%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SWW181+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n012.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 13:22:03 EDT 2022

% Result   : Unknown 12.72s 12.63s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW181+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13  % Command  : otter-tptp-script %s
% 0.12/0.34  % Computer : n012.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Jul 27 03:03:20 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 12.57/12.54  ----- Otter 3.3f, August 2004 -----
% 12.57/12.54  The process was started by sandbox on n012.cluster.edu,
% 12.57/12.54  Wed Jul 27 03:03:20 2022
% 12.57/12.54  The command was "./otter".  The process ID is 4047.
% 12.57/12.54  
% 12.57/12.54  set(prolog_style_variables).
% 12.57/12.54  set(auto).
% 12.57/12.54     dependent: set(auto1).
% 12.57/12.54     dependent: set(process_input).
% 12.57/12.54     dependent: clear(print_kept).
% 12.57/12.54     dependent: clear(print_new_demod).
% 12.57/12.54     dependent: clear(print_back_demod).
% 12.57/12.54     dependent: clear(print_back_sub).
% 12.57/12.54     dependent: set(control_memory).
% 12.57/12.54     dependent: assign(max_mem, 12000).
% 12.57/12.54     dependent: assign(pick_given_ratio, 4).
% 12.57/12.54     dependent: assign(stats_level, 1).
% 12.57/12.54     dependent: assign(max_seconds, 10800).
% 12.57/12.54  clear(print_given).
% 12.57/12.54  
% 12.57/12.54  formula_list(usable).
% 12.57/12.54  all A (A=A).
% 12.57/12.54  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).
% 12.57/12.54  all B_z (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)->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_cs____),B_z)),v_m____)).
% 12.57/12.54  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),v_r)->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_cs____),B_z)),B_m)))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  -(all 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),v_r)->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_cs____),B_z)),B_m))))).
% 12.57/12.54  all V_x T_a (class_Orderings_Opreorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x)).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  all V_pa_2 V_a_2 T_a (class_Groups_Ozero(T_a)-> (c_Polynomial_OpCons(T_a,V_a_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))<->V_a_2=c_Groups_Ozero__class_Ozero(T_a)&V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 12.57/12.54  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).
% 12.57/12.54  all V_pa_2 T_a (class_Int_Oring__char__0(T_a)&class_Rings_Oidom(T_a)-> (c_Polynomial_Opoly(T_a,V_pa_2)=c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))<->V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 12.57/12.54  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))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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))))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  all V_x T_a (class_Orderings_Opreorder(T_a)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_x)).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  all V_w c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_w).
% 12.57/12.54  all V_q_2 V_b_2 V_pa_2 V_a_2 T_a (class_Groups_Ozero(T_a)-> (c_Polynomial_OpCons(T_a,V_a_2,V_pa_2)=c_Polynomial_OpCons(T_a,V_b_2,V_q_2)<->V_a_2=V_b_2&V_pa_2=V_q_2)).
% 12.57/12.54  all V_q_2 V_pa_2 T_a (class_Int_Oring__char__0(T_a)&class_Rings_Oidom(T_a)-> (c_Polynomial_Opoly(T_a,V_pa_2)=c_Polynomial_Opoly(T_a,V_q_2)<->V_pa_2=V_q_2)).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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).
% 12.57/12.54  all V_z_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z_2),v_r)->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,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),V_z_2)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))).
% 12.57/12.54  all V_pa_2 V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_a_2,V_pa_2))<->c_Polynomial_Opos__poly(T_a,V_pa_2)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))&c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 12.57/12.54  all V_a_2 V_pa_2 T_a (class_Rings_Oidom(T_a)-> (hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Oorder(T_a,V_a_2,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.57/12.54  all V_pa_2 V_a_2 T_a V_z_2 V_f_2 T_b (class_Groups_Ozero(T_b)-> (hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2)=V_z_2->c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_a_2,V_pa_2))=hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2)))).
% 12.57/12.54  all V_pa_2 V_a_2 V_f_2 V_z_2 T_a T_b (class_Groups_Ozero(T_b)->c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_a_2,V_pa_2))=hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_If(T_a,c_fe_qual(V_pa_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2,c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2)))).
% 12.57/12.54  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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))).
% 12.57/12.54  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))).
% 12.57/12.54  all T_a V_z_2 V_f_2 T_b (class_Groups_Ozero(T_b)-> (hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2)=V_z_2->c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))=V_z_2)).
% 12.57/12.54  all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)<-> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K)))))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  all V_r (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)).
% 12.57/12.54  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)))).
% 12.57/12.54  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).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))))))).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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)).
% 12.57/12.54  all V_ca_2 V_a_2 V_b_2 T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)=c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2)<->V_b_2=V_ca_2)).
% 12.57/12.54  all V_ca_2 V_b_2 V_a_2 T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2)<->V_b_2=V_ca_2)).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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).
% 12.57/12.54  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).
% 12.57/12.54  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))).
% 12.57/12.54  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).
% 12.57/12.54  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).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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)))).
% 12.57/12.54  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)).
% 12.57/12.54  all V_a_2 T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Groups_Oabs__class_Oabs(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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).
% 12.57/12.54  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).
% 12.57/12.54  all V_a_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_a_2,V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.57/12.54  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).
% 12.57/12.54  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).
% 12.57/12.54  all V_b_2 V_ca_2 V_a_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_a_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_a_2,V_b_2))).
% 12.57/12.54  all V_b_2 V_a_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_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  all V_b_2 V_ca_2 V_a_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_a_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_a_2,V_b_2))).
% 12.57/12.54  all V_b_2 V_a_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_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  all V_b_2 V_a_2 T_a (class_Rings_Oring__no__zero__divisors(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  all V_a_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_a_2),c_Groups_Ozero__class_Ozero(T_a))<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  all V_a_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_a_2))<->V_a_2!=c_Groups_Ozero__class_Ozero(T_a))).
% 12.57/12.54  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)).
% 12.57/12.54  all V_b_2 V_a_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_a_2),V_ca_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2)<->V_a_2=V_b_2)).
% 12.57/12.54  all V_b_2 V_a_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_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2)<->V_a_2=V_b_2)).
% 12.57/12.54  c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.57/12.54  all V_a_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_a_2,V_a_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 12.57/12.54  all V_a_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_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  all V_a_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_a_2,V_a_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 12.57/12.54  all V_a_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_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))).
% 12.57/12.54  all V_b_2 V_a_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_a_2),V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_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_a_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)))).
% 12.57/12.54  all V_b_2 V_a_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_a_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_a_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_a_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))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))))).
% 12.57/12.54  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))))))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  all V_b_2 V_ca_2 V_a_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_a_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_a_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_a_2))).
% 12.57/12.54  all V_b_2 V_a_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_a_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_a_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_a_2))).
% 12.57/12.54  all V_b_2 V_a_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_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  all V_b_2 V_a_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_a_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_a_2)))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  all V_b_2 V_a_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_a_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_a_2,V_b_2)))).
% 12.57/12.54  all V_b_2 V_a_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_a_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_a_2)))).
% 12.57/12.54  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))))))).
% 12.57/12.54  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))))))).
% 12.57/12.54  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))))))).
% 12.57/12.54  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))))))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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).
% 12.57/12.54  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).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))))).
% 12.57/12.54  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))))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  all V_a_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_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.57/12.54  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).
% 12.57/12.54  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).
% 12.57/12.54  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))).
% 12.57/12.54  all V_d_2 V_ca_2 V_b_2 V_a_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_a_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_a_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_a_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  all V_z_2 V_x_2 V_y_2 V_w_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_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_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))<->V_w_2=V_x_2|V_y_2=V_z_2)).
% 12.57/12.54  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).
% 12.57/12.54  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).
% 12.57/12.54  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))))).
% 12.57/12.54  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))).
% 12.57/12.54  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)))).
% 12.57/12.54  all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 12.57/12.54  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.57/12.54  all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 12.57/12.54  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).
% 12.57/12.54  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)))))).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)<-> (exists B_n (V_l_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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).
% 12.57/12.54  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).
% 12.57/12.54  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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))))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  all V_t V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)->V_s!=V_t).
% 12.57/12.54  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)->V_m!=V_n).
% 12.57/12.54  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 12.57/12.54  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))).
% 12.57/12.54  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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).
% 12.57/12.54  all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)<->V_b_2=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))).
% 12.57/12.54  all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=V_b_2<->c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)=V_a_2)).
% 12.57/12.54  all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)<->V_a_2=V_b_2)).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  all V_n V_m (V_m=V_n->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 12.57/12.54  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)).
% 12.57/12.54  all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n).
% 12.57/12.54  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)).
% 12.57/12.54  all V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)<->c_Groups_Ozero__class_Ozero(T_a)=V_a_2)).
% 12.57/12.54  all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.57/12.54  all V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.57/12.54  all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=V_a_2<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.57/12.54  all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a_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_a_2)))).
% 12.57/12.54  all V_b_2 V_a_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_a_2),V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2))).
% 12.57/12.54  all V_a_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_a_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2))).
% 12.57/12.54  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)))).
% 12.57/12.54  all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a_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_a_2)))).
% 12.57/12.54  all V_b_2 V_a_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_a_2),V_b_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2))).
% 12.57/12.54  all V_a_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_a_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  all V_b_2 V_a_2 T_a (class_Rings_Oidom(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)<->V_a_2=V_b_2|V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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).
% 12.57/12.54  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).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  all V_a_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_a_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 12.57/12.54  all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 12.57/12.54  all V_a_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_a_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_a_2))).
% 12.57/12.54  all V_a_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_a_2),V_a_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 12.57/12.54  all V_a_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_a_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 12.57/12.54  all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 12.57/12.54  all V_a_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_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 12.57/12.54  all V_a_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_a_2),V_a_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 12.57/12.54  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)).
% 12.57/12.54  all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)<->c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a))).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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)))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  all V_b_2 V_a_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_a_2),V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2))).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  all V_b_2 V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)&c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2))).
% 12.57/12.54  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)).
% 12.57/12.54  all V_a_2 V_x_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_x_2=V_a_2).
% 12.57/12.54  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)).
% 12.57/12.54  all V_ra_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_ra_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ra_2),V_x_2)&c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_ra_2)).
% 12.57/12.54  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)))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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))))).
% 12.57/12.54  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.57/12.54  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)).
% 12.57/12.54  all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 12.57/12.54  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)).
% 12.57/12.54  all V_n_2 V_k_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_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)).
% 12.57/12.54  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))<-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2))).
% 12.57/12.54  all V_n_2 V_k_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_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))<-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2))).
% 12.57/12.54  all V_n_2 V_ma_2 V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)<->V_ma_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.57/12.54  all V_n_2 V_k_2 V_ma_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)<->V_ma_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.57/12.54  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)))).
% 12.57/12.54  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)))).
% 12.57/12.54  all V_n (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n).
% 12.57/12.54  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)).
% 12.57/12.54  all V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.57/12.54  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2))).
% 12.57/12.54  all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)<-> (exists B_k (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k)& (exists B_x all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,B_x))),B_k)))))).
% 12.57/12.54  all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)<-> (exists B_k (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k)& (exists B_N all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_X_2,B_N)))),B_k)))))).
% 12.57/12.54  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)).
% 12.57/12.54  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)))))).
% 12.57/12.54  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)))))).
% 12.57/12.54  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)).
% 12.57/12.54  all V_n_2 V_k_2 V_ma_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_k_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)<->V_ma_2=V_n_2).
% 12.57/12.54  all V_n_2 V_ma_2 V_k_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)<->V_ma_2=V_n_2).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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))).
% 12.57/12.54  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))).
% 12.57/12.54  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)).
% 12.57/12.54  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)).
% 12.57/12.54  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).
% 12.57/12.54  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)).
% 12.57/12.54  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).
% 12.57/12.54  all V_n_2 V_ma_2 V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)<->V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_ma_2=V_n_2).
% 12.57/12.54  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2))).
% 12.57/12.55  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)<->V_ma_2=V_n_2)).
% 12.57/12.55  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))).
% 12.57/12.55  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))).
% 12.57/12.55  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)).
% 12.57/12.55  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))).
% 12.57/12.55  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))).
% 12.57/12.55  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)))))).
% 12.57/12.55  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)))).
% 12.57/12.55  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))).
% 12.57/12.55  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)))))).
% 12.57/12.55  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)).
% 12.57/12.55  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))).
% 12.57/12.55  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)).
% 12.57/12.55  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))).
% 12.57/12.55  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))).
% 12.57/12.55  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)).
% 12.57/12.55  all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.57/12.55  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)).
% 12.57/12.55  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))).
% 12.57/12.55  all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 12.57/12.55  all V_a_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_a_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 12.57/12.55  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))).
% 12.57/12.55  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).
% 12.57/12.55  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).
% 12.57/12.55  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).
% 12.57/12.55  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)).
% 12.57/12.55  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).
% 12.57/12.55  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))).
% 12.57/12.55  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)).
% 12.57/12.55  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))).
% 12.57/12.55  all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_a_2)=c_Groups_Oone__class_Oone(T_a)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 12.57/12.55  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)))).
% 12.57/12.55  all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_a_2)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 12.57/12.55  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))))).
% 12.57/12.55  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))).
% 12.57/12.55  all V_X_2 V_K_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),V_K_2)-> ((all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2))->c_SEQ_OBse_q(T_a,V_X_2)))).
% 12.57/12.55  all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)-> (exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K)))))).
% 12.57/12.55  all V_n_2 V_P_2 (-hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))-> (hBOOL(hAPP(V_P_2,V_n_2))-> (exists B_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2)& (all B_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i,B_k)-> -hBOOL(hAPP(V_P_2,B_i))))&hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))).
% 12.57/12.55  all V_y T_a (class_RealVector_Oreal__normed__algebra(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,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)))))).
% 12.57/12.55  all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.57/12.55  all V_a ((V_a=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))& (V_a!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal))& (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))).
% 12.57/12.55  all V_x ((V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))& (V_x!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal))& (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))).
% 12.57/12.55  all T_a (class_RealVector_Oreal__normed__algebra(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_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)))))).
% 12.57/12.55  all V_x T_a (class_RealVector_Oreal__normed__algebra(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,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)))))).
% 12.57/12.55  all V_ca_2 V_pa_2 T_a (class_Rings_Oidom(T_a)-> (hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_ca_2)=c_Groups_Ozero__class_Ozero(T_a)<->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2))).
% 12.57/12.55  all V_pa_2 V_ca_2 T_a (class_Rings_Oidom(T_a)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_ca_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2)<->hAPP(c_Polynomial_Opoly(T_a,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2))=c_Groups_Ozero__class_Ozero(T_a))).
% 12.57/12.55  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))).
% 12.57/12.55  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))).
% 12.57/12.55  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))).
% 12.57/12.55  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->V_a=c_Groups_Ozero__class_Ozero(T_a))).
% 12.57/12.55  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)))).
% 12.57/12.55  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Rings_Odvd__class_Odvd(T_a,V_a,V_a)).
% 12.57/12.55  all V_k V_l T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Oabs__class_Oabs(T_a,V_l)=c_Groups_Oabs__class_Oabs(T_a,V_k)->c_Rings_Odvd__class_Odvd(T_a,V_l,V_k))).
% 12.57/12.55  all V_k_2 V_ma_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oabs__class_Oabs(T_a,V_ma_2),V_k_2)<->c_Rings_Odvd__class_Odvd(T_a,V_ma_2,V_k_2))).
% 12.57/12.55  all V_k_2 V_ma_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_ma_2,c_Groups_Oabs__class_Oabs(T_a,V_k_2))<->c_Rings_Odvd__class_Odvd(T_a,V_ma_2,V_k_2))).
% 12.57/12.55  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)).
% 12.57/12.55  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))))).
% 12.57/12.55  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)->c_Rings_Odvd__class_Odvd(T_a,V_b,V_c))).
% 12.57/12.55  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)->c_Rings_Odvd__class_Odvd(T_a,V_a,V_c))).
% 12.57/12.55  all V_k V_b V_a T_a (class_Rings_Odvd(T_a)-> (V_a=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)->c_Rings_Odvd__class_Odvd(T_a,V_b,V_a))).
% 12.57/12.55  all V_d V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)-> (c_Rings_Odvd__class_Odvd(T_a,V_c,V_d)->c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))).
% 12.57/12.55  all V_b V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)->c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))).
% 12.57/12.55  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)->c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))).
% 12.57/12.55  all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))).
% 12.57/12.55  all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 12.57/12.55  all V_b_2 V_a_2 V_ca_2 T_a (class_Rings_Oidom(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))<->V_ca_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a_2,V_b_2))).
% 12.57/12.55  all V_b_2 V_ca_2 V_a_2 T_a (class_Rings_Oidom(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))<->V_ca_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a_2,V_b_2))).
% 12.57/12.55  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)))))).
% 12.57/12.55  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)).
% 12.57/12.55  all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Oincse_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_m),hAPP(V_X_2,B_n)))))).
% 12.57/12.55  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))).
% 12.57/12.55  all V_ma_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,c_Groups_Oone__class_Oone(tc_Nat_Onat))<->V_ma_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 12.57/12.55  all V_n_2 V_k_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2))<->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,V_n_2)).
% 12.57/12.55  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).
% 12.57/12.55  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))).
% 12.57/12.55  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))).
% 12.57/12.55  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)).
% 12.57/12.55  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)).
% 12.57/12.55  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))).
% 12.57/12.55  c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.57/12.55  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)).
% 12.57/12.55  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))).
% 12.57/12.55  c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.57/12.55  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)).
% 12.57/12.55  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))).
% 12.57/12.55  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)-> -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m))).
% 12.57/12.55  all V_n_2 V_ma_2 V_k_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))<->V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,V_n_2)).
% 12.57/12.55  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)).
% 12.57/12.55  all V_n V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n))).
% 12.57/12.55  all V_n V_m V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n))).
% 12.57/12.55  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))<->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,V_n_2))).
% 12.57/12.55  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))).
% 12.57/12.55  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2),V_ma_2)<->V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 12.57/12.55  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ma_2),V_ma_2)<->V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 12.57/12.55  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)))))).
% 12.57/12.55  all V_x V_n T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|V_x=c_Groups_Oone__class_Oone(T_a)->c_Rings_Odvd__class_Odvd(T_a,V_x,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)))).
% 12.57/12.55  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))))).
% 12.57/12.55  all V_x c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_x).
% 12.57/12.55  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)-> -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y))).
% 12.57/12.55  all V_z V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x))).
% 12.64/12.55  all V_b V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)-> -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b))).
% 12.64/12.55  all V_z V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x))).
% 12.64/12.55  all V_c V_b V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)-> (V_b=V_c->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a))).
% 12.64/12.55  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)->V_y!=V_x).
% 12.64/12.55  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)->V_x!=V_y).
% 12.64/12.55  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)-> -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y))).
% 12.64/12.55  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)).
% 12.64/12.55  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)-> -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y))).
% 12.64/12.55  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)->V_x!=V_y).
% 12.64/12.55  all V_z V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x))).
% 12.64/12.55  all V_c V_b V_a (V_a=V_b-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_b)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a))).
% 12.64/12.55  all V_z V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z))).
% 12.64/12.55  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)->V_x=V_y)).
% 12.64/12.55  all V_n V_m (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m)->V_m=V_n)).
% 12.64/12.55  all V_c V_b V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)-> (V_b=V_c->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c))).
% 12.64/12.55  all V_c V_b V_a (V_a=V_b-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c))).
% 12.64/12.55  all V_b V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)-> (V_a!=V_b->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a))).
% 12.64/12.55  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)|V_x=V_y).
% 12.64/12.55  all V_x_2 V_y_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)<->V_x_2=V_y_2)).
% 12.64/12.55  all V_y V_x (V_x=V_y->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)).
% 12.64/12.55  all V_b V_a (V_a!=V_b-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a))).
% 12.64/12.55  all V_y_2 V_x_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)<->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)&V_x_2!=V_y_2).
% 12.64/12.55  all V_y_2 V_x_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)<->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)|V_x_2=V_y_2).
% 12.64/12.55  all V_y_2 V_x_2 (V_x_2=V_y_2<->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)&c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)).
% 12.64/12.55  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))).
% 12.64/12.55  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))).
