=35): 221 [] -class_Rings_Oring(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D)!=F.
% 13.12/13.02  ** KEPT (pick-wt=21): 222 [] -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)).
% 13.12/13.02  ** KEPT (pick-wt=15): 223 [] -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).
% 13.12/13.02  ** KEPT (pick-wt=17): 224 [] -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)).
% 13.12/13.02  ** KEPT (pick-wt=25): 225 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 13.12/13.02  ** KEPT (pick-wt=25): 226 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 13.12/13.02  ** KEPT (pick-wt=25): 227 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 13.12/13.02  ** KEPT (pick-wt=25): 228 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 13.12/13.02  ** KEPT (pick-wt=34): 229 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 13.12/13.02  ** KEPT (pick-wt=34): 230 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 13.12/13.02  ** KEPT (pick-wt=34): 231 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 13.12/13.02  ** KEPT (pick-wt=34): 232 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 13.12/13.02  ** KEPT (pick-wt=25): 233 [] -class_Rings_Olinordered__semiring(A)| -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))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,B,D).
% 13.12/13.02  ** KEPT (pick-wt=25): 234 [] -class_Rings_Olinordered__semiring__strict(A)| -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))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,B,D).
% 13.12/13.02  ** KEPT (pick-wt=25): 235 [] -class_Rings_Olinordered__semiring(A)| -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))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,C,D).
% 13.12/13.02  ** KEPT (pick-wt=25): 236 [] -class_Rings_Olinordered__semiring__strict(A)| -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))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,C,D).
% 13.12/13.02  ** KEPT (pick-wt=25): 237 [] -class_Rings_Olinordered__semiring__strict(A)| -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))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.12/13.02  ** KEPT (pick-wt=25): 238 [] -class_Rings_Olinordered__semiring__strict(A)| -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))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 13.12/13.02  ** KEPT (pick-wt=26): 239 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),B).
% 13.12/13.02  ** KEPT (pick-wt=26): 240 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),B).
% 13.12/13.02  ** KEPT (pick-wt=12): 241 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A))).
% 13.12/13.02  ** KEPT (pick-wt=37): 242 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F))|c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F)).
% 13.12/13.02  ** KEPT (pick-wt=37): 243 [] -class_Rings_Oordered__ring(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F))| -c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F)).
% 13.12/13.02  ** KEPT (pick-wt=37): 244 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D),F).
% 13.12/13.02  ** KEPT (pick-wt=37): 245 [] -class_Rings_Oordered__ring(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D),F).
% 13.12/13.02  ** KEPT (pick-wt=37): 246 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F))|c_Orderings_Oord__class_Oless(A,D,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F)).
% 13.12/13.02  ** KEPT (pick-wt=37): 247 [] -class_Rings_Oordered__ring(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F))| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F)).
% 13.12/13.02  ** KEPT (pick-wt=37): 248 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D),F).
% 13.12/13.02  ** KEPT (pick-wt=37): 249 [] -class_Rings_Oordered__ring(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F))| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D),F).
% 13.12/13.02  ** KEPT (pick-wt=29): 250 [] -class_Groups_Omonoid__mult(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),C)=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B).
% 13.12/13.02  ** KEPT (pick-wt=5): 251 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.12/13.02  ** KEPT (pick-wt=15): 252 [] -class_Power_Opower(A)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B)=c_Groups_Oone__class_Oone(A).
% 13.12/13.02  ** KEPT (pick-wt=28): 254 [copy,253,flip.3] -class_Power_Opower(A)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B).
% 13.12/13.02  ** KEPT (pick-wt=13): 255 [] A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),A)=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.12/13.02  ** KEPT (pick-wt=12): 256 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Rings_Oinverse__class_Oinverse(A,C)|B=C.
% 13.12/13.02    Following clause subsumed by 256 during input processing: 0 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Rings_Oinverse__class_Oinverse(A,C)|B=C.
% 13.12/13.02  ** KEPT (pick-wt=12): 257 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)=c_Rings_Oinverse__class_Oinverse(A,C)|B!=C.
% 13.12/13.02  ** KEPT (pick-wt=9): 258 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Rings_Oinverse__class_Oinverse(A,B))=B.
% 13.12/13.02  ** KEPT (pick-wt=15): 259 [] -class_RealVector_Oreal__normed__div__algebra(A)| -class_Rings_Odivision__ring__inverse__zero(A)|c_RealVector_Onorm__class_Onorm(A,c_Rings_Oinverse__class_Oinverse(A,B))=c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B)).
% 13.12/13.02  ** KEPT (pick-wt=15): 260 [] -class_RealVector_Oreal__div__algebra(A)| -class_Rings_Odivision__ring__inverse__zero(A)|c_RealVector_Oof__real(A,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B))=c_Rings_Oinverse__class_Oinverse(A,c_RealVector_Oof__real(A,B)).
% 13.12/13.02  ** KEPT (pick-wt=17): 261 [] -class_RealVector_Oreal__normed__div__algebra(A)|B=c_Groups_Ozero__class_Ozero(A)|c_RealVector_Onorm__class_Onorm(A,c_Rings_Oinverse__class_Oinverse(A,B))=c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B)).
% 13.12/13.02  ** KEPT (pick-wt=17): 262 [] -class_RealVector_Oreal__div__algebra(A)|B=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_RealVector_Oof__real(A,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B))=c_Rings_Oinverse__class_Oinverse(A,c_RealVector_Oof__real(A,B)).
% 13.12/13.02  ** KEPT (pick-wt=9): 263 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.02  ** KEPT (pick-wt=12): 264 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.02  ** KEPT (pick-wt=12): 265 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.02  ** KEPT (pick-wt=12): 266 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.02  ** KEPT (pick-wt=13): 267 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Rings_Oinverse__class_Oinverse(A,B))=B.
% 13.12/13.02    Following clause subsumed by 266 during input processing: 0 [] -class_Rings_Odivision__ring(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.02  ** KEPT (pick-wt=20): 268 [] -class_Rings_Odivision__ring(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Rings_Oinverse__class_Oinverse(A,C)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|B=C.
% 13.12/13.02  ** KEPT (pick-wt=9): 269 [] -class_Rings_Odivision__ring(A)|c_Rings_Oinverse__class_Oinverse(A,c_Groups_Oone__class_Oone(A))=c_Groups_Oone__class_Oone(A).
% 13.12/13.02  ** KEPT (pick-wt=19): 271 [copy,270,flip.2] -class_Rings_Odivision__ring__inverse__zero(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Rings_Oinverse__class_Oinverse(A,B)),C)=c_Rings_Oinverse__class_Oinverse(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=13): 272 [] -class_Rings_Odivision__ring__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ouminus__class_Ouminus(A,B))=c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Oinverse(A,B)).
% 13.12/13.02  ** KEPT (pick-wt=29): 273 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Oinverse(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Rings_Oinverse__class_Oinverse(A,C)),c_Rings_Oinverse__class_Oinverse(A,B)).