% 12.64/12.55  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)).
% 12.64/12.55  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)).
% 12.64/12.55  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))).
% 12.64/12.55  all V_n V_m V_i (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_i)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n))).
% 12.64/12.55  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))).
% 12.64/12.55  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))).
% 12.64/12.55  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))).
% 12.64/12.55  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)).
% 12.64/12.55  all V_n V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)->c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)))).
% 12.64/12.55  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)).
% 12.64/12.55  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)).
% 12.64/12.55  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).
% 12.64/12.55  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)))).
% 12.64/12.55  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))))).
% 12.64/12.55  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)))).
% 12.64/12.55  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)))).
% 12.64/12.55  all V_n_2 V_a_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_a_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a)&V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.64/12.55  all V_n_2 V_ma_2 V_a_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_ma_2)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)<->V_ma_2=V_n_2))).
% 12.64/12.55  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)).
% 12.64/12.55  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))).
% 12.64/12.55  all V_a V_n V_m T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))).
% 12.64/12.55  all V_m V_n V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m))))).
% 12.64/12.55  all V_m V_b V_n V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),V_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),V_b)))).
% 12.64/12.55  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))).
% 12.64/12.55  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)))).
% 12.64/12.55  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))))).
% 12.64/12.55  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))))).
% 12.64/12.55  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))).
% 12.64/12.55  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))).
% 12.64/12.55  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))).
% 12.64/12.55  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)))).
% 12.64/12.55  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)))).
% 12.64/12.55  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))))).
% 12.64/12.55  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))))).
% 12.64/12.55  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))))).
% 12.64/12.55  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)))))).
% 12.64/12.55  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))))).
% 12.64/12.55  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)))))).
% 12.64/12.55  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)))).
% 12.64/12.55  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)))).
% 12.64/12.55  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m))).
% 12.64/12.55  all V_a V_p T_a (class_Rings_Oidom(T_a)-> (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p)& -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p))).
% 12.64/12.55  all V_a V_p T_a (class_Rings_Oidom(T_a)-> (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))-> -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p))).
% 12.64/12.55  all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)).
% 12.64/12.55  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))).
% 12.64/12.55  all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)).
% 12.64/12.55  all V_k c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k).
% 12.64/12.55  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)-> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n)-> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m)->V_m=V_n)))).
% 12.64/12.55  all V_t_2 V_ma_2 V_k_2 (V_k_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)-> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ma_2,V_t_2)<->c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2)))).
% 12.64/12.55  all V_x_2 (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_x_2,c_Groups_Oone__class_Oone(tc_Int_Oint))<->c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)=c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 12.64/12.55  all V_ma_2 V_n_2 V_k_2 (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_n_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_ma_2)))<->c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,V_n_2)).
% 12.64/12.55  all V_ca_2 V_t_2 V_x_2 V_d_2 V_a_2 (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_d_2)-> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2))<->c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_d_2)),V_t_2)))).
% 12.64/12.55  all V_b V_a (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b)-> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_b,V_a)->c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_a)=c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_b))).
% 12.64/12.55  all V_n V_m V_k (c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n))-> (V_k!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n))).
% 12.64/12.55  all V_n V_z (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_z,V_n)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_n))).
% 12.64/12.55  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m,V_n)-> -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m))).
% 12.64/12.55  all V_d V_i (V_i!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)-> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d,V_i)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_d),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)))).
% 12.64/12.55  all V_n_2 V_ma_2 (V_ma_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)-> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2),V_ma_2)<->c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 12.64/12.55  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)).
% 12.64/12.55  all V_ma_2 V_x_2 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_ma_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_ma_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.64/12.55  all V_n (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.64/12.55  all V_i ((V_i=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))& (V_i!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i)->c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=c_Groups_Oone__class_Oone(tc_Int_Oint))& (-c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i)->c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))))).
% 12.64/12.55  c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.64/12.55  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)).
% 12.64/12.55  c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 12.64/12.55  all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)=V_z).
% 12.64/12.55  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)).
% 12.64/12.55  all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z).
% 12.64/12.55  all V_w_2 V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_w_2)&V_z_2!=V_w_2).
% 12.64/12.55  all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,V_z_2)).
% 12.64/12.55  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)).
% 12.64/12.55  all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)).
% 12.64/12.55  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))).
% 12.64/12.55  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))).
% 12.64/12.55  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))).
% 12.64/12.55  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)).
% 12.64/12.55  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)))).
% 12.64/12.55  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)))).
% 12.64/12.55  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)).
% 12.64/12.55  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))).
% 12.64/12.55  all V_n_2 V_ma_2 V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)<->V_ma_2=V_n_2).
% 12.64/12.55  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))).
% 12.64/12.55  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))).
% 12.64/12.55  all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))).
% 12.64/12.55  all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))).
% 12.64/12.55  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))).
% 12.64/12.55  all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)|V_w_2=V_z_2).
% 12.64/12.55  all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))).
% 12.64/12.55  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)).
% 12.64/12.55  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)).
% 12.64/12.55  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).
% 12.64/12.55  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).
% 12.64/12.55  all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m)).
% 12.64/12.55  all V_nat_H (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_nat_H)).
% 12.65/12.55  all V_m (c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.55  all V_nat_H_1 (c_Nat_OSuc(V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.55  all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m)).
% 12.65/12.55  all V_m (c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.55  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(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2))).
% 12.65/12.55  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2=V_n_2).
% 12.65/12.55  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),c_Nat_OSuc(V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)).
% 12.65/12.55  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(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2))<->V_n_2=V_ma_2)).
% 12.65/12.55  all V_m V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))->V_m=V_n)).
% 12.65/12.55  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))).
% 12.65/12.55  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)-> (c_Nat_OSuc(V_m)!=V_n->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n))).
% 12.65/12.55  all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k))).
% 12.65/12.55  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))-> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->V_m=V_n)).
% 12.65/12.55  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)).
% 12.65/12.55  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)).
% 12.65/12.55  all V_n (-c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n)).
% 12.65/12.55  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__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2)).
% 12.65/12.55  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2=c_Nat_OSuc(V_n_2)).
% 12.65/12.55  all V_ma_2 V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_ma_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_ma_2)).
% 12.65/12.55  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))).
% 12.65/12.55  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))-> (-c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->V_m=c_Nat_OSuc(V_n))).
% 12.65/12.55  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 12.65/12.55  all V_n (V_n!=c_Nat_OSuc(V_n)).
% 12.65/12.55  all V_n (c_Nat_OSuc(V_n)!=V_n).
% 12.65/12.55  all V_nat_H_2 V_nat_2 (c_Nat_OSuc(V_nat_2)=c_Nat_OSuc(V_nat_H_2)<->V_nat_2=V_nat_H_2).
% 12.65/12.55  all V_y V_x (c_Nat_OSuc(V_x)=c_Nat_OSuc(V_y)->V_x=V_y).
% 12.65/12.55  c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.65/12.55  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))).
% 12.65/12.55  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)).
% 12.65/12.55  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)).
% 12.65/12.55  all V_n T_a (class_Power_Opower(T_a)&class_Rings_Osemiring__0(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_OSuc(V_n))=c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.55  all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))).
% 12.65/12.55  all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))).
% 12.65/12.55  all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))).
% 12.65/12.55  all V_n V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)).
% 12.65/12.55  all V_n V_a T_a (class_Power_Opower(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 12.65/12.55  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))<->V_ma_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| (exists B_j (V_ma_2=c_Nat_OSuc(B_j)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)))).
% 12.65/12.55  all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.55  all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)<-> (exists B_m (V_n_2=c_Nat_OSuc(B_m)))).
% 12.65/12.55  all V_ma_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<->V_ma_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.65/12.55  all V_n_2 V_ma_2 (c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)<->V_ma_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.65/12.55  all V_n_2 V_ma_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_ma_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.65/12.55  all V_n V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))).
% 12.65/12.55  all V_n_2 V_ma_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_ma_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.65/12.55  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)<-> (exists B_k (V_n_2=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k))))).
% 12.65/12.55  all V_m V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))).
% 12.65/12.55  all V_m V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))).
% 12.65/12.55  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_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2)).
% 12.65/12.55  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)).
% 12.65/12.55  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),V_n_2)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)).
% 12.65/12.55  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))).
% 12.65/12.55  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)).
% 12.65/12.55  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_n_2,c_Nat_OSuc(V_ma_2))<->V_n_2=V_ma_2)).
% 12.65/12.55  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)).
% 12.65/12.55  c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.55  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)).
% 12.65/12.55  all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))).
% 12.65/12.55  all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))).
% 12.65/12.55  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)).
% 12.65/12.55  all V_n (c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)).
% 12.65/12.55  all V_n (c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 12.65/12.55  all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(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__e_q(T_a,V_a,V_b)))).
% 12.65/12.55  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),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(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)->V_a=V_b)))).
% 12.65/12.55  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))))).
% 12.65/12.55  all V_y_2 V_x_2 T_a (class_Rings_Oidom(T_a)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))<->V_x_2=V_y_2|V_x_2=c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))).
% 12.65/12.55  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))).
% 12.65/12.55  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)))).
% 12.65/12.55  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))).
% 12.65/12.55  all V_n_2 V_ma_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ma_2)&c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 12.65/12.55  all V_b V_n V_a (c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b),V_n))-> (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b))).
% 12.65/12.55  all V_b_2 V_a_2 V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2))<->c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_b_2))).
% 12.65/12.55  all V_n V_r 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_r)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_r,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_r),c_Nat_OSuc(V_n)),V_r)))).
% 12.65/12.55  all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a))))).
% 12.65/12.55  all V_x c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.55  all V_b V_n V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b),V_n))-> (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b))).
% 12.65/12.55  all V_b_2 V_a_2 V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2))<->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a_2,V_b_2))).
% 12.65/12.55  all V_x c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_x).
% 12.65/12.55  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)).
% 12.65/12.55  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))))).
% 12.65/12.55  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)))).
% 12.65/12.55  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))).
% 12.65/12.55  all V_z (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z))=V_z).
% 12.65/12.55  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)).
% 12.65/12.55  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))).
% 12.65/12.55  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)).
% 12.65/12.55  all V_w c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_w).
% 12.65/12.55  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)).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  all V_t_2 V_d_2 (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)<->c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2))).
% 12.65/12.55  all V_t_2 V_d_2 (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)<->c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2),V_t_2)).
% 12.65/12.55  all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))->V_x=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.65/12.55  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))))))).
% 12.65/12.55  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))))).
% 12.65/12.55  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))))))).
% 12.65/12.55  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))))).
% 12.65/12.55  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))))).
% 12.65/12.55  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)))).
% 12.65/12.55  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))).
% 12.65/12.55  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)))).
% 12.65/12.55  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)).
% 12.65/12.55  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)).
% 12.65/12.55  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)))).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.65/12.55  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))).
% 12.65/12.55  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)).
% 12.65/12.55  c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.55  all V_a_2 V_times_2 V_one_2 T_a (hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_one_2).
% 12.65/12.55  all V_n_2 V_a_2 V_times_2 V_one_2 T_a (hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2))=hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2))).
% 12.65/12.55  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)).
% 12.65/12.55  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)).
% 12.65/12.55  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))))).
% 12.65/12.55  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)))).
% 12.65/12.55  all V_k_2 V_P_2 V_d_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)-> ((all B_x (hBOOL(hAPP(V_P_2,B_x))->hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,V_d_2)))))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)-> (all B_x (hBOOL(hAPP(V_P_2,B_x))->hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2))))))))).
% 12.65/12.55  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)).
% 12.65/12.55  all V_n (c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n).
% 12.65/12.55  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)).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.65/12.55  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))).
% 12.65/12.55  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)).
% 12.65/12.55  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))).
% 12.65/12.55  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).
% 12.65/12.55  all V_n (c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n).
% 12.65/12.55  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)).
% 12.65/12.55  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))).
% 12.65/12.55  c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.65/12.55  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)).
% 12.65/12.55  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)).
% 12.65/12.55  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)).
% 12.65/12.55  all V_n c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))).
% 12.65/12.55  c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.65/12.55  all V_n (c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 12.65/12.55  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)).
% 12.65/12.55  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))).
% 12.65/12.55  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)).
% 12.65/12.55  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)).
% 12.65/12.55  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)).
% 12.65/12.55  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))).
% 12.65/12.55  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)))).
% 12.65/12.55  all V_a_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_a_2,c_RComplete_Onatfloor(V_x_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_x_2))).
% 12.65/12.55  all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)<-> (exists B_N all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))))).
% 12.65/12.55  all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)<-> (exists B_N all B_n c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))))).
% 12.65/12.55  all V_a_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_a_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)))).
% 12.65/12.55  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))).
% 12.65/12.55  all V_X_2 T_b (class_RealVector_Oreal__normed__vector(T_b)-> ((exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K))))<-> (exists B_N all B_n c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))))).
% 12.65/12.55  all V_X_2 T_b (class_RealVector_Oreal__normed__vector(T_b)-> ((exists B_K (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)& (all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K))))<-> (exists B_N all B_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))))).
% 12.65/12.55  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))).
% 12.65/12.55  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)).
% 12.65/12.55  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))).
% 12.65/12.55  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)).
% 12.65/12.55  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)).
% 12.65/12.55  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))).
% 12.65/12.55  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,B_n),V_r)&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n)))))).
% 12.65/12.55  all V_a 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_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)-> (exists B_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_x)&hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n)=V_a& (all B_y (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y)&hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n)=V_a->B_y=B_x)))))).
% 12.65/12.55  all V_a 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_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)-> (exists B_r (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r)&hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n)=V_a)))).
% 12.65/12.55  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)))).
% 12.65/12.55  all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_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_a_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_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2))).
% 12.65/12.55  all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_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_a_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_a_2)),V_e_2),V_d_2)))).
% 12.65/12.55  all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_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_a_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_a_2)),V_e_2),V_d_2)))).
% 12.65/12.55  all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_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_a_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_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2))).
% 12.65/12.55  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)))).
% 12.65/12.55  all V_t_2 V_D_2 V_d_2 T_a (class_Rings_Ocomm__ring(T_a)&class_Rings_Odvd(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)-> (all B_x B_k (c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))<->c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)))))).
% 12.65/12.55  all V_t_2 V_D_2 V_d_2 T_a (class_Rings_Ocomm__ring(T_a)&class_Rings_Odvd(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)-> (all B_x B_k (c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))<->c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)))))).
% 12.65/12.55  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))))).
% 12.65/12.55  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)))).
% 12.65/12.55  all V_ra_2 V_a_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_a_2)),V_ra_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2)&c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2)))).
% 12.65/12.55  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)))).
% 12.65/12.55  all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))).
% 12.65/12.55  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))).
% 12.65/12.55  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)))).
% 12.65/12.55  all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_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_a_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_a_2,V_b_2)),V_e_2),V_ca_2)=V_d_2)).
% 12.65/12.55  all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_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_a_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_a_2)),V_e_2),V_d_2))).
% 12.65/12.55  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)).
% 12.65/12.55  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)).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  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)))).
% 12.65/12.55  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)))).
% 12.65/12.55  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)))).
% 12.65/12.55  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)).
% 12.65/12.55  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))).
% 12.65/12.55  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)).
% 12.65/12.55  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)))).
% 12.65/12.55  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).
% 12.65/12.55  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).
% 12.65/12.55  all V_d_2 V_ca_2 V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_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_a_2,V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_ca_2,V_d_2)))).
% 12.65/12.55  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))))).
% 12.65/12.55  all V_n V_m V_k (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n))-> (c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_n)->c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_m))).
% 12.65/12.55  all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  all V_d_2 V_ca_2 V_b_2 V_a_2 T_a (class_Groups_Oab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)-> (V_a_2=V_b_2<->V_ca_2=V_d_2))).
% 12.65/12.55  all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  all V_d_2 V_ca_2 V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_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_a_2,V_b_2)<->c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_d_2)))).
% 12.65/12.55  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).
% 12.65/12.55  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)).
% 12.65/12.55  all V_b_2 V_a_2 T_a (class_Groups_Oab__group__add(T_a)-> (V_a_2=V_b_2<->c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a))).
% 12.65/12.55  all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=V_b_2)).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  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)))).
% 12.65/12.55  all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)).
% 12.65/12.55  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))))).
% 12.65/12.55  all V_y V_x T_a (class_Rings_Ocomm__ring__1(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))).
% 12.65/12.55  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)).
% 12.65/12.55  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)))))))).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  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)))).
% 12.65/12.55  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_ma_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)))).
% 12.65/12.55  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))).
% 12.65/12.55  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_ma_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)<->V_ma_2=V_n_2))).
% 12.65/12.55  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).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  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).
% 12.65/12.55  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).
% 12.65/12.55  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).
% 12.65/12.55  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))).
% 12.65/12.55  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)).
% 12.65/12.55  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)).
% 12.65/12.55  all V_n V_m V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))).
% 12.65/12.55  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))).
% 12.65/12.55  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)).
% 12.65/12.55  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))).
% 12.65/12.55  all V_n V_m c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)).
% 12.65/12.55  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)).
% 12.65/12.55  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)).
% 12.65/12.55  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)).
% 12.65/12.55  all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))).
% 12.65/12.55  all V_k_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2)).
% 12.65/12.55  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).
% 12.65/12.55  all V_n_2 V_ma_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_ma_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)))).
% 12.65/12.55  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)))).
% 12.65/12.55  all V_n V_m V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)))).
% 12.65/12.55  all V_n V_m V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)))).
% 12.65/12.55  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)).
% 12.65/12.55  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)).
% 12.65/12.55  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))).
% 12.65/12.55  all V_k_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_k_2<->V_j_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2))).
% 12.65/12.55  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).
% 12.65/12.55  all V_i_2 V_j_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2))).
% 12.65/12.55  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)).
% 12.65/12.55  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).
% 12.65/12.55  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))).
% 12.65/12.55  all V_i_2 V_k_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2))).
% 12.65/12.55  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)).
% 12.65/12.55  all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)).
% 12.65/12.55  all V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  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)).
% 12.65/12.55  all V_k V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k)).
% 12.65/12.55  all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 12.65/12.55  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).
% 12.65/12.55  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)))).
% 12.65/12.55  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)).
% 12.65/12.55  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)).
% 12.65/12.55  all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.55  all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 12.65/12.55  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)).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  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))).
% 12.65/12.55  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)).
% 12.65/12.55  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)).
% 12.65/12.55  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)))).
% 12.65/12.55  all V_i V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n)).
% 12.65/12.55  all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n).
% 12.65/12.55  all V_b_2 V_a_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))<-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)->hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))& (all B_d (V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)->hBOOL(hAPP(V_P_2,B_d))))).
% 12.65/12.55  all V_b_2 V_a_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))<-> -(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)& -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| (exists B_d (V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)& -hBOOL(hAPP(V_P_2,B_d)))))).
% 12.65/12.55  all V_m V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m))).
% 12.65/12.55  all V_m V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j))).
% 12.65/12.55  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))).
% 12.65/12.55  all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 12.65/12.55  class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex).
% 12.65/12.55  class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat).
% 12.65/12.55  class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint).
% 12.65/12.55  all T_2 T_1 (class_Lattices_Oboolean__algebra(T_1)->class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))).
% 12.65/12.55  all T_2 T_1 (class_Orderings_Opreorder(T_1)->class_Orderings_Opreorder(tc_fun(T_2,T_1))).
% 12.65/12.55  all T_2 T_1 (class_Orderings_Oorder(T_1)->class_Orderings_Oorder(tc_fun(T_2,T_1))).
% 12.65/12.55  all T_2 T_1 (class_Orderings_Oord(T_1)->class_Orderings_Oord(tc_fun(T_2,T_1))).
% 12.65/12.55  all T_2 T_1 (class_Groups_Ouminus(T_1)->class_Groups_Ouminus(tc_fun(T_2,T_1))).
% 12.65/12.55  all T_2 T_1 (class_Groups_Ominus(T_1)->class_Groups_Ominus(tc_fun(T_2,T_1))).
% 12.65/12.55  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 12.65/12.55  class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 12.65/12.55  class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 12.65/12.55  class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 12.65/12.55  class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint).
% 12.65/12.55  class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 12.65/12.55  class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint).