% 13.12/13.02  ** KEPT (pick-wt=16): 274 [] -class_Rings_Odivision__ring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)!=c_Groups_Oone__class_Oone(A)|c_Rings_Oinverse__class_Oinverse(A,B)=C.
% 13.12/13.02  ** KEPT (pick-wt=23): 276 [copy,275,flip.3] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Rings_Oinverse__class_Oinverse(A,B)),C)=c_Rings_Oinverse__class_Oinverse(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 13.12/13.02  ** KEPT (pick-wt=17): 277 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ouminus__class_Ouminus(A,B))=c_Groups_Ouminus__class_Ouminus(A,c_Rings_Oinverse__class_Oinverse(A,B)).
% 13.12/13.02  ** KEPT (pick-wt=42): 278 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),D))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),D),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B))).
% 13.12/13.02  ** KEPT (pick-wt=42): 279 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),D))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,A)),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)),D)).
% 13.12/13.02  ** KEPT (pick-wt=13): 280 [] -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)).
% 13.12/13.02  ** KEPT (pick-wt=13): 281 [] -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)).
% 13.12/13.02  ** KEPT (pick-wt=37): 283 [copy,282,flip.4] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Oplus__class_Oplus(A,B,C))),c_Rings_Oinverse__class_Oinverse(A,C))=c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)).
% 13.12/13.02  ** KEPT (pick-wt=17): 284 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Rings_Oinverse__class_Oinverse(A,B)),B)=c_Groups_Oone__class_Oone(A).
% 13.12/13.02  ** KEPT (pick-wt=17): 285 [] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Rings_Oinverse__class_Oinverse(A,B))=c_Groups_Oone__class_Oone(A).
% 13.12/13.02  ** KEPT (pick-wt=37): 287 [copy,286,flip.4] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Ominus__class_Ominus(A,C,B))),c_Rings_Oinverse__class_Oinverse(A,C))=c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)).
% 13.12/13.02  ** KEPT (pick-wt=17): 288 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=B.
% 13.12/13.02  ** KEPT (pick-wt=12): 289 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,C).
% 13.12/13.02  ** KEPT (pick-wt=11): 290 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,A)|A=B.
% 13.12/13.02  ** KEPT (pick-wt=18): 291 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)).
% 13.12/13.02  ** KEPT (pick-wt=11): 292 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),B).
% 13.12/13.02  ** KEPT (pick-wt=7): 293 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 13.12/13.02  ** KEPT (pick-wt=7): 294 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=A.
% 13.12/13.02  ** KEPT (pick-wt=4): 295 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 13.12/13.02    Following clause subsumed by 293 during input processing: 0 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 13.12/13.02    Following clause subsumed by 294 during input processing: 0 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 13.12/13.02    Following clause subsumed by 295 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 13.12/13.02  ** KEPT (pick-wt=12): 296 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)|A=C.
% 13.12/13.02  ** KEPT (pick-wt=12): 297 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)|A!=C.
% 13.12/13.02  ** KEPT (pick-wt=12): 298 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)|B=C.
% 13.12/13.02  ** KEPT (pick-wt=12): 299 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)|B!=C.
% 13.12/13.02  ** KEPT (pick-wt=22): 300 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 13.12/13.02  ** KEPT (pick-wt=22): 301 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 13.12/13.02  ** KEPT (pick-wt=23): 302 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C).
% 13.12/13.02  ** KEPT (pick-wt=20): 303 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)|B=C.
% 13.12/13.02  ** KEPT (pick-wt=20): 304 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)|B!=C.
% 13.12/13.03  ** KEPT (pick-wt=11): 305 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,A)|A=B.
% 13.12/13.03  ** KEPT (pick-wt=12): 306 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 13.12/13.03  ** KEPT (pick-wt=13): 307 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=A.
% 13.12/13.03  ** KEPT (pick-wt=14): 308 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)).
% 13.12/13.03  ** KEPT (pick-wt=14): 309 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)).
% 13.12/13.03  ** KEPT (pick-wt=7): 310 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 13.12/13.03    Following clause subsumed by 251 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.12/13.03    Following clause subsumed by 294 during input processing: 0 [] A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 13.12/13.03    Following clause subsumed by 251 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.12/13.03  ** KEPT (pick-wt=8): 311 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.03  ** KEPT (pick-wt=12): 312 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 13.12/13.03  ** KEPT (pick-wt=12): 313 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 13.12/13.03  ** KEPT (pick-wt=17): 314 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),B).
% 13.12/13.03  ** KEPT (pick-wt=11): 315 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|A=B.
% 13.12/13.03  ** KEPT (pick-wt=8): 316 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B).
% 13.12/13.03  ** KEPT (pick-wt=7): 317 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|A!=B.
% 13.12/13.03    Following clause subsumed by 316 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B).
% 13.12/13.03  ** KEPT (pick-wt=7): 318 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|A!=B.
% 13.12/13.03    Following clause subsumed by 315 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|A=B.
% 13.12/13.03  ** KEPT (pick-wt=11): 319 [] 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).
% 13.12/13.03  ** KEPT (pick-wt=11): 320 [] 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).
% 13.12/13.03  ** KEPT (pick-wt=15): 321 [] 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).
% 13.12/13.03  ** KEPT (pick-wt=10): 322 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=A|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.03  ** KEPT (pick-wt=9): 323 [] -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).
% 13.12/13.03    Following clause subsumed by 310 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.03  ** KEPT (pick-wt=11): 324 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.03  ** KEPT (pick-wt=11): 325 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 13.12/13.03    Following clause subsumed by 324 during input processing: 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 13.12/13.03  ** KEPT (pick-wt=17): 326 [] 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).
% 13.12/13.03  ** KEPT (pick-wt=13): 327 [] 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).
% 13.12/13.03  ** KEPT (pick-wt=13): 328 [] 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).
% 13.12/13.03  ** KEPT (pick-wt=20): 329 [] 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).
% 13.12/13.03  ** KEPT (pick-wt=16): 330 [] 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.
% 13.12/13.03  ** KEPT (pick-wt=17): 331 [] 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).
% 13.12/13.03  ** KEPT (pick-wt=20): 332 [] 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).
% 13.12/13.03  ** KEPT (pick-wt=16): 333 [] 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.
% 13.12/13.03  ** KEPT (pick-wt=17): 334 [] 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).
% 13.12/13.03  ** KEPT (pick-wt=11): 335 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C).
% 13.12/13.03  ** KEPT (pick-wt=17): 336 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,D)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D).
% 13.12/13.03  ** KEPT (pick-wt=18): 337 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)).
% 13.12/13.03  ** KEPT (pick-wt=14): 338 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 13.12/13.03  ** KEPT (pick-wt=11): 339 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 13.12/13.03  ** KEPT (pick-wt=11): 340 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 13.12/13.03  ** KEPT (pick-wt=14): 341 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 13.12/13.03  ** KEPT (pick-wt=14): 342 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 13.12/13.03  ** KEPT (pick-wt=14): 343 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),B).
% 13.12/13.03  ** KEPT (pick-wt=14): 344 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),B).
% 13.12/13.03  ** KEPT (pick-wt=7): 345 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),B).
% 13.12/13.03  ** KEPT (pick-wt=7): 346 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),A).
% 13.12/13.03  ** KEPT (pick-wt=20): 347 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)|B=C.
% 13.12/13.03  ** KEPT (pick-wt=20): 348 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)|B!=C.
% 13.12/13.03  ** KEPT (pick-wt=20): 349 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)|B=C.
% 13.12/13.03  ** KEPT (pick-wt=20): 350 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)|B!=C.
% 13.12/13.03  ** KEPT (pick-wt=8): 351 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 13.12/13.03    Following clause subsumed by 310 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 13.12/13.03  ** KEPT (pick-wt=22): 352 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 13.12/13.03  ** KEPT (pick-wt=22): 353 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 13.12/13.03  ** KEPT (pick-wt=18): 354 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)).
% 13.12/13.03  ** KEPT (pick-wt=11): 355 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 13.12/13.03    Following clause subsumed by 351 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 13.12/13.03    Following clause subsumed by 355 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B.
% 13.12/13.03    Following clause subsumed by 351 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 13.12/13.03    Following clause subsumed by 310 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A!=B.
% 13.12/13.03    Following clause subsumed by 351 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 13.12/13.03    Following clause subsumed by 293 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 13.12/13.03    Following clause subsumed by 355 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B.
% 13.12/13.03  ** KEPT (pick-wt=11): 356 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 13.12/13.03  ** KEPT (pick-wt=11): 357 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 13.12/13.03    Following clause subsumed by 356 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 13.12/13.03    Following clause subsumed by 357 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 13.12/13.03  ** KEPT (pick-wt=18): 358 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)).
% 13.12/13.03  ** KEPT (pick-wt=19): 360 [copy,359,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C),A).
% 13.12/13.03    Following clause subsumed by 360 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C),A).
% 13.12/13.03  ** KEPT (pick-wt=19): 362 [copy,361,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B),A).
% 13.12/13.03  ** KEPT (pick-wt=16): 363 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=C|B=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A).
% 13.12/13.03  ** KEPT (pick-wt=16): 364 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)=C|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A).
% 13.12/13.03  ** KEPT (pick-wt=13): 365 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),A)=B.
% 13.12/13.03  ** KEPT (pick-wt=18): 366 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A),B).
% 13.12/13.03  ** KEPT (pick-wt=18): 367 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A),B).
% 13.12/13.03    Following clause subsumed by 362 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B),A).
% 13.12/13.03  ** KEPT (pick-wt=13): 368 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=B.
% 13.12/13.03  ** KEPT (pick-wt=14): 369 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 13.12/13.03  ** KEPT (pick-wt=14): 370 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C),A)).
% 13.12/13.03  ** KEPT (pick-wt=11): 371 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 13.12/13.03  ** KEPT (pick-wt=11): 372 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 13.12/13.03  ** KEPT (pick-wt=14): 373 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 13.12/13.03  ** KEPT (pick-wt=14): 374 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 13.12/13.03  ** KEPT (pick-wt=14): 375 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 13.12/13.03  ** KEPT (pick-wt=14): 376 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B),C)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 13.12/13.03  ** KEPT (pick-wt=19): 377 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A),B).
% 13.12/13.03  ** KEPT (pick-wt=12): 379 [copy,378,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,$f6(B,A))=B.
% 13.12/13.03    Following clause subsumed by 113 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C).
% 13.12/13.03  ** KEPT (pick-wt=5): 380 [] c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.12/13.03  ** KEPT (pick-wt=14): 381 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,A),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B)).
% 13.12/13.03  ** KEPT (pick-wt=22): 382 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)).
% 13.12/13.03  ** KEPT (pick-wt=18): 383 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|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)).
% 13.12/13.03  ** KEPT (pick-wt=18): 384 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|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)).
% 13.12/13.03  ** KEPT (pick-wt=13): 385 [] 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).
% 13.12/13.03  ** KEPT (pick-wt=13): 386 [] 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).
% 13.12/13.03  ** KEPT (pick-wt=17): 387 [] 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).
% 13.12/13.03    Following clause subsumed by 385 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).
% 13.12/13.03    Following clause subsumed by 386 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).
% 13.12/13.03    Following clause subsumed by 387 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).
% 13.12/13.03  ** KEPT (pick-wt=23): 388 [] -class_Rings_Olinordered__ring__strict(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.03  ** KEPT (pick-wt=23): 389 [] -class_Rings_Olinordered__ring__strict(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.03  ** KEPT (pick-wt=27): 390 [] -class_Rings_Olinordered__ring__strict(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.03  ** KEPT (pick-wt=37): 392 [copy,391,flip.2] -class_Rings_Oring(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ominus__class_Ominus(A,C,D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),D))=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),D)).
% 13.12/13.03  ** KEPT (pick-wt=14): 393 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ouminus__class_Ouminus(A,B).
% 13.12/13.03  ** KEPT (pick-wt=14): 394 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ouminus__class_Ouminus(A,B).
% 13.12/13.03  ** KEPT (pick-wt=18): 395 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 13.12/13.03    Following clause subsumed by 340 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 13.12/13.03    Following clause subsumed by 339 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 13.12/13.03  ** KEPT (pick-wt=16): 396 [] -hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.12/13.03  ** KEPT (pick-wt=17): 397 [] -hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)|hBOOL(hAPP(A,D)).
% 13.12/13.03  ** KEPT (pick-wt=18): 398 [] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)| -hBOOL(hAPP(A,$f7(C,B,A))).
% 13.12/13.03  ** KEPT (pick-wt=21): 400 [copy,399,flip.3] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,$f7(C,B,A))=B.
% 13.12/13.03  ** KEPT (pick-wt=19): 401 [] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,$f7(C,B,A))).
% 13.12/13.03    Following clause subsumed by 396 during input processing: 0 [] -hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.12/13.03    Following clause subsumed by 397 during input processing: 0 [] -hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)|hBOOL(hAPP(A,D)).
% 13.12/13.03  ** KEPT (pick-wt=18): 402 [] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)| -hBOOL(hAPP(A,$f8(C,B,A))).
% 13.12/13.03  ** KEPT (pick-wt=21): 404 [copy,403,flip.3] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,$f8(C,B,A))=B.
% 13.12/13.03  ** KEPT (pick-wt=19): 405 [] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,$f8(C,B,A))).
% 13.12/13.03  ** KEPT (pick-wt=23): 406 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C).
% 13.12/13.03  ** KEPT (pick-wt=23): 407 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C).
% 13.12/13.03  ** KEPT (pick-wt=20): 408 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)).
% 13.12/13.03  ** KEPT (pick-wt=23): 409 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)).