% 12.65/12.55  class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint).
% 12.65/12.55  class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 12.65/12.55  class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 12.65/12.55  class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 12.65/12.55  class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 12.65/12.55  class_Rings_Oordered__cancel__semiring(tc_Int_Oint).
% 12.65/12.55  class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 12.65/12.55  class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 12.65/12.55  class_Rings_Oordered__comm__semiring(tc_Int_Oint).
% 12.65/12.55  class_Rings_Olinordered__semiring__1(tc_Int_Oint).
% 12.65/12.55  class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 12.65/12.55  class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 12.65/12.55  class_Rings_Olinordered__semiring(tc_Int_Oint).
% 12.65/12.55  class_Rings_Olinordered__semidom(tc_Int_Oint).
% 12.65/12.55  class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 12.65/12.55  class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 12.65/12.55  class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 12.65/12.55  class_Rings_Oordered__semiring(tc_Int_Oint).
% 12.65/12.55  class_Rings_Oordered__ring__abs(tc_Int_Oint).
% 12.65/12.55  class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 12.65/12.55  class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 12.65/12.55  class_Rings_Olinordered__ring(tc_Int_Oint).
% 12.65/12.55  class_Rings_Olinordered__idom(tc_Int_Oint).
% 12.65/12.55  class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 12.65/12.55  class_Rings_Ocomm__semiring__0(tc_Int_Oint).
% 12.65/12.55  class_Rings_Ocomm__semiring(tc_Int_Oint).
% 12.65/12.55  class_Groups_Oab__group__add(tc_Int_Oint).
% 12.65/12.55  class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 12.65/12.55  class_Rings_Oordered__ring(tc_Int_Oint).
% 12.65/12.55  class_Orderings_Opreorder(tc_Int_Oint).
% 12.65/12.55  class_Orderings_Olinorder(tc_Int_Oint).
% 12.65/12.55  class_Groups_Omonoid__mult(tc_Int_Oint).
% 12.65/12.55  class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 12.65/12.55  class_Groups_Omonoid__add(tc_Int_Oint).
% 12.65/12.55  class_Rings_Osemiring__0(tc_Int_Oint).
% 12.65/12.55  class_Groups_Ogroup__add(tc_Int_Oint).
% 12.65/12.55  class_Rings_Omult__zero(tc_Int_Oint).
% 12.65/12.55  class_Rings_Ocomm__ring(tc_Int_Oint).
% 12.65/12.55  class_Orderings_Oorder(tc_Int_Oint).
% 12.65/12.55  class_Int_Oring__char__0(tc_Int_Oint).
% 12.65/12.55  class_Rings_Osemiring(tc_Int_Oint).
% 12.65/12.55  class_Orderings_Oord(tc_Int_Oint).
% 12.65/12.55  class_Groups_Ouminus(tc_Int_Oint).
% 12.65/12.55  class_Groups_Osgn__if(tc_Int_Oint).
% 12.65/12.55  class_Groups_Oabs__if(tc_Int_Oint).
% 12.65/12.55  class_Rings_Oring__1(tc_Int_Oint).
% 12.65/12.55  class_Groups_Ominus(tc_Int_Oint).
% 12.65/12.55  class_Power_Opower(tc_Int_Oint).
% 12.65/12.55  class_Groups_Ozero(tc_Int_Oint).
% 12.65/12.55  class_Rings_Oring(tc_Int_Oint).
% 12.65/12.55  class_Rings_Oidom(tc_Int_Oint).
% 12.65/12.55  class_Groups_Oone(tc_Int_Oint).
% 12.65/12.55  class_Rings_Odvd(tc_Int_Oint).
% 12.65/12.55  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 12.65/12.55  class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 12.65/12.55  class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 12.65/12.55  class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 12.65/12.55  class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 12.65/12.55  class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 12.65/12.55  class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 12.65/12.55  class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 12.65/12.55  class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 12.65/12.55  class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 12.65/12.55  class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 12.65/12.55  class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 12.65/12.55  class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 12.65/12.55  class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 12.65/12.55  class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 12.65/12.55  class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 12.65/12.55  class_Rings_Oordered__semiring(tc_Nat_Onat).
% 12.65/12.55  class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 12.65/12.55  class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 12.65/12.55  class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 12.65/12.55  class_Rings_Ocomm__semiring__0(tc_Nat_Onat).
% 12.65/12.55  class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 12.65/12.55  class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 12.65/12.55  class_Orderings_Opreorder(tc_Nat_Onat).
% 12.65/12.55  class_Orderings_Olinorder(tc_Nat_Onat).
% 12.65/12.55  class_Groups_Omonoid__mult(tc_Nat_Onat).
% 12.65/12.55  class_Groups_Omonoid__add(tc_Nat_Onat).
% 12.65/12.55  class_Rings_Osemiring__0(tc_Nat_Onat).
% 12.65/12.55  class_Rings_Omult__zero(tc_Nat_Onat).
% 12.65/12.55  class_Orderings_Oorder(tc_Nat_Onat).
% 12.65/12.55  class_Rings_Osemiring(tc_Nat_Onat).
% 12.65/12.55  class_Orderings_Oord(tc_Nat_Onat).
% 12.65/12.55  class_Groups_Ominus(tc_Nat_Onat).
% 12.65/12.55  class_Power_Opower(tc_Nat_Onat).
% 12.65/12.55  class_Groups_Ozero(tc_Nat_Onat).
% 12.65/12.55  class_Groups_Oone(tc_Nat_Onat).
% 12.65/12.55  class_Rings_Odvd(tc_Nat_Onat).
% 12.65/12.55  class_Lattices_Oboolean__algebra(tc_HOL_Obool).
% 12.65/12.55  class_Orderings_Opreorder(tc_HOL_Obool).
% 12.65/12.55  class_Orderings_Oorder(tc_HOL_Obool).
% 12.65/12.55  class_Orderings_Oord(tc_HOL_Obool).
% 12.65/12.55  class_Groups_Ouminus(tc_HOL_Obool).
% 12.65/12.55  class_Groups_Ominus(tc_HOL_Obool).
% 12.65/12.55  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal).
% 12.65/12.55  class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal).
% 12.65/12.55  class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal).
% 12.65/12.55  class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal).
% 12.65/12.55  class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Olinordered__semiring(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Olinordered__semidom(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Oab__semigroup__add(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Oordered__semiring(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Oordered__ring__abs(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Ono__zero__divisors(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Olinordered__ring(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Olinordered__idom(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Ocomm__semiring(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Oab__group__add(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Oordered__ring(tc_RealDef_Oreal).
% 12.65/12.55  class_Orderings_Opreorder(tc_RealDef_Oreal).
% 12.65/12.55  class_Orderings_Olinorder(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Omonoid__mult(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Ocomm__ring__1(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Omonoid__add(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Osemiring__0(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Ogroup__add(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Omult__zero(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Ocomm__ring(tc_RealDef_Oreal).
% 12.65/12.55  class_Orderings_Oorder(tc_RealDef_Oreal).
% 12.65/12.55  class_Int_Oring__char__0(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Osemiring(tc_RealDef_Oreal).
% 12.65/12.55  class_Orderings_Oord(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Ouminus(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Osgn__if(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Oabs__if(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Oring__1(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Ominus(tc_RealDef_Oreal).
% 12.65/12.55  class_Power_Opower(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Ozero(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Oring(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Oidom(tc_RealDef_Oreal).
% 12.65/12.55  class_Groups_Oone(tc_RealDef_Oreal).
% 12.65/12.55  class_Rings_Odvd(tc_RealDef_Oreal).
% 12.65/12.55  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex).
% 12.65/12.55  class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex).
% 12.65/12.55  class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex).
% 12.65/12.55  class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex).
% 12.65/12.55  class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex).
% 12.65/12.55  class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex).
% 12.65/12.55  class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex).
% 12.65/12.55  class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex).
% 12.65/12.55  class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex).
% 12.65/12.55  class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex).
% 12.65/12.55  class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex).
% 12.65/12.55  class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex).
% 12.65/12.55  class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex).
% 12.65/12.55  class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex).
% 12.65/12.55  class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex).
% 12.65/12.55  class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex).
% 12.65/12.55  class_Rings_Ocomm__semiring(tc_Complex_Ocomplex).
% 12.65/12.55  class_Groups_Oab__group__add(tc_Complex_Ocomplex).
% 12.65/12.55  class_Rings_Ozero__ne_q__one(tc_Complex_Ocomplex).
% 12.65/12.55  class_Groups_Omonoid__mult(tc_Complex_Ocomplex).
% 12.65/12.55  class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex).
% 12.65/12.55  class_Groups_Omonoid__add(tc_Complex_Ocomplex).
% 12.65/12.55  class_Rings_Osemiring__0(tc_Complex_Ocomplex).
% 12.65/12.55  class_Groups_Ogroup__add(tc_Complex_Ocomplex).
% 12.65/12.55  class_Rings_Omult__zero(tc_Complex_Ocomplex).
% 12.65/12.55  class_Rings_Ocomm__ring(tc_Complex_Ocomplex).
% 12.65/12.55  class_Int_Oring__char__0(tc_Complex_Ocomplex).
% 12.65/12.55  class_Rings_Osemiring(tc_Complex_Ocomplex).
% 12.65/12.55  class_Groups_Ouminus(tc_Complex_Ocomplex).
% 12.65/12.55  class_Rings_Oring__1(tc_Complex_Ocomplex).
% 12.65/12.55  class_Groups_Ominus(tc_Complex_Ocomplex).
% 12.65/12.55  class_Power_Opower(tc_Complex_Ocomplex).
% 12.65/12.55  class_Groups_Ozero(tc_Complex_Ocomplex).
% 12.65/12.55  class_Rings_Oring(tc_Complex_Ocomplex).
% 12.65/12.55  class_Rings_Oidom(tc_Complex_Ocomplex).
% 12.65/12.55  class_Groups_Oone(tc_Complex_Ocomplex).
% 12.65/12.55  class_Rings_Odvd(tc_Complex_Ocomplex).
% 12.65/12.55  all T_1 (class_Rings_Oidom(T_1)->class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))).
% 12.65/12.55  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 12.65/12.55  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1))).
% 12.65/12.55  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1))).
% 12.65/12.55  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1))).
% 12.65/12.55  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1))).
% 12.65/12.55  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 12.65/12.55  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1))).
% 12.65/12.55  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Oorder(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Osemiring(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Oord(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ouminus(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Oring__1(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ominus(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Power_Opower(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Groups_Ozero(T_1)->class_Groups_Ozero(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Oring(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oidom(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Oone(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Odvd(tc_Polynomial_Opoly(T_1))).
% 12.65/12.56  all V_y_2 V_x_2 (-hBOOL(c_fe_qual(V_x_2,V_y_2))|V_x_2=V_y_2).
% 12.65/12.56  all V_y_2 V_x_2 (V_x_2!=V_y_2|hBOOL(c_fe_qual(V_x_2,V_y_2))).
% 12.65/12.56  -(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),v_r)->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,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),B_z)),B_m))))).
% 12.65/12.56  end_of_list.
% 12.65/12.56  
% 12.65/12.56  -------> usable clausifies to:
% 12.65/12.56  
% 12.65/12.56  list(usable).
% 12.65/12.56  0 [] A=A.
% 12.65/12.56  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.
% 12.65/12.56  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)|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_cs____),B_z)),v_m____).
% 12.65/12.56  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$c1).
% 12.65/12.56  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),B_z)),$c1).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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)).
% 12.65/12.56  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)).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)|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_cs____),B_z)),$c2).
% 12.65/12.56  0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x).
% 12.65/12.56  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).
% 12.65/12.56  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)).
% 12.65/12.56  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_a_2,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.56  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_a_2,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 12.65/12.56  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_a_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_a_2!=c_Groups_Ozero__class_Ozero(T_a)|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 12.65/12.56  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).
% 12.65/12.56  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 12.65/12.56  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.
% 12.65/12.56  0 [] -class_Int_Oring__char__0(T_a)| -class_Rings_Oidom(T_a)|c_Polynomial_Opoly(T_a,V_pa_2)!=c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 12.65/12.56  0 [] -class_Int_Oring__char__0(T_a)| -class_Rings_Oidom(T_a)|c_Polynomial_Opoly(T_a,V_pa_2)=c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 12.65/12.56  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).
% 12.65/12.56  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)).
% 12.65/12.56  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).
% 12.65/12.56  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.
% 12.65/12.56  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).
% 12.65/12.56  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.
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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.
% 12.65/12.56  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.
% 12.65/12.56  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)).
% 12.65/12.56  0 [] -class_Orderings_Opreorder(T_a)|V_x!=V_y|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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)).
% 12.65/12.56  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,$f2(V_g_2,V_f_2,T_a,T_b)),hAPP(V_g_2,$f2(V_g_2,V_f_2,T_a,T_b))).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_y!=V_x.
% 12.65/12.56  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 12.65/12.56  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).
% 12.65/12.56  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.
% 12.65/12.56  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.
% 12.65/12.56  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).
% 12.65/12.56  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.
% 12.65/12.56  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).
% 12.65/12.56  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.
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_x).
% 12.65/12.56  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.
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_w).
% 12.65/12.56  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_a_2,V_pa_2)!=c_Polynomial_OpCons(T_a,V_b_2,V_q_2)|V_a_2=V_b_2.
% 12.65/12.56  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_a_2,V_pa_2)!=c_Polynomial_OpCons(T_a,V_b_2,V_q_2)|V_pa_2=V_q_2.
% 12.65/12.56  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_a_2,V_pa_2)=c_Polynomial_OpCons(T_a,V_b_2,V_q_2)|V_a_2!=V_b_2|V_pa_2!=V_q_2.
% 12.65/12.56  0 [] -class_Int_Oring__char__0(T_a)| -class_Rings_Oidom(T_a)|c_Polynomial_Opoly(T_a,V_pa_2)!=c_Polynomial_Opoly(T_a,V_q_2)|V_pa_2=V_q_2.
% 12.65/12.56  0 [] -class_Int_Oring__char__0(T_a)| -class_Rings_Oidom(T_a)|c_Polynomial_Opoly(T_a,V_pa_2)=c_Polynomial_Opoly(T_a,V_q_2)|V_pa_2!=V_q_2.
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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.
% 12.65/12.56  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.
% 12.65/12.56  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.
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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.
% 12.65/12.56  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.
% 12.65/12.56  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).
% 12.65/12.56  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).
% 12.65/12.56  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.
% 12.65/12.57  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).
% 12.65/12.57  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.
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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.
% 12.65/12.57  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.
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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.
% 12.65/12.57  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).
% 12.65/12.57  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z_2),v_r)|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,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),V_z_2)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))).
% 12.65/12.57  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_a_2,V_pa_2))|c_Polynomial_Opos__poly(T_a,V_pa_2)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 12.65/12.57  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_a_2,V_pa_2))|c_Polynomial_Opos__poly(T_a,V_pa_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.65/12.57  0 [] -class_Rings_Olinordered__idom(T_a)|c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_a_2,V_pa_2))| -c_Polynomial_Opos__poly(T_a,V_pa_2).
% 12.65/12.57  0 [] -class_Rings_Olinordered__idom(T_a)|c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_a_2,V_pa_2))|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.65/12.57  0 [] -class_Rings_Oidom(T_a)|hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Oorder(T_a,V_a_2,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.57  0 [] -class_Rings_Oidom(T_a)|hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 12.65/12.57  0 [] -class_Rings_Oidom(T_a)|hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|c_Polynomial_Oorder(T_a,V_a_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.57  0 [] -class_Groups_Ozero(T_b)|hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2)!=V_z_2|c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_a_2,V_pa_2))=hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2)).
% 12.65/12.57  0 [] -class_Groups_Ozero(T_b)|c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_a_2,V_pa_2))=hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_If(T_a,c_fe_qual(V_pa_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2,c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2))).
% 12.65/12.57  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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))).
% 12.65/12.57  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)).
% 12.65/12.57  0 [] -class_Groups_Ozero(T_b)|hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2)!=V_z_2|c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))=V_z_2.
% 12.65/12.57  0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f3(V_X_2,T_a)).
% 12.65/12.57  0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),$f3(V_X_2,T_a)).
% 12.65/12.57  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_OBse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,$f4(V_X_2,T_a,B_K))),B_K).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  0 [] c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r).
% 12.65/12.57  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))).
% 12.65/12.57  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z)=V_z.
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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.
% 12.65/12.57  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.
% 12.65/12.57  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.
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)!=c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2)|V_b_2=V_ca_2.
% 12.65/12.57  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)=c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2)|V_b_2!=V_ca_2.
% 12.65/12.57  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)!=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2)|V_b_2=V_ca_2.
% 12.65/12.57  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2)|V_b_2!=V_ca_2.
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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.
% 12.65/12.57  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.
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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.
% 12.65/12.57  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.
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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))).
% 12.65/12.57  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).
% 12.65/12.57  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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.
% 12.65/12.57  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.
% 12.65/12.57  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  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.
% 12.65/12.57  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.
% 12.65/12.57  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_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_a_2,V_b_2).
% 12.65/12.57  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_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_a_2,V_b_2).
% 12.65/12.57  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_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.65/12.57  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_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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_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_a_2,V_b_2).
% 12.65/12.57  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_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_a_2,V_b_2).
% 12.65/12.57  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_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.65/12.57  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_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_b_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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))).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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))).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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))).
% 12.65/12.57  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)).
% 12.65/12.57  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))).
% 12.65/12.57  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)).
% 12.65/12.57  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))).
% 12.65/12.57  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))).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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_2),c_Groups_Ozero__class_Ozero(T_a))|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  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_2),c_Groups_Ozero__class_Ozero(T_a))|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  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.
% 12.65/12.57  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)).
% 12.65/12.57  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_a_2))|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  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_a_2))|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  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.
% 12.65/12.57  0 [] V_ca_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_ca_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2)|V_a_2=V_b_2.
% 12.65/12.57  0 [] V_ca_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_ca_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2)|V_a_2!=V_b_2.
% 12.65/12.57  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_a_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2)|V_a_2=V_b_2.
% 12.65/12.57  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_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2)|V_a_2!=V_b_2.
% 12.65/12.57  0 [] c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.65/12.57  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_a_2,V_a_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.65/12.57  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_a_2,V_a_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.65/12.57  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_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  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_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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_a_2,V_a_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.65/12.57  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_a_2,V_a_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.65/12.57  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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_a_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  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_a_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  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_a_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_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  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_a_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)).
% 12.65/12.57  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_a_2),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 12.65/12.57  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_a_2),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_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)).
% 12.65/12.57  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_a_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_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  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_a_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_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 12.65/12.57  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_a_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_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  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_a_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).
% 12.65/12.57  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_a_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_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  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_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_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).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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_a_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)).
% 12.65/12.57  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_a_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_a_2).
% 12.65/12.57  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_a_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_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  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_a_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_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2).
% 12.65/12.57  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_a_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_a_2,V_b_2).
% 12.65/12.57  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_a_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_a_2).
% 12.65/12.57  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_a_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)).
% 12.65/12.57  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_a_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_a_2).
% 12.65/12.57  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_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  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_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2).
% 12.65/12.57  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_a_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_a_2,V_b_2).
% 12.65/12.57  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_a_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_a_2).
% 12.65/12.57  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_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.65/12.57  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_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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_a_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_a_2).
% 12.65/12.57  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_a_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_a_2).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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_a_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_a_2,V_b_2).
% 12.65/12.57  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_a_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_a_2,V_b_2).
% 12.65/12.57  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_a_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_a_2).
% 12.65/12.57  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_a_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_a_2).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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))).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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.
% 12.65/12.57  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.
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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))).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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))).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  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_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  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.
% 12.65/12.57  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.
% 12.65/12.57  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)).
% 12.65/12.57  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_a_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_a_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_a_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)).
% 12.65/12.57  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_a_2!=V_b_2|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_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_a_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)).
% 12.65/12.57  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_a_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_a_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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_w_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_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))|V_w_2=V_x_2|V_y_2=V_z_2.
% 12.65/12.57  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_w_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_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))|V_w_2!=V_x_2.
% 12.65/12.57  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_w_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_w_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.