% 13.12/13.03  ** KEPT (pick-wt=15): 410 [] -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))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 13.12/13.03  ** KEPT (pick-wt=15): 411 [] -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))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 13.12/13.03  ** KEPT (pick-wt=20): 412 [] 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))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 13.12/13.03  ** KEPT (pick-wt=19): 413 [] -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))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 13.12/13.03  ** KEPT (pick-wt=18): 414 [] -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))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 13.12/13.03  ** KEPT (pick-wt=23): 415 [] 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))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 13.12/13.03  ** KEPT (pick-wt=19): 416 [] -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))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 13.12/13.03  ** KEPT (pick-wt=18): 417 [] -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))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C).
% 13.12/13.03  ** KEPT (pick-wt=23): 418 [] 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))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C).
% 13.12/13.03    Following clause subsumed by 418 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)).
% 13.12/13.03    Following clause subsumed by 415 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)).
% 13.12/13.03  ** KEPT (pick-wt=16): 420 [copy,419,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).
% 13.12/13.03  ** KEPT (pick-wt=12): 421 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.12/13.03  ** KEPT (pick-wt=12): 422 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.12/13.03  ** KEPT (pick-wt=21): 423 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/13.03  ** KEPT (pick-wt=21): 424 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/13.03  ** KEPT (pick-wt=25): 425 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.12/13.03  ** KEPT (pick-wt=12): 426 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A).
% 13.12/13.03  ** KEPT (pick-wt=12): 427 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A).
% 13.12/13.03  ** KEPT (pick-wt=12): 428 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=B.
% 13.12/13.03  ** KEPT (pick-wt=12): 429 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=B.
% 13.12/13.03  ** KEPT (pick-wt=12): 430 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B),A).
% 13.12/13.03  ** KEPT (pick-wt=10): 431 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B).
% 13.12/13.03  ** KEPT (pick-wt=16): 432 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B),A)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B).
% 13.12/13.03  ** KEPT (pick-wt=24): 433 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)),c_Groups_Ozero__class_Ozero(A))|B=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.03  ** KEPT (pick-wt=24): 434 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)),c_Groups_Ozero__class_Ozero(A))|C=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.03  ** KEPT (pick-wt=28): 435 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)),c_Groups_Ozero__class_Ozero(A))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.03  ** KEPT (pick-wt=20): 436 [] -class_Rings_Olinordered__ring(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))).
% 13.12/13.03  ** KEPT (pick-wt=28): 437 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.03  ** KEPT (pick-wt=24): 438 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))|B=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.03  ** KEPT (pick-wt=24): 439 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))|C=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.03  ** KEPT (pick-wt=20): 440 [] -class_Rings_Olinordered__ring(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.03  ** KEPT (pick-wt=27): 442 [copy,441,flip.2] -class_Rings_Oring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))),c_Groups_Ominus__class_Ominus(A,B,c_Groups_Oone__class_Oone(A)))=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),c_Groups_Oone__class_Oone(A)).
% 13.12/13.03  ** KEPT (pick-wt=23): 443 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,C).
% 13.12/13.03  ** KEPT (pick-wt=23): 444 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,C).
% 13.12/13.03  ** KEPT (pick-wt=23): 445 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,C).
% 13.12/13.03  ** KEPT (pick-wt=23): 446 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,C).
% 13.12/13.03  ** KEPT (pick-wt=23): 447 [] -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))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 13.12/13.03    Following clause subsumed by 383 during input processing: 0 [] 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))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 13.12/13.03  ** KEPT (pick-wt=23): 448 [] -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))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 13.12/13.03    Following clause subsumed by 384 during input processing: 0 [] 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))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 13.12/13.03    Following clause subsumed by 327 during input processing: 0 [] A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.12/13.03  ** KEPT (pick-wt=14): 449 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B).
% 13.12/13.03  ** KEPT (pick-wt=14): 450 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B).
% 13.12/13.03  ** KEPT (pick-wt=14): 451 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)).
% 13.12/13.03  ** KEPT (pick-wt=14): 452 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)).
% 13.12/13.03  ** KEPT (pick-wt=14): 453 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B).
% 13.12/13.03  ** KEPT (pick-wt=14): 454 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B).
% 13.12/13.03  ** KEPT (pick-wt=14): 455 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)).
% 13.12/13.03  ** KEPT (pick-wt=14): 456 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)).
% 13.12/13.03  ** KEPT (pick-wt=12): 458 [copy,457,flip.2] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A).
% 13.12/13.03    Following clause subsumed by 458 during input processing: 0 [flip.2] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A).
% 13.12/13.03  ** KEPT (pick-wt=10): 459 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A).
% 13.12/13.03  ** KEPT (pick-wt=23): 460 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,A),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____))|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,A))|hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,A),$f9(A))=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.12/13.03    Following clause subsumed by 107 during input processing: 0 [flip.1,flip.2] c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)!=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____)|c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),$c5).
% 13.12/13.03  ** KEPT (pick-wt=23): 461 [] -class_RealVector_Oreal__normed__div__algebra(A)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,c_RealVector_Onorm__class_Onorm(A,C))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Rings_Oinverse__class_Oinverse(A,C)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,B)).
% 13.12/13.03  ** KEPT (pick-wt=9): 462 [] hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.12/13.03  ** KEPT (pick-wt=6): 463 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)).
% 13.12/13.03    Following clause subsumed by 463 during input processing: 0 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)).
% 13.12/13.03  ** KEPT (pick-wt=39): 464 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C),E))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,D,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)),C),E)).
% 13.12/13.03  ** KEPT (pick-wt=39): 465 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C),E))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,D,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)),C),E)).
% 13.12/13.03  ** KEPT (pick-wt=39): 466 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),E))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)),C),D),E).
% 13.12/13.03  ** KEPT (pick-wt=39): 467 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),E))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)),C),D),E).
% 13.12/13.03  ** KEPT (pick-wt=39): 469 [copy,468,flip.4] -class_Rings_Odivision__ring(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Rings_Oinverse__class_Oinverse(A,B)),c_Groups_Ominus__class_Ominus(A,B,C))),c_Rings_Oinverse__class_Oinverse(A,C)))=c_Groups_Ominus__class_Ominus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)).
% 13.12/13.03  ** KEPT (pick-wt=14): 470 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.03  ** KEPT (pick-wt=14): 471 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Oone__class_Oone(A)).
% 13.12/13.03  ** KEPT (pick-wt=19): 472 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Oone__class_Oone(A)).
% 13.12/13.03  ** KEPT (pick-wt=16): 473 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____))).
% 13.12/13.03  ** KEPT (pick-wt=38): 474 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))).
% 13.12/13.03  ** KEPT (pick-wt=38): 475 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),A)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))).
% 13.12/13.03  ** KEPT (pick-wt=23): 477 [copy,476,flip.2] -class_Groups_Oab__group__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ominus__class_Ominus(A,D,E))=c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 13.12/13.03  ** KEPT (pick-wt=9): 478 [] -class_Fields_Ofield__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.03  ** KEPT (pick-wt=21): 480 [copy,479,flip.2] -class_Fields_Ofield__inverse__zero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Rings_Oinverse__class_Oinverse(A,B)),c_Rings_Oinverse__class_Oinverse(A,C))=c_Rings_Oinverse__class_Oinverse(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.12/13.03    Following clause subsumed by 329 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.
% 13.12/13.03    Following clause subsumed by 331 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).
% 13.12/13.03    Following clause subsumed by 330 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.
% 13.12/13.03  ** KEPT (pick-wt=12): 481 [] -class_Fields_Ofield__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)!=c_Groups_Oone__class_Oone(A)|B=c_Groups_Oone__class_Oone(A).
% 13.12/13.03  ** KEPT (pick-wt=12): 482 [] -class_Fields_Ofield__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,B)=c_Groups_Oone__class_Oone(A)|B!=c_Groups_Oone__class_Oone(A).
% 13.12/13.03  ** KEPT (pick-wt=13): 484 [copy,483,flip.2] -class_Fields_Olinordered__field__inverse__zero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Groups_Oabs__class_Oabs(A,B))=c_Groups_Oabs__class_Oabs(A,c_Rings_Oinverse__class_Oinverse(A,B)).
% 13.12/13.03  ** KEPT (pick-wt=14): 485 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.03  ** KEPT (pick-wt=14): 486 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.03  ** KEPT (pick-wt=14): 487 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.03  ** KEPT (pick-wt=14): 488 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.03  ** KEPT (pick-wt=14): 489 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.03  ** KEPT (pick-wt=14): 490 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.03  ** KEPT (pick-wt=14): 491 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.03  ** KEPT (pick-wt=14): 492 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.03  ** KEPT (pick-wt=14): 493 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B)).
% 13.12/13.03  ** KEPT (pick-wt=18): 494 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Rings_Oinverse__class_Oinverse(A,B))|B=c_Groups_Ozero__class_Ozero(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.03  ** KEPT (pick-wt=14): 495 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.03  ** KEPT (pick-wt=19): 496 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)).
% 13.12/13.03  ** KEPT (pick-wt=19): 497 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)).
% 13.12/13.03  ** KEPT (pick-wt=18): 498 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Ozero__class_Ozero(A))|B=c_Groups_Ozero__class_Ozero(A)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.03  ** KEPT (pick-wt=19): 499 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,C,B).
% 13.12/13.03  ** KEPT (pick-wt=19): 500 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,C,B).
% 13.12/13.03  ** KEPT (pick-wt=17): 502 [copy,501,flip.3] -class_Fields_Olinordered__field(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Oinverse__class_Oinverse(A,c_Groups_Oabs__class_Oabs(A,B))=c_Groups_Oabs__class_Oabs(A,c_Rings_Oinverse__class_Oinverse(A,B)).
% 13.12/13.03  ** KEPT (pick-wt=21): 503 [] -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.
% 13.12/13.03    Following clause subsumed by 330 during input processing: 0 [] -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.
% 13.12/13.03    Following clause subsumed by 414 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 13.12/13.03    Following clause subsumed by 415 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 13.12/13.03  ** KEPT (pick-wt=19): 504 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)).
% 13.12/13.03  ** KEPT (pick-wt=19): 505 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Oinverse(A,C),c_Rings_Oinverse__class_Oinverse(A,B)).
% 13.12/13.03  ** KEPT (pick-wt=19): 506 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 13.12/13.03  ** KEPT (pick-wt=19): 507 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 13.12/13.03  ** KEPT (pick-wt=19): 508 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),B).
% 13.12/13.03  ** KEPT (pick-wt=14): 509 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.03  ** KEPT (pick-wt=14): 510 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),B).
% 13.12/13.03  ** KEPT (pick-wt=37): 512 [copy,511,flip.4] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),c_Rings_Oinverse__class_Oinverse(A,B))),c_Rings_Oinverse__class_Oinverse(A,C))=c_Groups_Oplus__class_Oplus(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Rings_Oinverse__class_Oinverse(A,C)).
% 13.12/13.03  ** KEPT (pick-wt=19): 513 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)).
% 13.12/13.03  ** KEPT (pick-wt=14): 514 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.03  ** KEPT (pick-wt=14): 515 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Oone__class_Oone(A)).
% 13.12/13.03  ** KEPT (pick-wt=19): 516 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Oone__class_Oone(A)).
% 13.12/13.03  ** KEPT (pick-wt=17): 517 [] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Rings_Oinverse__class_Oinverse(A,B)),B)=c_Groups_Oone__class_Oone(A).
% 13.12/13.03    Following clause subsumed by 447 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 13.12/13.03    Following clause subsumed by 383 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 13.12/13.03  ** KEPT (pick-wt=39): 518 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),E))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)),C),D),E).
% 13.12/13.03  ** KEPT (pick-wt=39): 519 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),E))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)),C),D),E).
% 13.12/13.03  ** KEPT (pick-wt=40): 520 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),E))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)),C),D),E).
% 13.12/13.03  ** KEPT (pick-wt=37): 521 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C),D)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),E)|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,B,A)),C),D)=E.
% 13.12/13.03  ** KEPT (pick-wt=37): 522 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C),D)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),E)|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,B,A)),C),D)!=E.
% 13.12/13.03  ** KEPT (pick-wt=39): 523 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C),E))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,D,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)),C),E)).
% 13.12/13.03  ** KEPT (pick-wt=39): 524 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C),E))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,D,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)),C),E)).
% 13.12/13.03  ** KEPT (pick-wt=40): 525 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C),E))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,D,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)),C),E)).
% 13.12/13.03  ** KEPT (pick-wt=37): 526 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),D)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C),E)|D=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,B,A)),C),E).
% 13.12/13.03  ** KEPT (pick-wt=37): 527 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),D)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C),E)|D!=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,B,A)),C),E).
% 13.12/13.03  ** KEPT (pick-wt=19): 528 [] -class_Fields_Olinordered__field(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),c_Rings_Oinverse__class_Oinverse(A,B)).
% 13.12/13.03  ** KEPT (pick-wt=19): 529 [] -class_Fields_Olinordered__field__inverse__zero(A)| -c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B).
% 13.12/13.03  ** KEPT (pick-wt=14): 530 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.03  ** KEPT (pick-wt=14): 531 [] -class_Fields_Olinordered__field__inverse__zero(A)|c_Orderings_Oord__class_Oless(A,c_Rings_Oinverse__class_Oinverse(A,B),c_Groups_Oone__class_Oone(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B).
% 13.12/13.03    Following clause subsumed by 110 during input processing: 0 [flip.1] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),$c6)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.12/13.03  ** KEPT (pick-wt=31): 532 [] hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),$c8)!=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),$c7).
% 13.12/13.03  ** KEPT (pick-wt=18): 533 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,C,D),B).
% 13.12/13.03  ** KEPT (pick-wt=18): 534 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)),D)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 13.12/13.03  ** KEPT (pick-wt=25): 535 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)),D)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,C,D),B)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 13.12/13.03  ** KEPT (pick-wt=18): 536 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C)),c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C))).