% 12.65/12.57  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.
% 12.65/12.57  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.
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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))).
% 12.65/12.57  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.57  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 12.65/12.57  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.
% 12.65/12.57  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f5(V_y,T_a)).
% 12.65/12.57  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),$f5(V_y,T_a))).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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))).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)|V_l_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,$f6(V_l_2,V_k_2)).
% 12.65/12.57  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)|V_l_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)|V_n_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,$f7(V_n_2,V_ma_2)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2!=V_n_2.
% 12.65/12.57  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.
% 12.65/12.57  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.
% 12.65/12.57  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).
% 12.65/12.57  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2!=V_n_2.
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.57  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)|V_s!=V_t.
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)|V_m!=V_n.
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 12.65/12.57  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).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.57  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.57  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).
% 12.65/12.57  0 [] V_ma_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.57  0 [] V_ma_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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.
% 12.65/12.57  0 [] -class_Groups_Ogroup__add(T_a)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_b_2=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2).
% 12.65/12.57  0 [] -class_Groups_Ogroup__add(T_a)|V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_b_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2).
% 12.65/12.57  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)!=V_b_2|c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)=V_a_2.
% 12.65/12.57  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=V_b_2|c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)!=V_a_2.
% 12.65/12.57  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_a_2=V_b_2.
% 12.65/12.57  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_a_2!=V_b_2.
% 12.65/12.57  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.
% 12.65/12.57  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).
% 12.65/12.57  0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 12.65/12.57  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).
% 12.65/12.57  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n).
% 12.65/12.57  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).
% 12.65/12.57  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)|c_Groups_Ozero__class_Ozero(T_a)=V_a_2.
% 12.65/12.57  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)|c_Groups_Ozero__class_Ozero(T_a)!=V_a_2.
% 12.65/12.57  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)!=V_a_2|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=V_a_2|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_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_a_2)).
% 12.65/12.57  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_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_a_2)).
% 12.65/12.57  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_a_2),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2).
% 12.65/12.57  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_a_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2).
% 12.65/12.57  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_a_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.65/12.57  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_a_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.65/12.57  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)).
% 12.65/12.57  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_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_a_2)).
% 12.65/12.57  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_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_a_2)).
% 12.65/12.57  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2).
% 12.65/12.57  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2).
% 12.65/12.57  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_a_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.65/12.57  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_a_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)|V_a_2=V_b_2|V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2).
% 12.65/12.57  0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)|V_a_2!=V_b_2.
% 12.65/12.57  0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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.
% 12.65/12.57  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.
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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.
% 12.65/12.57  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_a_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  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_a_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  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_a_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_a_2).
% 12.65/12.57  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_a_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_a_2).
% 12.65/12.57  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_a_2),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.65/12.57  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_a_2),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.65/12.57  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_a_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  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_a_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.57  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.65/12.57  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.65/12.57  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.65/12.57  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.65/12.57  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).
% 12.65/12.57  0 [] -class_Groups_Ogroup__add(T_a)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  0 [] -class_Groups_Ogroup__add(T_a)|V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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.
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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_2),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.65/12.57  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_2),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2).
% 12.65/12.57  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_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.65/12.57  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2).
% 12.65/12.57  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2).
% 12.65/12.57  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)).
% 12.65/12.57  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=V_a_2.
% 12.65/12.57  0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2!=V_a_2.
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ra_2),V_x_2).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_ra_2).
% 12.65/12.57  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ra_2),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,V_ra_2).
% 12.65/12.57  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))).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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.
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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)).
% 12.65/12.57  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)).
% 12.65/12.57  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).
% 12.65/12.57  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.
% 12.65/12.57  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).
% 12.65/12.57  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.
% 12.65/12.57  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))))).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  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).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.57  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.57  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.57  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.57  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 12.65/12.57  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.57  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_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.57  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_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 12.65/12.57  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_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.57  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_ma_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.57  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_ma_2!=V_n_2.
% 12.65/12.57  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.57  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)|V_ma_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.57  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)|V_ma_2!=V_n_2.
% 12.65/12.58  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n.
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.58  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f9(V_X_2,T_a)).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,$f8(V_X_2,T_a)))),$f9(V_X_2,T_a)).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_OBse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,$f10(V_X_2,T_a,B_k,B_x)),c_Groups_Ouminus__class_Ouminus(T_a,B_x))),B_k).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f12(V_X_2,T_a)).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_X_2,$f11(V_X_2,T_a))))),$f12(V_X_2,T_a)).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_OBse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,$f13(V_X_2,T_a,B_k,B_N)),c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_X_2,B_N)))),B_k).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f14(T_a)).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),$f14(T_a))).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f15(V_x,T_a)).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),$f15(V_x,T_a))).
% 12.65/12.58  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).
% 12.65/12.58  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_k_2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)|V_ma_2=V_n_2.
% 12.65/12.58  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_k_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)|V_ma_2!=V_n_2.
% 12.65/12.58  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)|V_ma_2=V_n_2.
% 12.65/12.58  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)|V_ma_2!=V_n_2.
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)=V_n.
% 12.65/12.58  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_ma_2=V_n_2.
% 12.65/12.58  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_ma_2!=V_n_2.
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_ma_2=V_n_2.
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_ma_2!=V_n_2.
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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,$f17(V_X_2,T_a),$f16(V_X_2,T_a)).
% 12.65/12.58  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,$f16(V_X_2,T_a)),hAPP(V_X_2,$f17(V_X_2,T_a))).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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))).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.58  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.58  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.58  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_a_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.65/12.58  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_a_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.65/12.58  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)).
% 12.65/12.58  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.
% 12.65/12.58  0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)=V_a.
% 12.65/12.58  0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)=V_x.
% 12.65/12.58  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).
% 12.65/12.58  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.
% 12.65/12.58  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)).
% 12.65/12.58  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.
% 12.65/12.58  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.
% 12.65/12.58  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).
% 12.65/12.58  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)!=c_Groups_Oone__class_Oone(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.65/12.58  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)=c_Groups_Oone__class_Oone(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)!=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.58  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_a_2)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_K_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,$f18(V_X_2,V_K_2,T_a))),V_K_2)|c_SEQ_OBse_q(T_a,V_X_2).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f19(V_X_2,T_a)).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),$f19(V_X_2,T_a)).
% 12.65/12.58  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f20(V_n_2,V_P_2),V_n_2).
% 12.65/12.58  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i,$f20(V_n_2,V_P_2))| -hBOOL(hAPP(V_P_2,B_i)).
% 12.65/12.58  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))|hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,$f20(V_n_2,V_P_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f21(V_y,T_a)).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),$f21(V_y,T_a))).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.65/12.58  0 [] V_a!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.65/12.58  0 [] V_a=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.65/12.58  0 [] V_a=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.65/12.58  0 [] V_x!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.65/12.58  0 [] V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.65/12.58  0 [] V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x)=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f22(T_a)).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),$f22(T_a))).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f23(V_x,T_a)).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),$f23(V_x,T_a))).
% 12.65/12.58  0 [] -class_Rings_Oidom(T_a)|hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_ca_2)!=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2).
% 12.65/12.58  0 [] -class_Rings_Oidom(T_a)|hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_ca_2)=c_Groups_Ozero__class_Ozero(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2).
% 12.65/12.58  0 [] -class_Rings_Oidom(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_ca_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2)|hAPP(c_Polynomial_Opoly(T_a,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2))=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.58  0 [] -class_Rings_Oidom(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_ca_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2)|hAPP(c_Polynomial_Opoly(T_a,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2))!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|V_a=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.58  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).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a,V_a).
% 12.65/12.58  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,V_l)!=c_Groups_Oabs__class_Oabs(T_a,V_k)|c_Rings_Odvd__class_Odvd(T_a,V_l,V_k).
% 12.65/12.58  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oabs__class_Oabs(T_a,V_ma_2),V_k_2)|c_Rings_Odvd__class_Odvd(T_a,V_ma_2,V_k_2).
% 12.65/12.58  0 [] -class_Rings_Olinordered__idom(T_a)|c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oabs__class_Oabs(T_a,V_ma_2),V_k_2)| -c_Rings_Odvd__class_Odvd(T_a,V_ma_2,V_k_2).
% 12.65/12.58  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_ma_2,c_Groups_Oabs__class_Oabs(T_a,V_k_2))|c_Rings_Odvd__class_Odvd(T_a,V_ma_2,V_k_2).
% 12.65/12.58  0 [] -class_Rings_Olinordered__idom(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_ma_2,c_Groups_Oabs__class_Oabs(T_a,V_k_2))| -c_Rings_Odvd__class_Odvd(T_a,V_ma_2,V_k_2).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oone__class_Oone(T_a),V_a).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)|c_Rings_Odvd__class_Odvd(T_a,V_b,V_c).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)|c_Rings_Odvd__class_Odvd(T_a,V_a,V_c).
% 12.65/12.58  0 [] -class_Rings_Odvd(T_a)|V_a!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)|c_Rings_Odvd__class_Odvd(T_a,V_b,V_a).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)| -c_Rings_Odvd__class_Odvd(T_a,V_c,V_d)|c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)|c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)|c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 12.65/12.58  0 [] -class_Rings_Oidom(T_a)| -c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))|V_ca_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a_2,V_b_2).
% 12.65/12.58  0 [] -class_Rings_Oidom(T_a)|c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))|V_ca_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.58  0 [] -class_Rings_Oidom(T_a)|c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))| -c_Rings_Odvd__class_Odvd(T_a,V_a_2,V_b_2).
% 12.65/12.58  0 [] -class_Rings_Oidom(T_a)| -c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))|V_ca_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a_2,V_b_2).
% 12.65/12.58  0 [] -class_Rings_Oidom(T_a)|c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))|V_ca_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.58  0 [] -class_Rings_Oidom(T_a)|c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))| -c_Rings_Odvd__class_Odvd(T_a,V_a_2,V_b_2).
% 12.65/12.58  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,$f24(V_l_2,V_P_2,T_a),c_Groups_Ozero__class_Ozero(T_a))).
% 12.65/12.58  0 [] -class_Rings_Odvd(T_a)| -class_Rings_Osemiring__0(T_a)| -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x)))|hBOOL(hAPP(V_P_2,$f24(V_l_2,V_P_2,T_a))).
% 12.65/12.58  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),$f25(V_l_2,V_P_2,T_a))))| -c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,X1,c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(V_P_2,X1)).
% 12.65/12.58  0 [] -class_Rings_Oidom(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p).
% 12.65/12.58  0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Oincse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)).
% 12.65/12.58  0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Oincse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f27(V_X_2,T_a),$f26(V_X_2,T_a)).
% 12.65/12.58  0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Oincse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f27(V_X_2,T_a)),hAPP(V_X_2,$f26(V_X_2,T_a))).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,c_Groups_Oone__class_Oone(tc_Nat_Onat))|V_ma_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.65/12.58  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,c_Groups_Oone__class_Oone(tc_Nat_Onat))|V_ma_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2))|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,V_n_2).
% 12.65/12.58  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2))| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,V_n_2).
% 12.65/12.58  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.
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  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).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2),V_ma_2)|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2),V_ma_2)|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ma_2),V_ma_2)|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ma_2),V_ma_2)|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Rings_Odvd__class_Odvd(T_a,V_x,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)|V_x!=c_Groups_Oone__class_Oone(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_x,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_x).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)|V_b!=V_c|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)|V_b!=V_c| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)|V_y!=V_x.
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)|V_x!=V_y.
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)|V_x!=V_y.
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x).
% 12.65/12.58  0 [] V_a!=V_b| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_b)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c).
% 12.65/12.58  0 [] V_a!=V_b| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_b)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)|V_x=V_y.
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m)|V_m=V_n.
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)|V_b!=V_c|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c).
% 12.65/12.58  0 [] V_a!=V_b| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)|V_a=V_b| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)|V_x=V_y.
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)|V_x_2=V_y_2.
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 12.65/12.58  0 [] V_x!=V_y|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y).
% 12.65/12.58  0 [] V_a=V_b| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)|V_x_2!=V_y_2.
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)|V_x_2=V_y_2.
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)|V_x_2=V_y_2.
% 12.65/12.58  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 12.65/12.58  0 [] V_x_2!=V_y_2|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2).
% 12.65/12.58  0 [] V_x_2!=V_y_2|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2).
% 12.65/12.58  0 [] V_x_2=V_y_2| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_i)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)|c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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.
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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_a_2),V_n_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.58  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_a_2),V_n_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  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_a_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_ma_2)!=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)|V_ma_2=V_n_2.
% 12.65/12.58  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_ma_2)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)|V_ma_2!=V_n_2.
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m)).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),V_b)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),V_b).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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))).
% 12.65/12.58  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))).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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.
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m).
% 12.65/12.58  0 [] -class_Rings_Oidom(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p).
% 12.65/12.58  0 [] -class_Rings_Oidom(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p).
% 12.65/12.58  0 [] -class_Rings_Oidom(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)).
% 12.65/12.58  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m)|V_m=V_n.
% 12.65/12.58  0 [] V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ma_2,V_t_2)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2)).
% 12.65/12.58  0 [] V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ma_2,V_t_2)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2)).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_x_2,c_Groups_Oone__class_Oone(tc_Int_Oint))|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.65/12.58  0 [] c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_x_2,c_Groups_Oone__class_Oone(tc_Int_Oint))|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_n_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_ma_2)))|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,V_n_2).
% 12.65/12.58  0 [] c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_n_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_ma_2)))| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,V_n_2).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_d_2)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2))|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_d_2)),V_t_2)).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_d_2)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2))| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_d_2)),V_t_2)).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_b,V_a)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_a)=c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_b).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n))|V_k=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_z,V_n)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_n).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m,V_n)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m).
% 12.65/12.58  0 [] V_i=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d,V_i)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_d),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)).
% 12.65/12.58  0 [] V_ma_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2),V_ma_2)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.65/12.58  0 [] V_ma_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2),V_ma_2)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_n_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_ma_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_ma_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.58  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_ma_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_ma_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_ma_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_x_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.58  0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.58  0 [] V_i!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.65/12.58  0 [] V_i=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.65/12.58  0 [] V_i=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 12.65/12.58  0 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)=V_z.
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z.
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_w_2).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)|V_z_2!=V_w_2.
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_w_2)|V_z_2=V_w_2.
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,V_z_2).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,V_z_2).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)|V_ma_2=V_n_2.
% 12.65/12.58  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)|V_ma_2!=V_n_2.
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)).
% 12.65/12.58  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)|V_w_2=V_z_2.
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|V_w_2!=V_z_2.
% 12.65/12.58  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z.
% 12.65/12.58  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)=V_z.
% 12.65/12.58  0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m).
% 12.65/12.58  0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_nat_H).
% 12.65/12.58  0 [] c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] c_Nat_OSuc(V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m).
% 12.65/12.58  0 [] c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] 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,c_Nat_OSuc(V_ma_2)).
% 12.65/12.58  0 [] -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,c_Nat_OSuc(V_ma_2)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2=V_n_2.
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))|V_ma_2!=V_n_2.
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),c_Nat_OSuc(V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),c_Nat_OSuc(V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2))|V_n_2=V_ma_2.
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2))|V_n_2!=V_ma_2.
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))|V_m=V_n.
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Nat_OSuc(V_m)=V_n|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_m=V_n.
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2=c_Nat_OSuc(V_n_2).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))|V_ma_2!=c_Nat_OSuc(V_n_2).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_ma_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_ma_2).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_ma_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_ma_2).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|V_m=c_Nat_OSuc(V_n).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 12.65/12.58  0 [] V_n!=c_Nat_OSuc(V_n).
% 12.65/12.58  0 [] c_Nat_OSuc(V_n)!=V_n.
% 12.65/12.58  0 [] c_Nat_OSuc(V_nat_2)!=c_Nat_OSuc(V_nat_H_2)|V_nat_2=V_nat_H_2.
% 12.65/12.58  0 [] c_Nat_OSuc(V_nat_2)=c_Nat_OSuc(V_nat_H_2)|V_nat_2!=V_nat_H_2.
% 12.65/12.58  0 [] c_Nat_OSuc(V_x)!=c_Nat_OSuc(V_y)|V_x=V_y.
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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.
% 12.65/12.58  0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_OSuc(V_n))=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)).
% 12.65/12.58  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)).
% 12.65/12.58  0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a).
% 12.65/12.58  0 [] -class_Power_Opower(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))|V_ma_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_ma_2=c_Nat_OSuc($f28(V_n_2,V_ma_2)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))|V_ma_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f28(V_n_2,V_ma_2),V_n_2).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))|V_ma_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))|V_ma_2!=c_Nat_OSuc(B_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)|V_n_2=c_Nat_OSuc($f29(V_n_2)).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)|V_n_2!=c_Nat_OSuc(B_m).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_ma_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.58  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_ma_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.58  0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_ma_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.58  0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_ma_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.58  0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)|V_ma_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.58  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_ma_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_ma_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_ma_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.58  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_ma_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.58  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_ma_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_ma_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)).
% 12.65/12.58  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_ma_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.58  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.58  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_ma_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|V_n_2=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,$f30(V_n_2,V_ma_2))).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)|V_n_2!=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k)).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n).
% 12.65/12.58  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_n_2,c_Nat_OSuc(V_ma_2))|V_n_2=V_ma_2.
% 12.65/12.58  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_n_2,c_Nat_OSuc(V_ma_2))|V_n_2!=V_ma_2.
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 12.65/12.58  0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 12.65/12.58  0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.58  0 [] c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n).
% 12.65/12.58  0 [] c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 12.65/12.58  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(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__e_q(T_a,V_a,V_b).
% 12.65/12.58  0 [] -class_Rings_Olinordered__semidom(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))!=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(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)|V_a=V_b.
% 12.65/12.58  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))).
% 12.65/12.58  0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))!=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x_2=V_y_2|V_x_2=c_Groups_Ouminus__class_Ouminus(T_a,V_y_2).
% 12.65/12.58  0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x_2!=V_y_2.
% 12.65/12.58  0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_y_2).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ma_2).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ma_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b),V_n))|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b).
% 12.65/12.58  0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2))|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_b_2).
% 12.65/12.58  0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2))| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_b_2).
% 12.65/12.58  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_r,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_r),c_Nat_OSuc(V_n)),V_r).
% 12.65/12.58  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a)).
% 12.65/12.58  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b),V_n))|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b).
% 12.65/12.58  0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2))|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a_2,V_b_2).
% 12.65/12.58  0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2))| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a_2,V_b_2).
% 12.65/12.58  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_x).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z))=V_z.
% 12.65/12.58  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.
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_w).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2)).
% 12.65/12.58  0 [] c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2)).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2),V_t_2).
% 12.65/12.58  0 [] c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2),V_t_2).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)).
% 12.65/12.58  0 [] c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.58  0 [] hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_one_2.
% 12.65/12.58  0 [] hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2))=hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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))).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)|hBOOL(hAPP(V_P_2,$f31(V_k_2,V_P_2,V_d_2)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)| -hBOOL(hAPP(V_P_2,B_x))|hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)| -hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,$f31(V_k_2,V_P_2,V_d_2),V_d_2)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)| -hBOOL(hAPP(V_P_2,B_x))|hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n.
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))).
% 12.65/12.58  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.
% 12.65/12.58  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.
% 12.65/12.58  0 [] c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n.
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))).
% 12.65/12.58  0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.65/12.58  0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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))).
% 12.65/12.58  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))).
% 12.65/12.58  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_a_2,c_RComplete_Onatfloor(V_x_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_x_2).
% 12.65/12.58  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_a_2,c_RComplete_Onatfloor(V_x_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_x_2).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f32(V_X_2,T_a)))).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_OBse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,$f33(V_X_2,T_a,B_N))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f34(V_X_2,T_a)))).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_OBse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,$f35(V_X_2,T_a,B_N))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_b)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,$f36(V_X_2,T_b,B_K))),B_K)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f37(V_X_2,T_b)))).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_b)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f38(V_X_2,T_b))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,$f39(V_X_2,T_b,B_N))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_b)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,X2)),$f38(V_X_2,T_b))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,$f39(V_X_2,T_b,B_N))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_b)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,$f40(V_X_2,T_b,B_K))),B_K)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f41(V_X_2,T_b)))).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_b)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f42(V_X_2,T_b))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,$f43(V_X_2,T_b,B_N))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))).