% 13.12/13.03  ** KEPT (pick-wt=22): 537 [] -class_Rings_Ocomm__semiring__0(A)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C),c_Polynomial_OpCons(A,D,C))!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 13.12/13.03  ** KEPT (pick-wt=10): 538 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.03  ** KEPT (pick-wt=10): 539 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.03  ** KEPT (pick-wt=25): 540 [] -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)).
% 13.12/13.03  ** KEPT (pick-wt=17): 541 [] -class_Groups_Oab__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 13.12/13.03  ** KEPT (pick-wt=14): 542 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 13.12/13.04  ** KEPT (pick-wt=14): 543 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,B,D)|C!=D.
% 13.12/13.04  ** KEPT (pick-wt=14): 544 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,D,C)|B=D.
% 13.12/13.04  ** KEPT (pick-wt=14): 545 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,D,C)|B!=D.
% 13.12/13.04    Following clause subsumed by 542 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 13.12/13.04  ** KEPT (pick-wt=14): 546 [] -class_Groups_Ocancel__ab__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 13.12/13.04    Following clause subsumed by 544 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,D,C)|B=D.
% 13.12/13.04  ** KEPT (pick-wt=10): 547 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)!=B|B=c_Groups_Oone__class_Oone(A).
% 13.12/13.04  ** KEPT (pick-wt=10): 548 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)=B|B!=c_Groups_Oone__class_Oone(A).
% 13.12/13.04  ** KEPT (pick-wt=17): 549 [] -class_Groups_Oab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|B!=C|D=E.
% 13.12/13.04  ** KEPT (pick-wt=17): 550 [] -class_Groups_Oab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|B=C|D!=E.
% 13.12/13.04  ** KEPT (pick-wt=12): 551 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=c_Groups_Ouminus__class_Ouminus(A,C)|B=C.
% 13.12/13.04  ** KEPT (pick-wt=12): 552 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=c_Groups_Ouminus__class_Ouminus(A,C)|B!=C.
% 13.12/13.04  ** KEPT (pick-wt=12): 553 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=C|c_Groups_Ouminus__class_Ouminus(A,C)=B.
% 13.12/13.04    Following clause subsumed by 553 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.
% 13.12/13.04  ** KEPT (pick-wt=12): 554 [] -class_Groups_Ogroup__add(A)|B!=c_Groups_Ouminus__class_Ouminus(A,C)|C=c_Groups_Ouminus__class_Ouminus(A,B).
% 13.12/13.04    Following clause subsumed by 554 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).
% 13.12/13.04  ** KEPT (pick-wt=9): 555 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ouminus__class_Ouminus(A,B))=B.
% 13.12/13.04  ** KEPT (pick-wt=11): 556 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,c_Groups_Oabs__class_Oabs(A,B))=c_Groups_Oabs__class_Oabs(A,B).
% 13.12/13.04  ** KEPT (pick-wt=9): 557 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 13.12/13.04  ** KEPT (pick-wt=9): 558 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 13.12/13.04  ** KEPT (pick-wt=13): 559 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oplus__class_Oplus(A,B,B)|B=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=13): 560 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)=c_Groups_Oplus__class_Oplus(A,B,B)|B!=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=9): 561 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 13.12/13.04  ** KEPT (pick-wt=9): 562 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 13.12/13.04  ** KEPT (pick-wt=16): 563 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.12/13.04  ** KEPT (pick-wt=16): 564 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))| -c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.12/13.04  ** KEPT (pick-wt=16): 565 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 13.12/13.04  ** KEPT (pick-wt=16): 566 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))| -c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 13.12/13.04  ** KEPT (pick-wt=16): 567 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)).
% 13.12/13.04  ** KEPT (pick-wt=16): 568 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)).
% 13.12/13.04  ** KEPT (pick-wt=20): 569 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 13.12/13.04    Following clause subsumed by 563 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.12/13.04    Following clause subsumed by 565 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 13.12/13.04  ** KEPT (pick-wt=16): 570 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless(A,B,D).
% 13.12/13.04  ** KEPT (pick-wt=16): 571 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))| -c_Orderings_Oord__class_Oless(A,B,D).
% 13.12/13.04  ** KEPT (pick-wt=16): 572 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless(A,C,D).
% 13.12/13.04  ** KEPT (pick-wt=16): 573 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))| -c_Orderings_Oord__class_Oless(A,C,D).
% 13.12/13.04  ** KEPT (pick-wt=16): 574 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)).
% 13.12/13.04  ** KEPT (pick-wt=16): 575 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)).
% 13.12/13.04  ** KEPT (pick-wt=20): 576 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 13.12/13.04    Following clause subsumed by 570 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless(A,B,D).
% 13.12/13.04    Following clause subsumed by 572 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless(A,C,D).
% 13.12/13.04  ** KEPT (pick-wt=12): 577 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|B=C.
% 13.12/13.04  ** KEPT (pick-wt=12): 578 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)=c_Groups_Ozero__class_Ozero(A)|B!=C.
% 13.12/13.04  ** KEPT (pick-wt=12): 579 [] -class_Groups_Oab__group__add(A)|B!=C|c_Groups_Ominus__class_Ominus(A,B,C)=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=12): 580 [] -class_Groups_Oab__group__add(A)|B=C|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=9): 581 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,B)=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=9): 582 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 13.12/13.04  ** KEPT (pick-wt=19): 583 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,D,E).
% 13.12/13.04  ** KEPT (pick-wt=19): 584 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E).
% 13.12/13.04  ** KEPT (pick-wt=19): 585 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,D,E).
% 13.12/13.04  ** KEPT (pick-wt=19): 586 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E).
% 13.12/13.04  ** KEPT (pick-wt=11): 587 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 13.12/13.04  ** KEPT (pick-wt=11): 588 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 13.12/13.04  ** KEPT (pick-wt=11): 589 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 13.12/13.04  ** KEPT (pick-wt=11): 590 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 13.12/13.04  ** KEPT (pick-wt=11): 591 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=11): 592 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=12): 593 [] -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).
% 13.12/13.04  ** KEPT (pick-wt=12): 594 [] -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).
% 13.12/13.04    Following clause subsumed by 591 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).
% 13.12/13.04    Following clause subsumed by 592 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).
% 13.12/13.04  ** KEPT (pick-wt=12): 595 [] -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.
% 13.12/13.04  ** KEPT (pick-wt=12): 596 [] -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.
% 13.12/13.04  ** KEPT (pick-wt=9): 597 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=14): 598 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Groups_Ouminus__class_Ouminus(A,B)).
% 13.12/13.04  ** KEPT (pick-wt=14): 599 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C))|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 13.12/13.04    Following clause subsumed by 598 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C))| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 13.12/13.04  ** KEPT (pick-wt=14): 600 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,C),B).
% 13.12/13.04    Following clause subsumed by 600 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,C),B).
% 13.12/13.04  ** KEPT (pick-wt=14): 601 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ouminus__class_Ouminus(A,C))|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ouminus__class_Ouminus(A,B)).