% 12.65/12.58  0 [] -class_RealVector_Oreal__normed__vector(T_b)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,X3)),$f42(V_X_2,T_b))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,$f43(V_X_2,T_b,B_N))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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.
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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,$f44(V_r)),V_r).
% 12.65/12.58  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,c_Nat_OSuc($f44(V_r)))).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f45(V_a,V_n)).
% 12.65/12.58  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_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),$f45(V_a,V_n)),V_n)=V_a.
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n)!=V_a|B_y=$f45(V_a,V_n).
% 12.65/12.58  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_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f46(V_a,V_n)).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),$f46(V_a,V_n)),V_n)=V_a.
% 12.65/12.58  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))).
% 12.65/12.58  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_a_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_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2).
% 12.65/12.58  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_a_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_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2).
% 12.65/12.58  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_a_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_a_2)),V_e_2),V_d_2)).
% 12.65/12.58  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_a_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_a_2)),V_e_2),V_d_2)).
% 12.65/12.58  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_a_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_a_2)),V_e_2),V_d_2)).
% 12.65/12.58  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_a_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_a_2)),V_e_2),V_d_2)).
% 12.65/12.58  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_a_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_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2).
% 12.65/12.58  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_a_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_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2).
% 12.65/12.58  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))).
% 12.65/12.58  0 [] -class_Rings_Ocomm__ring(T_a)| -class_Rings_Odvd(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))|c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)).
% 12.65/12.58  0 [] -class_Rings_Ocomm__ring(T_a)| -class_Rings_Odvd(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)|c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)).
% 12.65/12.58  0 [] -class_Rings_Ocomm__ring(T_a)| -class_Rings_Odvd(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))|c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)).
% 12.65/12.58  0 [] -class_Rings_Ocomm__ring(T_a)| -class_Rings_Odvd(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)|c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)).
% 12.65/12.58  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)))).
% 12.65/12.58  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))).
% 12.65/12.58  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_a_2)),V_ra_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2).
% 12.65/12.58  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_a_2)),V_ra_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2)).
% 12.65/12.58  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_a_2)),V_ra_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2)).
% 12.65/12.58  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))).
% 12.65/12.58  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.58  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.58  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)).
% 12.65/12.58  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))).
% 12.65/12.58  0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_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_a_2,V_b_2)),V_e_2),V_ca_2)=V_d_2.
% 12.65/12.58  0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_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_a_2,V_b_2)),V_e_2),V_ca_2)!=V_d_2.
% 12.65/12.58  0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_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_a_2)),V_e_2),V_d_2).
% 12.65/12.58  0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_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_a_2)),V_e_2),V_d_2).
% 12.65/12.58  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).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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))).
% 12.65/12.58  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))).
% 12.65/12.58  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))).
% 12.65/12.58  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).
% 12.65/12.58  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)).
% 12.65/12.58  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).
% 12.65/12.58  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))).
% 12.65/12.58  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.
% 12.65/12.58  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.
% 12.65/12.58  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_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_a_2,V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_ca_2,V_d_2).
% 12.65/12.58  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_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_a_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_ca_2,V_d_2).
% 12.65/12.58  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)).
% 12.65/12.58  0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n))| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_n)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_m).
% 12.65/12.58  0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.65/12.58  0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.58  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)).
% 12.65/12.59  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)).
% 12.65/12.59  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)|V_a_2!=V_b_2|V_ca_2=V_d_2.
% 12.65/12.59  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)|V_a_2=V_b_2|V_ca_2!=V_d_2.
% 12.65/12.59  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.59  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.65/12.59  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)).
% 12.65/12.59  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)).
% 12.65/12.59  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)).
% 12.65/12.59  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)).
% 12.65/12.59  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)).
% 12.65/12.59  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_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_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_d_2).
% 12.65/12.59  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_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_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_d_2).
% 12.65/12.59  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.
% 12.65/12.59  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).
% 12.65/12.59  0 [] -class_Groups_Oab__group__add(T_a)|V_a_2!=V_b_2|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.59  0 [] -class_Groups_Oab__group__add(T_a)|V_a_2=V_b_2|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 12.65/12.59  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=V_b_2.
% 12.65/12.59  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=V_b_2.
% 12.65/12.59  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)).
% 12.65/12.59  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)).
% 12.65/12.59  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))).
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 12.65/12.59  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 12.65/12.59  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)))).
% 12.65/12.59  0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)).
% 12.65/12.59  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).
% 12.65/12.59  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,$f47(V_X_2,V_M_2,T_a,T_b))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2,B_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2)))).
% 12.65/12.59  0 [] -class_RealVector_Oreal__normed__vector(T_b)| -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,$f47(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)))).
% 12.65/12.59  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).
% 12.65/12.59  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).
% 12.65/12.59  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)).
% 12.65/12.59  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)).
% 12.65/12.59  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.
% 12.65/12.59  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)).
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_ma_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_ma_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.59  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).
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_ma_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)|V_ma_2=V_n_2.
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_ma_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)|V_ma_2!=V_n_2.
% 12.65/12.59  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.
% 12.65/12.59  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)).
% 12.65/12.59  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)).
% 12.65/12.59  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).
% 12.65/12.59  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.
% 12.65/12.59  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.
% 12.65/12.59  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)).
% 12.65/12.59  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).
% 12.65/12.59  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).
% 12.65/12.59  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 12.65/12.59  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)).
% 12.65/12.59  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)).
% 12.65/12.59  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).
% 12.65/12.59  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).
% 12.65/12.59  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).
% 12.65/12.59  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)).
% 12.65/12.59  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).
% 12.65/12.59  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).
% 12.65/12.59  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).
% 12.65/12.59  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).
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2).
% 12.65/12.59  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2).
% 12.65/12.59  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.
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_ma_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_ma_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2).
% 12.65/12.59  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)).
% 12.65/12.59  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m).
% 12.65/12.59  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n).
% 12.65/12.59  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).
% 12.65/12.59  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).
% 12.65/12.59  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)).
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)!=V_k_2|V_j_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2).
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_k_2|V_j_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2).
% 12.65/12.59  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.
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2).
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2).
% 12.65/12.59  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).
% 12.65/12.59  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.
% 12.65/12.59  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)).
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)).
% 12.65/12.59  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)).
% 12.65/12.59  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).
% 12.65/12.59  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n).
% 12.65/12.59  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 12.65/12.59  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)).
% 12.65/12.59  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)).
% 12.65/12.59  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).
% 12.65/12.59  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k).
% 12.65/12.59  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 12.65/12.59  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.
% 12.65/12.59  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)).
% 12.65/12.59  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).
% 12.65/12.59  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.
% 12.65/12.59  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.59  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 12.65/12.59  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).
% 12.65/12.59  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)).
% 12.65/12.59  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)).
% 12.65/12.59  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)).
% 12.65/12.59  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).
% 12.65/12.59  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).
% 12.65/12.59  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))).
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n).
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n.
% 12.65/12.59  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.65/12.59  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|V_a_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 12.65/12.59  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f48(V_b_2,V_a_2,V_P_2)).
% 12.65/12.59  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)| -hBOOL(hAPP(V_P_2,$f48(V_b_2,V_a_2,V_P_2))).
% 12.65/12.59  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f48(V_b_2,V_a_2,V_P_2)).
% 12.65/12.59  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f48(V_b_2,V_a_2,V_P_2))).
% 12.65/12.59  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.65/12.59  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|V_a_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 12.65/12.59  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f49(V_b_2,V_a_2,V_P_2)).
% 12.65/12.59  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)| -hBOOL(hAPP(V_P_2,$f49(V_b_2,V_a_2,V_P_2))).
% 12.65/12.59  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f49(V_b_2,V_a_2,V_P_2)).
% 12.65/12.59  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f49(V_b_2,V_a_2,V_P_2))).
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m)).
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j)).
% 12.65/12.59  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).
% 12.65/12.59  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).
% 12.65/12.59  0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint).
% 12.65/12.59  0 [] -class_Lattices_Oboolean__algebra(T_1)|class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)).
% 12.65/12.59  0 [] -class_Orderings_Opreorder(T_1)|class_Orderings_Opreorder(tc_fun(T_2,T_1)).
% 12.65/12.59  0 [] -class_Orderings_Oorder(T_1)|class_Orderings_Oorder(tc_fun(T_2,T_1)).
% 12.65/12.59  0 [] -class_Orderings_Oord(T_1)|class_Orderings_Oord(tc_fun(T_2,T_1)).
% 12.65/12.59  0 [] -class_Groups_Ouminus(T_1)|class_Groups_Ouminus(tc_fun(T_2,T_1)).
% 12.65/12.59  0 [] -class_Groups_Ominus(T_1)|class_Groups_Ominus(tc_fun(T_2,T_1)).
% 12.65/12.59  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Oordered__cancel__semiring(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Oordered__comm__semiring(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Olinordered__semiring__1(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Olinordered__semiring(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Olinordered__semidom(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Oordered__semiring(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Oordered__ring__abs(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Olinordered__ring(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Olinordered__idom(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Ocomm__semiring__0(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Ocomm__semiring(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Oab__group__add(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Oordered__ring(tc_Int_Oint).
% 12.65/12.59  0 [] class_Orderings_Opreorder(tc_Int_Oint).
% 12.65/12.59  0 [] class_Orderings_Olinorder(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Omonoid__mult(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Omonoid__add(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Osemiring__0(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Ogroup__add(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Omult__zero(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Ocomm__ring(tc_Int_Oint).
% 12.65/12.59  0 [] class_Orderings_Oorder(tc_Int_Oint).
% 12.65/12.59  0 [] class_Int_Oring__char__0(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Osemiring(tc_Int_Oint).
% 12.65/12.59  0 [] class_Orderings_Oord(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Ouminus(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Osgn__if(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Oabs__if(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Oring__1(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Ominus(tc_Int_Oint).
% 12.65/12.59  0 [] class_Power_Opower(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Ozero(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Oring(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Oidom(tc_Int_Oint).
% 12.65/12.59  0 [] class_Groups_Oone(tc_Int_Oint).
% 12.65/12.59  0 [] class_Rings_Odvd(tc_Int_Oint).
% 12.65/12.59  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Rings_Oordered__semiring(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Rings_Ocomm__semiring__0(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Orderings_Opreorder(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Orderings_Olinorder(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Groups_Omonoid__mult(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Groups_Omonoid__add(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Rings_Osemiring__0(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Rings_Omult__zero(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Orderings_Oorder(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Rings_Osemiring(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Orderings_Oord(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Groups_Ominus(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Power_Opower(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Groups_Ozero(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Groups_Oone(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Rings_Odvd(tc_Nat_Onat).
% 12.65/12.59  0 [] class_Lattices_Oboolean__algebra(tc_HOL_Obool).
% 12.65/12.59  0 [] class_Orderings_Opreorder(tc_HOL_Obool).
% 12.65/12.59  0 [] class_Orderings_Oorder(tc_HOL_Obool).
% 12.65/12.59  0 [] class_Orderings_Oord(tc_HOL_Obool).
% 12.65/12.59  0 [] class_Groups_Ouminus(tc_HOL_Obool).
% 12.65/12.59  0 [] class_Groups_Ominus(tc_HOL_Obool).
% 12.65/12.59  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Olinordered__semiring(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Olinordered__semidom(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Oab__semigroup__add(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Oordered__semiring(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Oordered__ring__abs(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Ono__zero__divisors(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Olinordered__ring(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Olinordered__idom(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Ocomm__semiring(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Oab__group__add(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Oordered__ring(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Orderings_Opreorder(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Orderings_Olinorder(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Omonoid__mult(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Ocomm__ring__1(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Omonoid__add(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Osemiring__0(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Ogroup__add(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Omult__zero(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Ocomm__ring(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Orderings_Oorder(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Int_Oring__char__0(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Osemiring(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Orderings_Oord(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Ouminus(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Osgn__if(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Oabs__if(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Oring__1(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Ominus(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Power_Opower(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Ozero(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Oring(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Oidom(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Groups_Oone(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Rings_Odvd(tc_RealDef_Oreal).
% 12.65/12.59  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Rings_Ocomm__semiring(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Groups_Oab__group__add(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Rings_Ozero__ne_q__one(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Groups_Omonoid__mult(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Groups_Omonoid__add(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Rings_Osemiring__0(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Groups_Ogroup__add(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Rings_Omult__zero(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Rings_Ocomm__ring(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Int_Oring__char__0(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Rings_Osemiring(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Groups_Ouminus(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Rings_Oring__1(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Groups_Ominus(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Power_Opower(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Groups_Ozero(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Rings_Oring(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Rings_Oidom(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Groups_Oone(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] class_Rings_Odvd(tc_Complex_Ocomplex).
% 12.65/12.59  0 [] -class_Rings_Oidom(T_1)|class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Oidom(T_1)|class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Oidom(T_1)|class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Oidom(T_1)|class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Oord(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ominus(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Power_Opower(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Groups_Ozero(T_1)|class_Groups_Ozero(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Oring(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Oidom(T_1)|class_Rings_Oidom(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Oone(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Odvd(tc_Polynomial_Opoly(T_1)).
% 12.65/12.59  0 [] -hBOOL(c_fe_qual(V_x_2,V_y_2))|V_x_2=V_y_2.
% 12.65/12.59  0 [] V_x_2!=V_y_2|hBOOL(c_fe_qual(V_x_2,V_y_2)).
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,$f50(B_m)),v_r).
% 12.65/12.59  0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),$f50(B_m))),B_m).
% 12.65/12.59  end_of_list.
% 12.65/12.59  
% 12.65/12.59  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 12.65/12.59  
% 12.65/12.59  This ia a non-Horn set with equality.  The strategy will be
% 12.65/12.59  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 12.65/12.59  deletion, with positive clauses in sos and nonpositive
% 12.65/12.59  clauses in usable.
% 12.65/12.59  
% 12.65/12.59     dependent: set(knuth_bendix).
% 12.65/12.59     dependent: set(anl_eq).
% 12.65/12.59     dependent: set(para_from).
% 12.65/12.59     dependent: set(para_into).
% 12.65/12.59     dependent: clear(para_from_right).
% 12.65/12.59     dependent: clear(para_into_right).
% 12.65/12.59     dependent: set(para_from_vars).
% 12.65/12.59     dependent: set(eq_units_both_ways).
% 12.65/12.59     dependent: set(dynamic_demod_all).
% 12.65/12.59     dependent: set(dynamic_demod).
% 12.65/12.59     dependent: set(order_eq).
% 12.65/12.59     dependent: set(back_demod).
% 12.65/12.59     dependent: set(lrpo).
% 12.65/12.59     dependent: set(hyper_res).
% 12.65/12.59     dependent: set(unit_deletion).
% 12.65/12.59     dependent: set(factor).
% 12.65/12.59  
% 12.65/12.59  ------------> process usable:
% 12.65/12.59  ** KEPT (pick-wt=14): 1 [] hAPP(A,$f1(B,A))!=hAPP(B,$f1(B,A))|A=B.
% 12.65/12.59  ** KEPT (pick-wt=16): 2 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),v_r)|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_cs____),A)),v_m____).
% 12.65/12.59  ** KEPT (pick-wt=16): 3 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),v_r)|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_cs____),A)),$c1).
% 12.65/12.59  ** KEPT (pick-wt=13): 4 [] -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).
% 12.65/12.59  ** KEPT (pick-wt=13): 5 [] -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).
% 12.65/12.59  ** KEPT (pick-wt=13): 6 [] -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).
% 12.65/12.59  ** KEPT (pick-wt=13): 7 [] -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).
% 12.65/12.59  ** KEPT (pick-wt=9): 8 [] -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)).
% 12.65/12.59  ** KEPT (pick-wt=9): 9 [] -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)).
% 12.65/12.59  ** KEPT (pick-wt=9): 10 [] -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).
% 12.65/12.59  ** KEPT (pick-wt=12): 11 [] -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).
% 12.65/12.59  ** KEPT (pick-wt=12): 12 [] -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).
% 12.65/12.59  ** KEPT (pick-wt=16): 13 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),v_r)|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_cs____),A)),$c2).
% 12.65/12.59  ** KEPT (pick-wt=6): 14 [] -class_Orderings_Opreorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,B).
% 12.65/12.59  ** KEPT (pick-wt=12): 15 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)=c_Groups_Ozero__class_Ozero(A).
% 12.65/12.59  ** KEPT (pick-wt=13): 16 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 12.65/12.59  ** KEPT (pick-wt=14): 17 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B=c_Groups_Ozero__class_Ozero(A).
% 12.65/12.59  ** KEPT (pick-wt=15): 18 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 12.65/12.59  ** KEPT (pick-wt=19): 19 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 12.65/12.59  ** KEPT (pick-wt=8): 20 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B).
% 12.65/12.59  ** KEPT (pick-wt=7): 21 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|A!=B.
% 12.65/12.59  ** KEPT (pick-wt=11): 22 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|A=B.
% 12.65/12.59  ** KEPT (pick-wt=18): 23 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)!=c_Polynomial_Opoly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 12.65/12.59  ** KEPT (pick-wt=18): 24 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)=c_Polynomial_Opoly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 12.65/12.59  ** KEPT (pick-wt=10): 25 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.65/12.59  ** KEPT (pick-wt=16): 26 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 12.65/12.59  ** KEPT (pick-wt=14): 27 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,B)|c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 12.65/12.59  ** KEPT (pick-wt=13): 28 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|C=B.
% 12.65/12.59  ** KEPT (pick-wt=14): 29 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 12.65/12.59    Following clause subsumed by 28 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|B=C.
% 12.65/12.59  ** KEPT (pick-wt=13): 30 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=D|c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 12.65/12.59  ** KEPT (pick-wt=13): 31 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|C!=D|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 12.65/12.59  ** KEPT (pick-wt=13): 32 [] -class_Orderings_Oorder(A)|B!=C| -c_Orderings_Oord__class_Oless__e_q(A,D,C)|c_Orderings_Oord__class_Oless__e_q(A,D,B).
% 12.65/12.59  ** KEPT (pick-wt=13): 33 [] -class_Orderings_Oord(A)|B!=C| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 12.65/12.59    Following clause subsumed by 28 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|C=B.
% 12.65/12.59  ** KEPT (pick-wt=13): 34 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B)|C!=B.
% 12.65/12.59    Following clause subsumed by 26 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 12.65/12.59  ** KEPT (pick-wt=9): 35 [] -class_Orderings_Opreorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.65/12.59  ** KEPT (pick-wt=9): 36 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.65/12.59  ** KEPT (pick-wt=9): 37 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.65/12.59    Following clause subsumed by 28 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.65/12.59    Following clause subsumed by 25 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.65/12.59    Following clause subsumed by 26 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 12.65/12.59  ** KEPT (pick-wt=24): 38 [] -class_Orderings_Oord(A)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,$f2(D,C,B,A)),hAPP(D,$f2(D,C,B,A))).
% 12.65/12.59  ** KEPT (pick-wt=13): 39 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59  ** KEPT (pick-wt=10): 40 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59  ** KEPT (pick-wt=14): 41 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C).
% 12.65/12.59  ** KEPT (pick-wt=14): 42 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 12.65/12.59  ** KEPT (pick-wt=13): 43 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=D|c_Orderings_Oord__class_Oless(A,D,C).
% 12.65/12.59  ** KEPT (pick-wt=13): 44 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=D|c_Orderings_Oord__class_Oless(A,B,D).
% 12.65/12.59  ** KEPT (pick-wt=13): 45 [] -class_Orderings_Oorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,D,C)|c_Orderings_Oord__class_Oless(A,D,B).
% 12.65/12.59  ** KEPT (pick-wt=13): 46 [] -class_Orderings_Oord(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 12.65/12.59  ** KEPT (pick-wt=10): 47 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59    Following clause subsumed by 40 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59  ** KEPT (pick-wt=9): 48 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=B.
% 12.65/12.59  ** KEPT (pick-wt=9): 49 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 12.65/12.59    Following clause subsumed by 40 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59    Following clause subsumed by 40 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59    Following clause subsumed by 49 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 12.65/12.59    Following clause subsumed by 39 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59    Following clause subsumed by 39 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B)|C=B.
% 12.65/12.59  ** KEPT (pick-wt=13): 50 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B)|C!=B.
% 12.65/12.59    Following clause subsumed by 39 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59    Following clause subsumed by 39 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B)|B=C.
% 12.65/12.59  ** KEPT (pick-wt=10): 51 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59  ** KEPT (pick-wt=9): 52 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 12.65/12.59    Following clause subsumed by 39 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59    Following clause subsumed by 52 during input processing: 0 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,B,C).
% 12.65/12.59  ** KEPT (pick-wt=9): 53 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59  ** KEPT (pick-wt=6): 54 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,B).
% 12.65/12.59  ** KEPT (pick-wt=11): 55 [] -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.
% 12.65/12.59  ** KEPT (pick-wt=12): 56 [] -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).
% 12.65/12.59  ** KEPT (pick-wt=14): 57 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)!=c_Polynomial_OpCons(A,D,E)|B=D.
% 12.65/12.59  ** KEPT (pick-wt=14): 58 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)!=c_Polynomial_OpCons(A,D,E)|C=E.
% 12.65/12.59  ** KEPT (pick-wt=17): 59 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)=c_Polynomial_OpCons(A,D,E)|B!=D|C!=E.
% 12.65/12.59  ** KEPT (pick-wt=14): 60 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)!=c_Polynomial_Opoly(A,C)|B=C.
% 12.65/12.59  ** KEPT (pick-wt=14): 61 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)=c_Polynomial_Opoly(A,C)|B!=C.
% 12.65/12.59  ** KEPT (pick-wt=14): 62 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C).
% 12.65/12.59  ** KEPT (pick-wt=14): 63 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 12.65/12.59  ** KEPT (pick-wt=14): 64 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C).
% 12.65/12.59  ** KEPT (pick-wt=14): 65 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 12.65/12.59  ** KEPT (pick-wt=13): 66 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|C=B|c_Orderings_Oord__class_Oless(A,B,C).
% 12.65/12.59  ** KEPT (pick-wt=13): 67 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,B,C).
% 12.65/12.59    Following clause subsumed by 67 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 12.65/12.59  ** KEPT (pick-wt=13): 68 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 12.65/12.59    Following clause subsumed by 52 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 12.65/12.59  ** KEPT (pick-wt=10): 69 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.65/12.59  ** KEPT (pick-wt=10): 70 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59    Following clause subsumed by 66 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59    Following clause subsumed by 67 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C).
% 12.65/12.59    Following clause subsumed by 68 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C.
% 12.65/12.59  ** KEPT (pick-wt=13): 71 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C.
% 12.65/12.59  ** KEPT (pick-wt=10): 72 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59    Following clause subsumed by 72 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.65/12.59    Following clause subsumed by 67 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 12.65/12.59  ** KEPT (pick-wt=10): 73 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,B,C).
% 12.65/12.59    Following clause subsumed by 36 during input processing: 0 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C.
% 12.65/12.59    Following clause subsumed by 69 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.65/12.59  ** KEPT (pick-wt=10): 74 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.65/12.59  ** KEPT (pick-wt=14): 75 [] -class_Orderings_Opreorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.65/12.59    Following clause subsumed by 73 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.65/12.59    Following clause subsumed by 49 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 12.65/12.59    Following clause subsumed by 67 during input processing: 0 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C.
% 12.65/12.59    Following clause subsumed by 72 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59    Following clause subsumed by 72 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59    Following clause subsumed by 70 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59    Following clause subsumed by 72 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.65/12.59    Following clause subsumed by 70 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.65/12.59    Following clause subsumed by 22 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|A=B.
% 12.65/12.59    Following clause subsumed by 20 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B).
% 12.65/12.59  ** KEPT (pick-wt=7): 76 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|A!=B.
% 12.65/12.59  ** KEPT (pick-wt=35): 77 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,A),v_r)|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,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),A)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))).
% 12.65/12.59  ** KEPT (pick-wt=16): 78 [] -class_Rings_Olinordered__idom(A)| -c_Polynomial_Opos__poly(A,c_Polynomial_OpCons(A,B,C))|c_Polynomial_Opos__poly(A,C)|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 12.65/12.59  ** KEPT (pick-wt=16): 79 [] -class_Rings_Olinordered__idom(A)| -c_Polynomial_Opos__poly(A,c_Polynomial_OpCons(A,B,C))|c_Polynomial_Opos__poly(A,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.65/12.59  ** KEPT (pick-wt=11): 80 [] -class_Rings_Olinordered__idom(A)|c_Polynomial_Opos__poly(A,c_Polynomial_OpCons(A,B,C))| -c_Polynomial_Opos__poly(A,C).
% 12.65/12.59  ** KEPT (pick-wt=18): 81 [] -class_Rings_Olinordered__idom(A)|c_Polynomial_Opos__poly(A,c_Polynomial_OpCons(A,B,C))|C!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.65/12.59  ** KEPT (pick-wt=22): 82 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Opoly(A,B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Oorder(A,C,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.59  ** KEPT (pick-wt=15): 83 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Opoly(A,B),C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 12.65/12.59  ** KEPT (pick-wt=17): 84 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Opoly(A,B),C)=c_Groups_Ozero__class_Ozero(A)|c_Polynomial_Oorder(A,C,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.59  ** KEPT (pick-wt=36): 86 [copy,85,flip.3] -class_Groups_Ozero(A)|hAPP(hAPP(hAPP(B,c_Groups_Ozero__class_Ozero(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)!=C|hAPP(hAPP(hAPP(B,D),E),c_Polynomial_Opoly__rec(F,A,C,B,E))=c_Polynomial_Opoly__rec(F,A,C,B,c_Polynomial_OpCons(A,D,E)).
% 12.65/12.59  ** KEPT (pick-wt=32): 88 [copy,87,flip.2] -class_Groups_Ozero(A)|hAPP(hAPP(hAPP(B,C),D),c_If(E,c_fe_qual(D,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),F,c_Polynomial_Opoly__rec(E,A,F,B,D)))=c_Polynomial_Opoly__rec(E,A,F,B,c_Polynomial_OpCons(A,C,D)).
% 12.65/12.59  ** KEPT (pick-wt=21): 89 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osynthetic__div(A,c_Polynomial_OpCons(A,B,C),D)=c_Polynomial_OpCons(A,hAPP(c_Polynomial_Opoly(A,C),D),c_Polynomial_Osynthetic__div(A,C,D)).
% 12.65/12.59  ** KEPT (pick-wt=24): 90 [] -class_Groups_Ozero(A)|hAPP(hAPP(hAPP(B,c_Groups_Ozero__class_Ozero(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)!=C|c_Polynomial_Opoly__rec(D,A,C,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=C.
% 12.65/12.59  ** KEPT (pick-wt=12): 91 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f3(B,A)).
% 12.65/12.59  ** KEPT (pick-wt=15): 92 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C)),$f3(B,A)).
% 12.65/12.59  ** KEPT (pick-wt=21): 93 [] -class_RealVector_Oreal__normed__vector(A)|c_SEQ_OBse_q(A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,$f4(B,A,C))),C).
% 12.65/12.59  ** KEPT (pick-wt=13): 94 [] -class_Rings_Olinordered__idom(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 12.65/12.59  ** KEPT (pick-wt=10): 95 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 12.65/12.59  ** KEPT (pick-wt=10): 96 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 12.65/12.59  ** KEPT (pick-wt=10): 97 [] -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).
% 12.65/12.59  ** KEPT (pick-wt=18): 98 [] -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))).
% 12.65/12.59  ** KEPT (pick-wt=14): 99 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D).
% 12.65/12.59  ** KEPT (pick-wt=14): 100 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D,C).
% 12.65/12.59  ** KEPT (pick-wt=20): 101 [] -class_Orderings_Oord(A)|c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D,C).
% 12.65/12.59  ** KEPT (pick-wt=26): 102 [] -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)).
% 12.65/12.59    Following clause subsumed by 102 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)).
% 12.65/12.59  ** KEPT (pick-wt=26): 103 [] -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)).
% 12.65/12.59    Following clause subsumed by 103 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)).
% 12.65/12.59  ** KEPT (pick-wt=44): 104 [] -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).
% 12.65/12.59  ** KEPT (pick-wt=14): 105 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,D,C)|B=D.
% 12.65/12.59  ** KEPT (pick-wt=14): 106 [] -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.
% 12.65/12.59  ** KEPT (pick-wt=14): 107 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 12.65/12.59  ** KEPT (pick-wt=32): 108 [] -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)).
% 12.65/12.59  ** KEPT (pick-wt=22): 109 [] -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)).
% 12.65/12.59  ** KEPT (pick-wt=32): 111 [copy,110,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)).
% 12.65/12.59    Following clause subsumed by 105 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.
% 12.65/12.59  ** KEPT (pick-wt=14): 112 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,D,C)|B!=D.
% 12.65/12.59    Following clause subsumed by 107 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.
% 12.65/12.59  ** KEPT (pick-wt=14): 113 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,B,D)|C!=D.
% 12.65/12.59  ** KEPT (pick-wt=26): 114 [] -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)).
% 12.65/12.59  ** KEPT (pick-wt=25): 115 [] -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)).
% 12.65/12.59  ** KEPT (pick-wt=17): 116 [] -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)).
% 12.65/12.59  ** KEPT (pick-wt=19): 117 [] -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).
% 12.65/12.59  ** KEPT (pick-wt=11): 118 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 12.65/12.59  ** KEPT (pick-wt=11): 119 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 12.65/12.59  ** KEPT (pick-wt=10): 120 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)!=B|B=c_Groups_Oone__class_Oone(A).
% 12.65/12.59  ** KEPT (pick-wt=10): 121 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)=B|B!=c_Groups_Oone__class_Oone(A).
% 12.65/12.59  ** KEPT (pick-wt=11): 122 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 12.65/12.59  ** KEPT (pick-wt=11): 123 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 12.65/12.59  ** KEPT (pick-wt=21): 124 [] -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)).
% 12.65/12.59  ** KEPT (pick-wt=21): 126 [copy,125,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)).
% 12.65/12.59  ** KEPT (pick-wt=11): 127 [] -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).
% 12.65/12.59  ** KEPT (pick-wt=9): 128 [] -class_Rings_Olinordered__idom(A)|c_Groups_Oabs__class_Oabs(A,c_Groups_Oone__class_Oone(A))=c_Groups_Oone__class_Oone(A).
% 12.65/12.59  ** KEPT (pick-wt=10): 129 [] -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))).
% 12.65/12.59  ** KEPT (pick-wt=9): 130 [] -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).
% 12.65/12.59  ** KEPT (pick-wt=12): 131 [] -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).
% 12.65/12.59  ** KEPT (pick-wt=12): 132 [] -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).
% 12.65/12.59  ** KEPT (pick-wt=21): 133 [] 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).
% 12.65/12.59  ** KEPT (pick-wt=21): 134 [] 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).
% 12.65/12.59  ** KEPT (pick-wt=25): 135 [] 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).
% 12.65/12.60  ** KEPT (pick-wt=8): 136 [] -class_Groups_Oordered__ab__group__add__abs(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Oabs__class_Oabs(A,B)).
% 12.65/12.60  ** KEPT (pick-wt=12): 137 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=21): 138 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=9): 139 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=25): 141 [copy,140,flip.2] -class_Groups_Ocomm__monoid__add(A)|c_Polynomial_OpCons(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,E))=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,B,D),c_Polynomial_OpCons(A,C,E)).
% 12.65/12.60  ** KEPT (pick-wt=9): 142 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 12.65/12.60  ** KEPT (pick-wt=9): 143 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 12.65/12.60  ** KEPT (pick-wt=13): 144 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=13): 145 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=9): 146 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 12.65/12.60  ** KEPT (pick-wt=9): 147 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 12.65/12.60  ** KEPT (pick-wt=16): 148 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=16): 149 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=16): 150 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=16): 151 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=16): 152 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=16): 153 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=20): 154 [] -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)).
% 12.65/12.60    Following clause subsumed by 148 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).
% 12.65/12.60    Following clause subsumed by 150 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).
% 12.65/12.60  ** KEPT (pick-wt=16): 155 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=16): 156 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=16): 157 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=16): 158 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=16): 159 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=16): 160 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=20): 161 [] -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)).
% 12.65/12.60    Following clause subsumed by 155 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).
% 12.65/12.60    Following clause subsumed by 157 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).
% 12.65/12.60  ** KEPT (pick-wt=12): 162 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=12): 163 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=19): 164 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=15): 165 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=15): 166 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=19): 167 [] -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).
% 12.65/12.60    Following clause subsumed by 167 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).
% 12.65/12.60  ** KEPT (pick-wt=7): 169 [copy,168,flip.2] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 12.65/12.60    Following clause subsumed by 169 during input processing: 0 [] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 12.65/12.60  ** KEPT (pick-wt=24): 170 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(c_Polynomial_Opoly(A,B),D),hAPP(c_Polynomial_Opoly(A,C),D)).
% 12.65/12.60  ** KEPT (pick-wt=28): 171 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Polynomial_Opoly(A,B),D)),hAPP(c_Polynomial_Opoly(A,C),D)).
% 12.65/12.60  ** KEPT (pick-wt=12): 172 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Polynomial_Opoly(A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)=c_Groups_Oone__class_Oone(A).
% 12.65/12.60  ** KEPT (pick-wt=24): 173 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=31): 175 [copy,174,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)).
% 12.65/12.60  ** KEPT (pick-wt=31): 177 [copy,176,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)).
% 12.65/12.60  ** KEPT (pick-wt=31): 179 [copy,178,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)).
% 12.65/12.60  ** KEPT (pick-wt=31): 181 [copy,180,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)).
% 12.65/12.60  ** KEPT (pick-wt=12): 182 [] -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))).
% 12.65/12.60  ** KEPT (pick-wt=26): 183 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=26): 184 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=44): 185 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=18): 186 [] -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))).
% 12.65/12.60  ** KEPT (pick-wt=26): 187 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 188 [] -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))).
% 12.65/12.60  ** KEPT (pick-wt=30): 189 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=13): 191 [copy,190,flip.2] -class_Rings_Ocomm__semiring__1(A)|c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)).
% 12.65/12.60  ** KEPT (pick-wt=24): 192 [] -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))).
% 12.65/12.60  ** KEPT (pick-wt=12): 193 [] -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).
% 12.65/12.60    Following clause subsumed by 193 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).
% 12.65/12.60  ** KEPT (pick-wt=12): 194 [] -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).
% 12.65/12.60    Following clause subsumed by 194 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).
% 12.65/12.60  ** KEPT (pick-wt=11): 195 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=14): 196 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=9): 197 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=13): 198 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=13): 199 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=12): 200 [] -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.
% 12.65/12.60  ** KEPT (pick-wt=9): 201 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=13): 202 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=13): 203 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=12): 204 [] -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.
% 12.65/12.60  ** KEPT (pick-wt=20): 205 [] 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.
% 12.65/12.60  ** KEPT (pick-wt=20): 206 [] 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.
% 12.65/12.60  ** KEPT (pick-wt=20): 207 [] 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.
% 12.65/12.60  ** KEPT (pick-wt=20): 208 [] 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.
% 12.65/12.60  ** KEPT (pick-wt=5): 209 [] c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.65/12.60  ** KEPT (pick-wt=15): 210 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=15): 211 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=15): 212 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=15): 213 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=20): 214 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=23): 215 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=23): 216 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=27): 217 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=18): 218 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=18): 219 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=20): 220 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=15): 221 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=15): 222 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=15): 223 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=15): 224 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=20): 225 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=18): 226 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=20): 227 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=20): 228 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=20): 229 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=12): 230 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 231 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 232 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 233 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 234 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 235 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=22): 236 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 237 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 238 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=22): 239 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 240 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=22): 241 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 242 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=22): 243 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 244 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 245 [] -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)).
% 12.65/12.60    Following clause subsumed by 245 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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 246 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=25): 247 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=25): 248 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=25): 249 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=25): 250 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=25): 251 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=34): 252 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=34): 253 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 254 [] -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)).
% 12.65/12.60    Following clause subsumed by 246 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)).
% 12.65/12.60    Following clause subsumed by 244 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)).
% 12.65/12.60    Following clause subsumed by 245 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)).
% 12.65/12.60  ** KEPT (pick-wt=12): 255 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=26): 256 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=25): 257 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=25): 258 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=24): 259 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=25): 260 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=25): 261 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=26): 262 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=25): 263 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=25): 264 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=24): 265 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=25): 266 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=25): 267 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=25): 268 [] -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).
% 12.65/12.60    Following clause subsumed by 266 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).
% 12.65/12.60  ** KEPT (pick-wt=22): 269 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 270 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 271 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 272 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=22): 273 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=25): 274 [] -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).
% 12.65/12.60    Following clause subsumed by 267 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).
% 12.65/12.60    Following clause subsumed by 271 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)).
% 12.65/12.60  ** KEPT (pick-wt=22): 275 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=25): 276 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=25): 277 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=25): 278 [] -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)).
% 12.65/12.60    Following clause subsumed by 261 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)).
% 12.65/12.60    Following clause subsumed by 267 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)).
% 12.65/12.60  ** KEPT (pick-wt=8): 279 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=8): 280 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=8): 281 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)).
% 12.65/12.60  ** KEPT (pick-wt=8): 282 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)).
% 12.65/12.60  ** KEPT (pick-wt=20): 283 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=20): 284 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=18): 285 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=18): 286 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=20): 287 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=20): 288 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=25): 289 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=25): 290 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=25): 291 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=25): 292 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=34): 293 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=34): 294 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=34): 295 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=34): 296 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=25): 297 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=25): 298 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=25): 299 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=25): 300 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=25): 301 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=25): 302 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=7): 303 [] -class_Rings_Olinordered__idom(A)| -c_Polynomial_Opos__poly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).
% 12.65/12.60  ** KEPT (pick-wt=23): 304 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=23): 305 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=20): 306 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=23): 307 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=12): 308 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osynthetic__div(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 12.65/12.60  ** KEPT (pick-wt=23): 309 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=23): 310 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=23): 311 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=23): 312 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=24): 313 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=22): 314 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=20): 315 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=28): 316 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=24): 317 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=24): 318 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=20): 319 [] -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))).
% 12.65/12.60  ** KEPT (pick-wt=24): 320 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=24): 321 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=28): 322 [] -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).
% 12.65/12.60  ** KEPT (pick-wt=14): 323 [] -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),A))|A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.65/12.60  ** KEPT (pick-wt=22): 325 [copy,324,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))),C)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),C).
% 12.65/12.60  ** KEPT (pick-wt=22): 327 [copy,326,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))),C)=c_Groups_Oplus__class_Oplus(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 12.65/12.60  ** KEPT (pick-wt=18): 329 [copy,328,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A))),B)=c_Groups_Oplus__class_Oplus(A,B,B).
% 12.65/12.60  ** KEPT (pick-wt=31): 330 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=11): 331 [] -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.
% 12.65/12.60  ** KEPT (pick-wt=11): 332 [] -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.
% 12.65/12.60  ** KEPT (pick-wt=15): 333 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=15): 334 [] -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)).
% 12.65/12.60  ** KEPT (pick-wt=15): 335 [] -class_Rings_Olinordered__idom(A)| -c_Polynomial_Opos__poly(A,B)| -c_Polynomial_Opos__poly(A,C)|c_Polynomial_Opos__poly(A,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C)).
% 12.65/12.60  ** KEPT (pick-wt=17): 336 [] -class_Rings_Olinordered__idom(A)| -c_Polynomial_Opos__poly(A,B)| -c_Polynomial_Opos__poly(A,C)|c_Polynomial_Opos__poly(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)).
% 12.65/12.60  ** KEPT (pick-wt=15): 337 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B).
% 12.65/12.60  ** KEPT (pick-wt=25): 338 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 12.65/12.60  ** KEPT (pick-wt=25): 340 [copy,339,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 12.65/12.60    Following clause subsumed by 340 during input processing: 0 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 12.65/12.60  ** KEPT (pick-wt=25): 341 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),C).