% 13.12/13.04    Following clause subsumed by 601 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ouminus__class_Ouminus(A,C))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ouminus__class_Ouminus(A,B)).
% 13.12/13.04  ** KEPT (pick-wt=11): 602 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,B,C),C)=B.
% 13.12/13.04  ** KEPT (pick-wt=11): 603 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,C),C)=B.
% 13.12/13.04  ** KEPT (pick-wt=14): 604 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,C))|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ouminus__class_Ouminus(A,B)).
% 13.12/13.04    Following clause subsumed by 604 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,C))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ouminus__class_Ouminus(A,B)).
% 13.12/13.04  ** KEPT (pick-wt=14): 605 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,C),B).
% 13.12/13.04    Following clause subsumed by 605 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,C),B).
% 13.12/13.04  ** KEPT (pick-wt=14): 606 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C))|c_Orderings_Oord__class_Oless(A,C,B).
% 13.12/13.04  ** KEPT (pick-wt=14): 607 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C))| -c_Orderings_Oord__class_Oless(A,C,B).
% 13.12/13.04  ** KEPT (pick-wt=17): 608 [] -class_Groups_Oab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oplus__class_Oplus(A,B,C))=c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)).
% 13.12/13.04  ** KEPT (pick-wt=17): 609 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oplus__class_Oplus(A,B,C))=c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Groups_Ouminus__class_Ouminus(A,B)).
% 13.12/13.04  ** KEPT (pick-wt=13): 610 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),C))=C.
% 13.12/13.04  ** KEPT (pick-wt=13): 611 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Oplus__class_Oplus(A,B,C))=C.
% 13.12/13.04  ** KEPT (pick-wt=13): 612 [] -class_Groups_Oab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ominus__class_Ominus(A,B,C))=c_Groups_Ominus__class_Ominus(A,C,B).
% 13.12/13.04  ** KEPT (pick-wt=12): 613 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=12): 614 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=9): 615 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=12): 616 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 13.12/13.04  ** KEPT (pick-wt=8): 617 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Oabs__class_Oabs(A,B)).
% 13.12/13.04  ** KEPT (pick-wt=21): 618 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)))=c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)).
% 13.12/13.04  ** KEPT (pick-wt=15): 619 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C))=c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,B)).
% 13.12/13.04  ** KEPT (pick-wt=11): 620 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Groups_Oabs__class_Oabs(A,c_Groups_Ouminus__class_Ouminus(A,B))=c_Groups_Oabs__class_Oabs(A,B).
% 13.12/13.04  ** KEPT (pick-wt=20): 621 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=18): 622 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Oplus__class_Oplus(A,D,B)).
% 13.12/13.04  ** KEPT (pick-wt=18): 623 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 13.12/13.04  ** KEPT (pick-wt=23): 624 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=23): 625 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=27): 626 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04    Following clause subsumed by 623 during input processing: 0 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 13.12/13.04  ** KEPT (pick-wt=15): 627 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=15): 628 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=15): 629 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.04  ** KEPT (pick-wt=15): 630 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.04  ** KEPT (pick-wt=15): 631 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.04  ** KEPT (pick-wt=15): 632 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.04  ** KEPT (pick-wt=15): 633 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=15): 634 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=20): 635 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 13.12/13.04  ** KEPT (pick-wt=20): 636 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=20): 637 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 13.12/13.04  ** KEPT (pick-wt=20): 638 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 13.12/13.04  ** KEPT (pick-wt=14): 639 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=14): 640 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=14): 641 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=14): 642 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=13): 643 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.04  ** KEPT (pick-wt=13): 644 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.04  ** KEPT (pick-wt=14): 645 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.04  ** KEPT (pick-wt=14): 646 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.04  ** KEPT (pick-wt=13): 647 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ouminus__class_Ouminus(A,B))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=13): 648 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ouminus__class_Ouminus(A,B))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=14): 649 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=14): 650 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=13): 651 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.04  ** KEPT (pick-wt=13): 652 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.04  ** KEPT (pick-wt=14): 653 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.04  ** KEPT (pick-wt=14): 654 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.12/13.04  ** KEPT (pick-wt=14): 655 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=14): 656 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=14): 657 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|c_Groups_Ouminus__class_Ouminus(A,B)=C.
% 13.12/13.04  ** KEPT (pick-wt=11): 658 [] -class_Groups_Oab__group__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),B)=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=11): 659 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),B)=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=14): 660 [] -class_Groups_Ogroup__add(A)|B!=c_Groups_Ouminus__class_Ouminus(A,C)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=14): 661 [] -class_Groups_Ogroup__add(A)|B=c_Groups_Ouminus__class_Ouminus(A,C)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=11): 662 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ouminus__class_Ouminus(A,B))=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=11): 663 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Ouminus__class_Ouminus(A,B).
% 13.12/13.04  ** KEPT (pick-wt=12): 664 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Groups_Oabs__class_Oabs(A,B)=B.
% 13.12/13.04  ** KEPT (pick-wt=13): 665 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Ozero__class_Ozero(A))|B=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=13): 666 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Ozero__class_Ozero(A))|B!=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=9): 667 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oabs__class_Oabs(A,B)).
% 13.12/13.04  ** KEPT (pick-wt=12): 668 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Groups_Oabs__class_Oabs(A,B)=B.
% 13.12/13.04  ** KEPT (pick-wt=13): 669 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oabs__class_Oabs(A,B))|B!=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=13): 670 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oabs__class_Oabs(A,B))|B=c_Groups_Ozero__class_Ozero(A).
% 13.12/13.04  ** KEPT (pick-wt=9): 671 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=13): 672 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,c_Groups_Ouminus__class_Ouminus(A,C))=c_Groups_Oplus__class_Oplus(A,B,C).
% 13.12/13.04  ** KEPT (pick-wt=13): 674 [copy,673,flip.2] -class_Groups_Oab__group__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ouminus__class_Ouminus(A,C))=c_Groups_Ominus__class_Ominus(A,B,C).
% 13.12/13.04  ** KEPT (pick-wt=13): 676 [copy,675,flip.2] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ouminus__class_Ouminus(A,C))=c_Groups_Ominus__class_Ominus(A,B,C).
% 13.12/13.04  ** KEPT (pick-wt=18): 677 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C))).
% 13.12/13.04  ** KEPT (pick-wt=18): 678 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,B))).
% 13.12/13.04  ** KEPT (pick-wt=18): 679 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C)),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C))).
% 13.12/13.04  ** KEPT (pick-wt=20): 680 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oabs__class_Oabs(A,B),c_Groups_Oabs__class_Oabs(A,C))),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,C))).
% 13.12/13.04  ** KEPT (pick-wt=14): 681 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),C).
% 13.12/13.04  ** KEPT (pick-wt=18): 682 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),C).
% 13.12/13.04    Following clause subsumed by 616 during input processing: 0 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 13.12/13.04    Following clause subsumed by 681 during input processing: 0 [] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),C).
% 13.12/13.04    Following clause subsumed by 682 during input processing: 0 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,B),C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),C).