% 12.65/12.60    Following clause subsumed by 340 during input processing: 0 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))).
% 12.65/12.60    Following clause subsumed by 338 during input processing: 0 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),E)).
% 12.65/12.60  ** KEPT (pick-wt=35): 342 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 12.65/12.60  ** KEPT (pick-wt=11): 343 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,C,B).
% 12.65/12.60  ** KEPT (pick-wt=17): 344 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 12.65/12.60  ** KEPT (pick-wt=17): 346 [copy,345,flip.2] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 12.65/12.60    Following clause subsumed by 346 during input processing: 0 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 12.65/12.60  ** KEPT (pick-wt=17): 347 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,D),C).
% 12.65/12.60  ** KEPT (pick-wt=23): 348 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,E))=c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 12.65/12.60  ** KEPT (pick-wt=12): 349 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 12.65/12.60  ** KEPT (pick-wt=12): 350 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 12.65/12.60  ** KEPT (pick-wt=12): 352 [copy,351,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=B|C=c_Groups_Ozero__class_Ozero(A).
% 12.65/12.60  ** KEPT (pick-wt=12): 354 [copy,353,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,B,C)=B|C!=c_Groups_Ozero__class_Ozero(A).
% 12.65/12.60  ** KEPT (pick-wt=9): 355 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 12.65/12.60  ** KEPT (pick-wt=9): 356 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 12.65/12.60  ** KEPT (pick-wt=26): 357 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 12.65/12.60  ** KEPT (pick-wt=37): 358 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B=C|D=E|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))!=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 12.65/12.60  ** KEPT (pick-wt=34): 359 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B!=C|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 12.65/12.60  ** KEPT (pick-wt=34): 360 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B!=C|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)).
% 12.65/12.60  ** KEPT (pick-wt=26): 361 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 12.65/12.60    Following clause subsumed by 361 during input processing: 0 [flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,D)),C)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)).
% 12.65/12.60    Following clause subsumed by 358 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))!=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|B=D|C=E.
% 12.65/12.61    Following clause subsumed by 359 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|B!=D.
% 12.65/12.61    Following clause subsumed by 360 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|C!=E.
% 12.65/12.61  ** KEPT (pick-wt=11): 362 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 12.65/12.61  ** KEPT (pick-wt=11): 363 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 12.65/12.61  ** KEPT (pick-wt=31): 364 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B=c_Groups_Ozero__class_Ozero(A)|C!=D|E=F|c_Groups_Oplus__class_Oplus(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E))!=c_Groups_Oplus__class_Oplus(A,D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),F)).
% 12.65/12.61  ** KEPT (pick-wt=23): 365 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=23): 366 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=27): 367 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=29): 368 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Opcompose(A,c_Polynomial_OpCons(A,B,C),D)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),D),c_Polynomial_Opcompose(A,C,D))).
% 12.65/12.61  ** KEPT (pick-wt=15): 369 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.65/12.61  ** KEPT (pick-wt=15): 370 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.65/12.61  ** KEPT (pick-wt=5): 371 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.61  ** KEPT (pick-wt=38): 372 [] -class_Rings_Ocomm__ring__1(A)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),c_Polynomial_Osynthetic__div(A,C,B)),c_Polynomial_OpCons(A,hAPP(c_Polynomial_Opoly(A,C),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))=C.
% 12.65/12.61  ** KEPT (pick-wt=9): 373 [] -class_RealVector_Oreal__normed__algebra(A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f5(B,A)).
% 12.65/12.61  ** KEPT (pick-wt=22): 374 [] -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)),$f5(C,A))).
% 12.65/12.61  ** KEPT (pick-wt=12): 376 [copy,375,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,$f6(B,A))=B.
% 12.65/12.61  ** KEPT (pick-wt=10): 377 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C).
% 12.65/12.61  ** 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,$f7(B,A))=B.
% 12.65/12.61    Following clause subsumed by 377 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).
% 12.65/12.61  ** KEPT (pick-wt=8): 380 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 12.65/12.61  ** KEPT (pick-wt=7): 381 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 12.65/12.61  ** KEPT (pick-wt=11): 382 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B.
% 12.65/12.61    Following clause subsumed by 382 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.
% 12.65/12.61    Following clause subsumed by 380 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).
% 12.65/12.61  ** KEPT (pick-wt=7): 383 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A!=B.
% 12.65/12.61  ** KEPT (pick-wt=14): 384 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=14): 385 [] 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).
% 12.65/12.61    Following clause subsumed by 380 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).
% 12.65/12.61  ** KEPT (pick-wt=11): 386 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=11): 387 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=14): 388 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=18): 389 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=18): 390 [] -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)).
% 12.65/12.61    Following clause subsumed by 382 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.65/12.61  ** KEPT (pick-wt=18): 391 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=22): 392 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=11): 393 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=11): 394 [] -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).
% 12.65/12.61    Following clause subsumed by 394 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).
% 12.65/12.61    Following clause subsumed by 393 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).
% 12.65/12.61    Following clause subsumed by 380 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).
% 12.65/12.61    Following clause subsumed by 383 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 12.65/12.61  ** KEPT (pick-wt=11): 395 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=17): 396 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=18): 397 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=14): 398 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=11): 399 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=11): 400 [] -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)).
% 12.65/12.61    Following clause subsumed by 381 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 12.65/12.61  ** KEPT (pick-wt=7): 401 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=A.
% 12.65/12.61  ** KEPT (pick-wt=4): 402 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 12.65/12.61  ** KEPT (pick-wt=14): 403 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=14): 404 [] 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).
% 12.65/12.61    Following clause subsumed by 381 during input processing: 0 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.65/12.61    Following clause subsumed by 401 during input processing: 0 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 12.65/12.61  ** KEPT (pick-wt=7): 405 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),B).
% 12.65/12.61  ** KEPT (pick-wt=7): 406 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),A).
% 12.65/12.61    Following clause subsumed by 402 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 12.65/12.61  ** KEPT (pick-wt=18): 407 [] -class_Rings_Ocomm__ring(A)|hAPP(c_Polynomial_Opoly(A,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)),C)=c_Groups_Ouminus__class_Ouminus(A,hAPP(c_Polynomial_Opoly(A,B),C)).
% 12.65/12.61  ** KEPT (pick-wt=19): 408 [] -class_Groups_Oab__group__add(A)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,B,C))=c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)).
% 12.65/12.61    Following clause subsumed by 408 during input processing: 0 [] -class_Groups_Oab__group__add(A)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,B,C))=c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),C)).
% 12.65/12.61  ** KEPT (pick-wt=9): 409 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ouminus__class_Ouminus(A,B))=B.
% 12.65/12.61  ** KEPT (pick-wt=12): 410 [] -class_Groups_Ogroup__add(A)|B!=c_Groups_Ouminus__class_Ouminus(A,C)|C=c_Groups_Ouminus__class_Ouminus(A,B).
% 12.65/12.61    Following clause subsumed by 410 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).
% 12.65/12.61  ** KEPT (pick-wt=12): 411 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=C|c_Groups_Ouminus__class_Ouminus(A,C)=B.
% 12.65/12.61    Following clause subsumed by 411 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.
% 12.65/12.61  ** KEPT (pick-wt=12): 412 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=c_Groups_Ouminus__class_Ouminus(A,C)|B=C.
% 12.65/12.61  ** KEPT (pick-wt=12): 413 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=c_Groups_Ouminus__class_Ouminus(A,C)|B!=C.
% 12.65/12.61  ** KEPT (pick-wt=11): 414 [] -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.
% 12.65/12.61  ** KEPT (pick-wt=12): 415 [] -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).
% 12.65/12.61    Following clause subsumed by 383 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 12.65/12.61  ** KEPT (pick-wt=9): 416 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 12.65/12.61  ** KEPT (pick-wt=12): 417 [] -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.
% 12.65/12.61  ** KEPT (pick-wt=12): 418 [] -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.
% 12.65/12.61  ** KEPT (pick-wt=11): 420 [copy,419,flip.2] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 12.65/12.61  ** KEPT (pick-wt=11): 422 [copy,421,flip.2] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 12.65/12.61  ** KEPT (pick-wt=12): 423 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=12): 424 [] -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).
% 12.65/12.61    Following clause subsumed by 420 during input processing: 0 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 12.65/12.61    Following clause subsumed by 422 during input processing: 0 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 12.65/12.61  ** KEPT (pick-wt=14): 425 [] -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)).
% 12.65/12.61    Following clause subsumed by 425 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)).
% 12.65/12.61  ** KEPT (pick-wt=14): 426 [] -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).
% 12.65/12.61    Following clause subsumed by 426 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).
% 12.65/12.61  ** KEPT (pick-wt=14): 427 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=14): 428 [] -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).
% 12.65/12.61    Following clause subsumed by 428 during input processing: 0 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=14): 429 [] -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)).
% 12.65/12.61    Following clause subsumed by 429 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)).
% 12.65/12.61  ** KEPT (pick-wt=14): 430 [] -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).
% 12.65/12.61    Following clause subsumed by 430 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).
% 12.65/12.61  ** KEPT (pick-wt=14): 431 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=14): 432 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=19): 433 [] -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)).
% 12.65/12.61    Following clause subsumed by 433 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)).
% 12.65/12.61  ** KEPT (pick-wt=19): 434 [] -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)).
% 12.65/12.61    Following clause subsumed by 434 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)).
% 12.65/12.61  ** KEPT (pick-wt=23): 435 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=18): 436 [] -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.
% 12.65/12.61  ** KEPT (pick-wt=20): 437 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=19): 438 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=19): 439 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=19): 441 [copy,440,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)).
% 12.65/12.61  ** KEPT (pick-wt=19): 443 [copy,442,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)).
% 12.65/12.61  ** KEPT (pick-wt=13): 444 [] -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.
% 12.65/12.61  ** KEPT (pick-wt=13): 445 [] -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.
% 12.65/12.61  ** KEPT (pick-wt=17): 446 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=17): 447 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=11): 448 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=11): 449 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=12): 450 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=18): 452 [copy,451,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).
% 12.65/12.61  ** KEPT (pick-wt=15): 453 [] -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.
% 12.65/12.61  ** KEPT (pick-wt=14): 454 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=14): 455 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=13): 456 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=13): 457 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=14): 458 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=14): 459 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=13): 460 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=13): 461 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=14): 462 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=14): 463 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=13): 464 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=13): 465 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=14): 466 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=14): 467 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=13): 468 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=13): 469 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=11): 470 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=14): 471 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=14): 472 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=11): 473 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=11): 474 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=14): 475 [] -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.
% 12.65/12.61  ** KEPT (pick-wt=14): 476 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=14): 477 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=21): 478 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=15): 479 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=17): 480 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=15): 482 [copy,481,flip.2] -class_Rings_Ocomm__ring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A))),B)=c_Groups_Ouminus__class_Ouminus(A,B).
% 12.65/12.61  ** KEPT (pick-wt=10): 483 [] -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)).
% 12.65/12.61    Following clause subsumed by 137 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).
% 12.65/12.61  ** KEPT (pick-wt=14): 484 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=18): 485 [] -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).
% 12.65/12.61    Following clause subsumed by 485 during input processing: 0 [] -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).
% 12.65/12.61    Following clause subsumed by 484 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).
% 12.65/12.61  ** KEPT (pick-wt=12): 486 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=14): 487 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=18): 488 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=12): 489 [] 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.
% 12.65/12.61  ** KEPT (pick-wt=12): 490 [] 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.
% 12.65/12.61  ** KEPT (pick-wt=12): 491 [] 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).
% 12.65/12.61  ** KEPT (pick-wt=12): 492 [] 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).
% 12.65/12.61  ** KEPT (pick-wt=12): 493 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=10): 494 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=16): 495 [] 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).
% 12.65/12.61  ** KEPT (pick-wt=16): 496 [] -class_Rings_Olinordered__idom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Opos__poly(A,B)|c_Polynomial_Opos__poly(A,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),B)).
% 12.65/12.61  ** KEPT (pick-wt=12): 497 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Opcompose(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 12.65/12.61  ** KEPT (pick-wt=11): 498 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=14): 500 [copy,499,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).
% 12.65/12.61  ** KEPT (pick-wt=14): 502 [copy,501,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).
% 12.65/12.61  ** KEPT (pick-wt=12): 503 [] -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.
% 12.65/12.61  ** KEPT (pick-wt=14): 505 [copy,504,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).
% 12.65/12.61  ** KEPT (pick-wt=20): 506 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,c_Polynomial_Opcompose(A,B,C)),D)=hAPP(c_Polynomial_Opoly(A,B),hAPP(c_Polynomial_Opoly(A,C),D)).
% 12.65/12.61  ** KEPT (pick-wt=14): 507 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=14): 508 [] 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).
% 12.65/12.61  ** KEPT (pick-wt=14): 509 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=14): 510 [] 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)).
% 12.65/12.61  ** KEPT (pick-wt=14): 511 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=14): 512 [] 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).
% 12.65/12.61  ** KEPT (pick-wt=14): 513 [] -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)).
% 12.65/12.61  ** KEPT (pick-wt=14): 514 [] 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)).
% 12.65/12.61  ** KEPT (pick-wt=12): 516 [copy,515,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).
% 12.65/12.61    Following clause subsumed by 516 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).
% 12.65/12.61    Following clause subsumed by 371 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.61    Following clause subsumed by 401 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).
% 12.65/12.61    Following clause subsumed by 371 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.65/12.61  ** KEPT (pick-wt=9): 517 [] -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).
% 12.65/12.61    Following clause subsumed by 383 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).
% 12.65/12.61  ** KEPT (pick-wt=8): 518 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.61  ** KEPT (pick-wt=15): 519 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=15): 520 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=20): 521 [] 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).
% 12.65/12.61  ** KEPT (pick-wt=17): 522 [] 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).
% 12.65/12.61  ** KEPT (pick-wt=13): 523 [] 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).
% 12.65/12.61  ** KEPT (pick-wt=13): 524 [] 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).
% 12.65/12.61  ** KEPT (pick-wt=19): 525 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=18): 526 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=23): 527 [] 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).
% 12.65/12.61  ** KEPT (pick-wt=19): 528 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=18): 529 [] -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).
% 12.65/12.61  ** KEPT (pick-wt=23): 530 [] 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).
% 12.65/12.61  ** KEPT (pick-wt=23): 531 [] -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).
% 12.65/12.61    Following clause subsumed by 390 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).
% 12.65/12.61  ** KEPT (pick-wt=23): 532 [] -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).
% 12.65/12.61    Following clause subsumed by 389 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).
% 12.65/12.61  ** KEPT (pick-wt=20): 533 [] 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).
% 12.65/12.61  ** KEPT (pick-wt=16): 534 [] 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.
% 12.65/12.61  ** KEPT (pick-wt=17): 535 [] 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).
% 12.65/12.61  ** KEPT (pick-wt=20): 536 [] 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).
% 12.65/12.61  ** KEPT (pick-wt=16): 537 [] 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.
% 12.65/12.61  ** KEPT (pick-wt=17): 538 [] 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).
% 12.65/12.61    Following clause subsumed by 530 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)).
% 12.65/12.61    Following clause subsumed by 527 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)).
% 12.65/12.61  ** KEPT (pick-wt=18): 539 [] -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).
% 12.65/12.61    Following clause subsumed by 400 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).
% 12.65/12.61    Following clause subsumed by 399 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).
% 12.65/12.61  ** KEPT (pick-wt=11): 540 [] 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).
% 12.65/12.61  ** KEPT (pick-wt=11): 541 [] 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).
% 12.65/12.61  ** KEPT (pick-wt=15): 542 [] 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).
% 12.65/12.61  ** KEPT (pick-wt=10): 543 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=A|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.65/12.61  ** KEPT (pick-wt=16): 545 [copy,544,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).
% 12.65/12.61  ** KEPT (pick-wt=13): 546 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Oplus__class_Oplus(A,B,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 12.65/12.61  ** KEPT (pick-wt=13): 547 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Oplus__class_Oplus(A,B,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 12.65/12.61    Following clause subsumed by 531 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).
% 12.65/12.61    Following clause subsumed by 390 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).
% 12.65/12.61  ** KEPT (pick-wt=12): 548 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f9(B,A)).
% 12.65/12.61  ** KEPT (pick-wt=22): 549 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Oplus__class_Oplus(A,hAPP(B,C),c_Groups_Ouminus__class_Ouminus(A,$f8(B,A)))),$f9(B,A)).
% 12.65/12.61  ** KEPT (pick-wt=27): 550 [] -class_RealVector_Oreal__normed__vector(A)|c_SEQ_OBse_q(A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Oplus__class_Oplus(A,hAPP(B,$f10(B,A,C,D)),c_Groups_Ouminus__class_Ouminus(A,D))),C).
% 12.65/12.61  ** KEPT (pick-wt=12): 551 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f12(B,A)).
% 12.65/12.61  ** KEPT (pick-wt=24): 552 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Oplus__class_Oplus(A,hAPP(B,C),c_Groups_Ouminus__class_Ouminus(A,hAPP(B,$f11(B,A))))),$f12(B,A)).
% 12.65/12.61  ** KEPT (pick-wt=29): 553 [] -class_RealVector_Oreal__normed__vector(A)|c_SEQ_OBse_q(A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,c_Groups_Oplus__class_Oplus(A,hAPP(B,$f13(B,A,C,D)),c_Groups_Ouminus__class_Ouminus(A,hAPP(B,D)))),C).
% 12.65/12.61  ** KEPT (pick-wt=8): 554 [] -class_RealVector_Oreal__normed__algebra(A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f14(A)).
% 12.65/12.61  ** KEPT (pick-wt=28): 555 [] -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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))),$f14(A))).
% 12.72/12.61  ** KEPT (pick-wt=9): 556 [] -class_RealVector_Oreal__normed__algebra(A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f15(B,A)).
% 12.72/12.61  ** KEPT (pick-wt=22): 557 [] -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,C)),$f15(B,A))).
% 12.72/12.61  ** KEPT (pick-wt=12): 558 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)|A=C.
% 12.72/12.61  ** KEPT (pick-wt=12): 559 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)|A!=C.
% 12.72/12.61  ** KEPT (pick-wt=12): 560 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)|B=C.
% 12.72/12.61  ** KEPT (pick-wt=12): 561 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)|B!=C.
% 12.72/12.61  ** KEPT (pick-wt=13): 562 [] 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).
% 12.72/12.61  ** KEPT (pick-wt=13): 563 [] 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).
% 12.72/12.61  ** KEPT (pick-wt=17): 564 [] 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).
% 12.72/12.61    Following clause subsumed by 562 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).
% 12.72/12.61    Following clause subsumed by 563 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).
% 12.72/12.61    Following clause subsumed by 564 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).
% 12.72/12.61    Following clause subsumed by 533 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.
% 12.72/12.61    Following clause subsumed by 535 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).
% 12.72/12.61    Following clause subsumed by 534 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.
% 12.72/12.61    Following clause subsumed by 526 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).
% 12.72/12.61    Following clause subsumed by 527 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).
% 12.72/12.61  ** KEPT (pick-wt=21): 565 [] -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.
% 12.72/12.61    Following clause subsumed by 534 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.
% 12.72/12.61    Following clause subsumed by 387 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 12.72/12.61    Following clause subsumed by 386 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 12.72/12.61    Following clause subsumed by 380 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).
% 12.72/12.61    Following clause subsumed by 400 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 12.72/12.61    Following clause subsumed by 399 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 12.72/12.61  ** KEPT (pick-wt=17): 566 [] -class_Orderings_Oorder(A)| -c_SEQ_Odecse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,D),hAPP(B,C)).
% 12.72/12.61  ** KEPT (pick-wt=13): 567 [] -class_Orderings_Oorder(A)|c_SEQ_Odecse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f17(B,A),$f16(B,A)).
% 12.72/12.61  ** KEPT (pick-wt=17): 568 [] -class_Orderings_Oorder(A)|c_SEQ_Odecse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f16(B,A)),hAPP(B,$f17(B,A))).
% 12.72/12.61  ** KEPT (pick-wt=14): 569 [] -class_Lattices_Oboolean__algebra(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)).
% 12.72/12.61  ** KEPT (pick-wt=14): 570 [] -class_Lattices_Oboolean__algebra(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).