% 13.12/13.04  ** KEPT (pick-wt=10): 683 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Oabs__class_Oabs(A,B)).
% 13.12/13.04  ** KEPT (pick-wt=20): 684 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 13.12/13.04  ** KEPT (pick-wt=20): 685 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 13.12/13.04  ** KEPT (pick-wt=18): 686 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 13.12/13.04  ** KEPT (pick-wt=18): 687 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 13.12/13.04  ** KEPT (pick-wt=20): 688 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=20): 689 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=14): 691 [copy,690,flip.3] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))|c_Groups_Ouminus__class_Ouminus(A,B)=c_Groups_Oabs__class_Oabs(A,B).
% 13.12/13.04  ** KEPT (pick-wt=11): 692 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oabs__class_Oabs(A,B)),c_Groups_Ozero__class_Ozero(A)).
% 13.12/13.04  ** KEPT (pick-wt=14): 694 [copy,693,flip.3] -class_Groups_Oordered__ab__group__add__abs(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Groups_Ouminus__class_Ouminus(A,B)=c_Groups_Oabs__class_Oabs(A,B).
% 13.12/13.04  ** KEPT (pick-wt=14): 696 [copy,695,flip.3] -class_Groups_Oabs__if(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Groups_Ouminus__class_Ouminus(A,B)=c_Groups_Oabs__class_Oabs(A,B).
% 13.12/13.04  ** KEPT (pick-wt=12): 697 [] -class_Groups_Oabs__if(A)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Groups_Oabs__class_Oabs(A,B)=B.
% 13.12/13.04  ** KEPT (pick-wt=30): 698 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,E))),c_Groups_Oplus__class_Oplus(A,c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,B,D)),c_Groups_Oabs__class_Oabs(A,c_Groups_Ominus__class_Ominus(A,C,E)))).
% 13.12/13.04  ** KEPT (pick-wt=17): 699 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))).
% 13.12/13.04  ** KEPT (pick-wt=24): 700 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,c_Polynomial_OpCons(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),hAPP(c_Polynomial_Opoly(A,C),D))).
% 13.12/13.04  ** KEPT (pick-wt=31): 701 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C)),D)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)).
% 13.12/13.04  ** KEPT (pick-wt=14): 702 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,B,C)!=c_Polynomial_Omonom(A,D,C)|B=D.
% 13.12/13.04  ** KEPT (pick-wt=14): 703 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,B,C)=c_Polynomial_Omonom(A,D,C)|B!=D.
% 13.12/13.04  ** KEPT (pick-wt=16): 704 [] -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).
% 13.12/13.04  ** KEPT (pick-wt=21): 705 [] -class_Groups_Oab__group__add(A)|c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Polynomial_Omonom(A,B,C),c_Polynomial_Omonom(A,D,C))=c_Polynomial_Omonom(A,c_Groups_Ominus__class_Ominus(A,B,D),C).
% 13.12/13.04  ** KEPT (pick-wt=21): 706 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Polynomial_Omonom(A,B,C),c_Polynomial_Omonom(A,D,C))=c_Polynomial_Omonom(A,c_Groups_Oplus__class_Oplus(A,B,D),C).
% 13.12/13.04  ** KEPT (pick-wt=28): 707 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Polynomial_Omonom(A,B,C)),c_Polynomial_Omonom(A,D,E))=c_Polynomial_Omonom(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,E)).
% 13.12/13.04  ** KEPT (pick-wt=14): 708 [] -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).
% 13.12/13.04  ** KEPT (pick-wt=14): 709 [] -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).
% 13.12/13.04  ** KEPT (pick-wt=11): 710 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 13.12/13.04  ** KEPT (pick-wt=19): 711 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osmult(A,B,c_Polynomial_Omonom(A,C,D))=c_Polynomial_Omonom(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D).
% 13.12/13.04  ** KEPT (pick-wt=22): 712 [] -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)).
% 13.12/13.04  ** KEPT (pick-wt=14): 714 [copy,713,flip.2] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Polynomial_Omonom(A,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.12/13.04  ** KEPT (pick-wt=14): 715 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)!=c_Polynomial_Opoly(A,C)|B=C.
% 13.12/13.04  ** KEPT (pick-wt=14): 716 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)=c_Polynomial_Opoly(A,C)|B!=C.
% 13.12/13.04  ** KEPT (pick-wt=12): 717 [] -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)).
% 13.12/13.04  ** KEPT (pick-wt=15): 718 [] -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)).
% 13.12/13.04  ** KEPT (pick-wt=11): 719 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B)=B.
% 13.12/13.04  ** KEPT (pick-wt=15): 720 [] -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)).
% 13.12/13.04  ** KEPT (pick-wt=11): 721 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=B.
% 13.12/13.04  ** KEPT (pick-wt=11): 722 [] -class_Groups_Oab__group__add(A)|c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))
% 13.12/13.04  Search stopped in tp_alloc by max_mem option.
% 13.12/13.04  )=B.
% 13.12/13.04  ** KEPT (pick-wt=14): 723 [] -class_Groups_Oab__group__add(A)|c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B).
% 13.12/13.04  ** KEPT (pick-wt=18): 725 [copy,724,flip.3] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)=c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B).
% 13.12/13.04  ** KEPT (pick-wt=15): 726 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))|c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(A),B)=B.
% 13.12/13.04  ** KEPT (pick-wt=14): 727 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)!=c_Polynomial_OpCons(A,D,E)|B=D.
% 13.12/13.04  ** KEPT (pick-wt=14): 728 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)!=c_Polynomial_OpCons(A,D,E)|C=E.
% 13.12/13.04  ** KEPT (pick-wt=17): 729 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)=c_Polynomial_OpCons(A,D,E)|B!=D|C!=E.
% 13.12/13.04  ** KEPT (pick-wt=17): 731 [copy,730,flip.2] -class_Rings_Ocomm__ring(A)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C))=c_Polynomial_Osmult(A,B,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)).
% 13.12/13.04  
% 13.12/13.04  Search stopped in tp_alloc by max_mem option.
% 13.12/13.04  
% 13.12/13.04  ============ end of search ============
% 13.12/13.04  
% 13.12/13.04  -------------- statistics -------------
% 13.12/13.04  clauses given                  0
% 13.12/13.04  clauses generated              0
% 13.12/13.04  clauses kept                 684
% 13.12/13.04  clauses forward subsumed      93
% 13.12/13.04  clauses back subsumed          0
% 13.12/13.04  Kbytes malloced            11718
% 13.12/13.04  
% 13.12/13.04  ----------- times (seconds) -----------
% 13.12/13.04  user CPU time          0.20          (0 hr, 0 min, 0 sec)
% 13.12/13.04  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 13.12/13.04  wall-clock time       13             (0 hr, 0 min, 13 sec)
% 13.12/13.04  
% 13.12/13.04  Process 20664 finished Wed Jul 27 03:04:09 2022
% 13.12/13.04  Otter interrupted
% 13.12/13.04  PROOF NOT FOUND
%------------------------------------------------------------------------------