% 12.72/12.61    Following clause subsumed by 569 during input processing: 0 [] -class_Lattices_Oboolean__algebra(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).
% 12.72/12.61  ** KEPT (pick-wt=15): 571 [] -class_Rings_Olinordered__idom(A)|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(A),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 12.72/12.61  ** KEPT (pick-wt=22): 572 [] -class_Rings_Olinordered__idom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))| -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B)|c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(A),B)=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)).
% 12.72/12.61  ** KEPT (pick-wt=25): 573 [] -class_Rings_Olinordered__idom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B)|c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(A),B)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))).
% 12.72/12.61  ** KEPT (pick-wt=11): 574 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,c_Groups_Osgn__class_Osgn(A,B))=c_Groups_Osgn__class_Osgn(A,B).
% 12.72/12.61  ** KEPT (pick-wt=13): 576 [copy,575,flip.2] -class_RealVector_Oreal__normed__vector(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Osgn__class_Osgn(A,B))=c_Groups_Osgn__class_Osgn(A,c_Groups_Ouminus__class_Ouminus(A,B)).
% 12.72/12.61  ** KEPT (pick-wt=9): 577 [] -class_RealVector_Oreal__normed__algebra__1(A)|c_Groups_Osgn__class_Osgn(A,c_Groups_Oone__class_Oone(A))=c_Groups_Oone__class_Oone(A).
% 12.72/12.61  ** KEPT (pick-wt=21): 579 [copy,578,flip.2] -class_RealVector_Oreal__normed__div__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Osgn__class_Osgn(A,B)),c_Groups_Osgn__class_Osgn(A,C))=c_Groups_Osgn__class_Osgn(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 12.72/12.61  ** KEPT (pick-wt=21): 581 [copy,580,flip.2] -class_Rings_Olinordered__idom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Osgn__class_Osgn(A,B)),c_Groups_Osgn__class_Osgn(A,C))=c_Groups_Osgn__class_Osgn(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 12.72/12.62  ** KEPT (pick-wt=9): 582 [] -class_Groups_Osgn__if(A)|c_Groups_Osgn__class_Osgn(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 12.72/12.62  ** KEPT (pick-wt=12): 583 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 12.72/12.62  ** KEPT (pick-wt=12): 584 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 12.72/12.62  ** KEPT (pick-wt=9): 585 [] -class_RealVector_Oreal__normed__vector(A)|c_Groups_Osgn__class_Osgn(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 12.72/12.62  ** KEPT (pick-wt=12): 586 [] -class_RealVector_Oreal__normed__vector(A)|c_Groups_Osgn__class_Osgn(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 12.72/12.62  ** KEPT (pick-wt=12): 587 [] -class_RealVector_Oreal__normed__vector(A)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 12.72/12.62  ** KEPT (pick-wt=14): 588 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Osgn__class_Osgn(A,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.72/12.62  ** KEPT (pick-wt=14): 589 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Osgn__class_Osgn(A,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.72/12.62  ** KEPT (pick-wt=14): 590 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Osgn__class_Osgn(A,B))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.72/12.62  ** KEPT (pick-wt=14): 591 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Osgn__class_Osgn(A,B))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.72/12.62  ** KEPT (pick-wt=14): 593 [copy,592,flip.2] -class_Rings_Olinordered__idom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Osgn__class_Osgn(A,B))=c_Groups_Oabs__class_Oabs(A,B).
% 12.72/12.62  ** KEPT (pick-wt=14): 594 [] -class_Rings_Olinordered__idom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Osgn__class_Osgn(A,B)),c_Groups_Oabs__class_Oabs(A,B))=B.
% 12.72/12.62  ** KEPT (pick-wt=10): 595 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=B.
% 12.72/12.62    Following clause subsumed by 595 during input processing: 0 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=B.
% 12.72/12.62  ** KEPT (pick-wt=20): 596 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C).
% 12.72/12.62  ** KEPT (pick-wt=9): 597 [] -class_Lattices_Oboolean__algebra(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ouminus__class_Ouminus(A,B))=B.
% 12.72/12.62  ** KEPT (pick-wt=15): 598 [] -class_Groups_Ouminus(A)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(B,A),C),D)=c_Groups_Ouminus__class_Ouminus(A,hAPP(C,D)).
% 12.72/12.62  ** KEPT (pick-wt=12): 599 [] -class_Lattices_Oboolean__algebra(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=c_Groups_Ouminus__class_Ouminus(A,C)|B=C.
% 12.72/12.62  ** KEPT (pick-wt=12): 600 [] -class_Lattices_Oboolean__algebra(A)|c_Groups_Ouminus__class_Ouminus(A,B)=c_Groups_Ouminus__class_Ouminus(A,C)|B!=C.
% 12.72/12.62  ** KEPT (pick-wt=13): 601 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Oone__class_Oone(A).
% 12.72/12.62  ** KEPT (pick-wt=13): 602 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)!=c_Groups_Oone__class_Oone(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.72/12.62    Following clause subsumed by 601 during input processing: 0 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Oone__class_Oone(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 12.72/12.62  ** KEPT (pick-wt=15): 603 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)).
% 12.72/12.62  ** KEPT (pick-wt=15): 604 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)!=c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.72/12.62    Following clause subsumed by 603 during input processing: 0 [] -class_Rings_Olinordered__idom(A)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.72/12.62  ** KEPT (pick-wt=12): 605 [] -class_Groups_Osgn__if(A)|B!=c_Groups_Ozero__class_Ozero(A)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Ozero__class_Ozero(A).
% 12.72/12.62  ** KEPT (pick-wt=17): 606 [] -class_Groups_Osgn__if(A)|B=c_Groups_Ozero__class_Ozero(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Oone__class_Oone(A).
% 12.72/12.62  ** KEPT (pick-wt=19): 607 [] -class_Groups_Osgn__if(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Groups_Osgn__class_Osgn(A,B)=c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)).
% 12.72/12.62  ** KEPT (pick-wt=14): 608 [] -class_RealVector_Oreal__normed__vector(A)|B!=c_Groups_Ozero__class_Ozero(A)|c_RealVector_Onorm__class_Onorm(A,c_Groups_Osgn__class_Osgn(A,B))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.72/12.62  ** KEPT (pick-wt=14): 609 [] -class_RealVector_Oreal__normed__vector(A)|B=c_Groups_Ozero__class_Ozero(A)|c_RealVector_Onorm__class_Onorm(A,c_Groups_Osgn__class_Osgn(A,B))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.72/12.62  ** KEPT (pick-wt=21): 610 [] -class_RealVector_Oreal__normed__vector(A)| -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,hAPP(C,$f18(C,B,A))),B)|c_SEQ_OBse_q(A,C).
% 12.72/12.62  ** KEPT (pick-wt=12): 611 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f19(B,A)).
% 12.72/12.62  ** KEPT (pick-wt=15): 612 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C)),$f19(B,A)).
% 12.72/12.62  ** KEPT (pick-wt=15): 613 [] hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f20(B,A),B).
% 12.72/12.62  ** KEPT (pick-wt=19): 614 [] hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,$f20(B,A))| -hBOOL(hAPP(A,C)).
% 12.72/12.62  ** KEPT (pick-wt=19): 615 [] hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,$f20(B,A),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 12.72/12.62  ** KEPT (pick-wt=9): 616 [] -class_RealVector_Oreal__normed__algebra(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f21(B,A)).
% 12.72/12.62  ** KEPT (pick-wt=22): 617 [] -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)),$f21(C,A))).
% 12.72/12.62  ** KEPT (pick-wt=11): 618 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.72/12.62  ** KEPT (pick-wt=10): 619 [] A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.72/12.62    Following clause subsumed by 618 during input processing: 0 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.72/12.62    Following clause subsumed by 619 during input processing: 0 [] A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.72/12.62    Following clause subsumed by 618 during input processing: 0 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,A)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.72/12.62  ** KEPT (pick-wt=8): 620 [] -class_RealVector_Oreal__normed__algebra(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f22(A)).
% 12.72/12.62  ** KEPT (pick-wt=28): 621 [] -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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))),$f22(A))).
% 12.72/12.62  ** KEPT (pick-wt=9): 622 [] -class_RealVector_Oreal__normed__algebra(A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f23(B,A)).
% 12.72/12.62  ** KEPT (pick-wt=22): 623 [] -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,C)),$f23(B,A))).
% 12.72/12.62  ** KEPT (pick-wt=26): 624 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Opoly(A,B),C)!=c_Groups_Ozero__class_Ozero(A)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))),B).
% 12.72/12.62  ** KEPT (pick-wt=26): 625 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Opoly(A,B),C)=c_Groups_Ozero__class_Ozero(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))),B).
% 12.72/12.62  ** KEPT (pick-wt=26): 626 [] -class_Rings_Oidom(A)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,B,c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))),C)|hAPP(c_Polynomial_Opoly(A,C),c_Groups_Ouminus__class_Ouminus(A,B))=c_Groups_Ozero__class_Ozero(A).
% 12.72/12.62  ** KEPT (pick-wt=26): 627 [] -class_Rings_Oidom(A)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,B,c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))),C)|hAPP(c_Polynomial_Opoly(A,C),c_Groups_Ouminus__class_Ouminus(A,B))!=c_Groups_Ozero__class_Ozero(A).
% 12.72/12.62  ** KEPT (pick-wt=7): 628 [] -class_Rings_Ocomm__semiring__1(A)|c_Rings_Odvd__class_Odvd(A,B,c_Groups_Ozero__class_Ozero(A)).
% 12.72/12.62  ** KEPT (pick-wt=12): 629 [] -class_Rings_Ocomm__ring__1(A)| -c_Rings_Odvd__class_Odvd(A,c_Groups_Ouminus__class_Ouminus(A,B),C)|c_Rings_Odvd__class_Odvd(A,B,C).
% 12.72/12.62  ** KEPT (pick-wt=12): 630 [] -class_Rings_Ocomm__ring__1(A)|c_Rings_Odvd__class_Odvd(A,c_Groups_Ouminus__class_Ouminus(A,B),C)| -c_Rings_Odvd__class_Odvd(A,B,C).
% 12.72/12.62  ** KEPT (pick-wt=12): 631 [] -class_Rings_Ocomm__ring__1(A)| -c_Rings_Odvd__class_Odvd(A,B,c_Groups_Ouminus__class_Ouminus(A,C))|c_Rings_Odvd__class_Odvd(A,B,C).
% 12.72/12.62  ** KEPT (pick-wt=12): 632 [] -class_Rings_Ocomm__ring__1(A)|c_Rings_Odvd__class_Odvd(A,B,c_Groups_Ouminus__class_Ouminus(A,C))| -c_Rings_Odvd__class_Odvd(A,B,C).
% 12.72/12.62  ** KEPT (pick-wt=11): 633 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,c_Groups_Ozero__class_Ozero(A),B)|B=c_Groups_Ozero__class_Ozero(A).
% 12.72/12.62  ** KEPT (pick-wt=14): 634 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,B,C)| -c_Rings_Odvd__class_Odvd(A,C,D)|c_Rings_Odvd__class_Odvd(A,B,D).
% 12.72/12.62  ** KEPT (pick-wt=6): 635 [] -class_Rings_Ocomm__semiring__1(A)|c_Rings_Odvd__class_Odvd(A,B,B).
% 12.72/12.62  ** KEPT (pick-wt=13): 636 [] -class_Rings_Olinordered__idom(A)|c_Groups_Oabs__class_Oabs(A,B)!=c_Groups_Oabs__class_Oabs(A,C)|c_Rings_Odvd__class_Odvd(A,B,C).
% 12.72/12.62  ** KEPT (pick-wt=12): 637 [] -class_Rings_Olinordered__idom(A)| -c_Rings_Odvd__class_Odvd(A,c_Groups_Oabs__class_Oabs(A,B),C)|c_Rings_Odvd__class_Odvd(A,B,C).
% 12.72/12.62  ** KEPT (pick-wt=12): 638 [] -class_Rings_Olinordered__idom(A)|c_Rings_Odvd__class_Odvd(A,c_Groups_Oabs__class_Oabs(A,B),C)| -c_Rings_Odvd__class_Odvd(A,B,C).
% 12.72/12.62  ** KEPT (pick-wt=12): 639 [] -class_Rings_Olinordered__idom(A)| -c_Rings_Odvd__class_Odvd(A,B,c_Groups_Oabs__class_Oabs(A,C))|c_Rings_Odvd__class_Odvd(A,B,C).
% 12.72/12.62  ** KEPT (pick-wt=12): 640 [] -class_Rings_Olinordered__idom(A)|c_Rings_Odvd__class_Odvd(A,B,c_Groups_Oabs__class_Oabs(A,C))| -c_Rings_Odvd__class_Odvd(A,B,C).
% 12.72/12.62  ** KEPT (pick-wt=7): 641 [] -class_Rings_Ocomm__semiring__1(A)|c_Rings_Odvd__class_Odvd(A,c_Groups_Oone__class_Oone(A),B).
% 12.72/12.62  ** KEPT (pick-wt=17): 642 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,B,C)| -c_Rings_Odvd__class_Odvd(A,B,D)|c_Rings_Odvd__class_Odvd(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 12.72/12.62  ** KEPT (pick-wt=15): 643 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D)|c_Rings_Odvd__class_Odvd(A,C,D).
% 12.72/12.62  ** KEPT (pick-wt=15): 644 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D)|c_Rings_Odvd__class_Odvd(A,B,D).
% 12.72/12.62  ** KEPT (pick-wt=14): 645 [] -class_Rings_Odvd(A)|B!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)|c_Rings_Odvd__class_Odvd(A,C,B).
% 12.72/12.62  ** KEPT (pick-wt=24): 646 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,B,C)| -c_Rings_Odvd__class_Odvd(A,D,E)|c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 12.72/12.62  ** KEPT (pick-wt=15): 647 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,B,C)|c_Rings_Odvd__class_Odvd(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)).
% 12.72/12.62  ** KEPT (pick-wt=15): 648 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,B,C)|c_Rings_Odvd__class_Odvd(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 12.72/12.62  ** KEPT (pick-wt=11): 649 [] -class_Rings_Ocomm__semiring__1(A)|c_Rings_Odvd__class_Odvd(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)).
% 12.72/12.62  ** KEPT (pick-wt=11): 650 [] -class_Rings_Ocomm__semiring__1(A)|c_Rings_Odvd__class_Odvd(A,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 12.72/12.62  ** KEPT (pick-wt=24): 651 [] -class_Rings_Oidom(A)| -c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|B=c_Groups_Ozero__class_Ozero(A)|c_Rings_Odvd__class_Odvd(A,C,D).
% 12.72/12.62  ** KEPT (pick-wt=20): 652 [] -class_Rings_Oidom(A)|c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|B!=c_Groups_Ozero__class_Ozero(A).
% 12.72/12.62  ** KEPT (pick-wt=20): 653 [] -class_Rings_Oidom(A)|c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -c_Rings_Odvd__class_Odvd(A,C,D).
% 12.72/12.62  ** KEPT (pick-wt=24): 654 [] -class_Rings_Oidom(A)| -c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|C=c_Groups_Ozero__class_Ozero(A)|c_Rings_Odvd__class_Odvd(A,B,D).
% 12.72/12.62  ** KEPT (pick-wt=20): 655 [] -class_Rings_Oidom(A)|c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|C!=c_Groups_Ozero__class_Ozero(A).
% 12.72/12.62  ** KEPT (pick-wt=20): 656 [] -class_Rings_Oidom(A)|c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))| -c_Rings_Odvd__class_Odvd(A,B,D).
% 12.72/12.62  ** KEPT (pick-wt=24): 657 [] -class_Rings_Odvd(A)| -class_Rings_Osemiring__0(A)| -hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)))|c_Rings_Odvd__class_Odvd(A,C,c_Groups_Oplus__class_Oplus(A,$f24(C,B,A),c_Groups_Ozero__class_Ozero(A))).
% 12.72/12.62  ** KEPT (pick-wt=20): 658 [] -class_Rings_Odvd(A)| -class_Rings_Osemiring__0(A)| -hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)))|hBOOL(hAPP(B,$f24(C,B,A))).
% 12.72/12.62  ** KEPT (pick-wt=28): 659 [] -class_Rings_Odvd(A)| -class_Rings_Osemiring__0(A)|hBOOL(hAPP(B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),$f25(C,B,A))))| -c_Rings_Odvd__class_Odvd(A,C,c_Groups_Oplus__class_Oplus(A,D,c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(B,D)).
% 12.72/12.62  ** KEPT (pick-wt=27): 660 [] -class_Rings_Oidom(A)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),c_Polynomial_Oorder(A,B,C)),C).
% 12.72/12.62  ** KEPT (pick-wt=17): 661 [] -class_Orderings_Oorder(A)| -c_SEQ_Oincse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,C),hAPP(B,D)).
% 12.72/12.62  ** KEPT (pick-wt=13): 662 [] -class_Orderings_Oorder(A)|c_SEQ_Oincse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f27(B,A),$f26(B,A)).
% 12.72/12.62  ** KEPT (pick-wt=17): 663 [] -class_Orderings_Oorder(A)|c_SEQ_Oincse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f27(B,A)),hAPP(B,$f26(B,A))).
% 12.72/12.62  ** KEPT (pick-wt=18): 664 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(A),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 12.72/12.62  ** KEPT (pick-wt=9): 665 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat))|A=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.72/12.62  ** KEPT (pick-wt=9): 666 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat))|A!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.72/12.62  ** KEPT (pick-wt=11): 667 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,A))|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B).
% 12.72/12.62  ** KEPT (pick-wt=11): 668 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,A))| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B).
% 12.72/12.62  ** KEPT (pick-wt=11): 669 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat))=B.
% 12.72/12.62  ** KEPT (pick-wt=25): 670 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)).
% 12.72/12.62  ** KEPT (pick-wt=30): 671 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)).
% 12.72/12.62  ** KEPT (pick-wt=19): 672 [] -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).
% 12.72/12.62  ** KEPT (pick-wt=24): 673 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Polynomial_Opoly(A,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),D)=hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Polynomial_Opoly(A,B),D)),C).
% 12.72/12.62  ** KEPT (pick-wt=20): 674 [] -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)).
% 12.72/12.62  ** KEPT (pick-wt=10): 675 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),c_RComplete_Onatceiling(B)).
% 12.72/12.62  ** KEPT (pick-wt=12): 676 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(A).
% 12.72/12.62  ** KEPT (pick-wt=28): 677 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)).
% 12.72/12.62  ** KEPT (pick-wt=13): 678 [] -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,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A).
% 12.72/12.62  ** KEPT (pick-wt=22): 679 [] -c_Rings_Odvd__class_Odvd(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))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C).
% 12.72/12.62  ** KEPT (pick-wt=18): 680 [] c_Rings_Odvd__class_Odvd(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))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.72/12.62  ** KEPT (pick-wt=18): 681 [] c_Rings_Odvd__class_Odvd(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_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C).
% 12.72/12.62  ** KEPT (pick-wt=10): 682 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatceiling(A)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.72/12.62  ** KEPT (pick-wt=13): 683 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,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,B).
% 12.72/12.62  ** KEPT (pick-wt=23): 684 [] -c_Rings_Odvd__class_Odvd(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_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C).
% 12.72/12.62    Following clause subsumed by 684 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Rings_Odvd__class_Odvd(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_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C).
% 12.72/12.62    Following clause subsumed by 681 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Rings_Odvd__class_Odvd(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_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C).
% 12.72/12.62  ** KEPT (pick-wt=11): 685 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.72/12.62  ** KEPT (pick-wt=11): 686 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),c_Groups_Oone__class_Oone(tc_Nat_Onat))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.72/12.62  ** KEPT (pick-wt=18): 687 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),A)|B=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.72/12.62  ** KEPT (pick-wt=18): 688 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),A)|B!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.72/12.62  ** KEPT (pick-wt=18): 689 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A),A)|B=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.72/12.62  ** KEPT (pick-wt=18): 690 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A),A)|B!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.72/12.62  ** KEPT (pick-wt=30): 691 [] -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)).
% 12.72/12.62  ** KEPT (pick-wt=16): 692 [] -class_Rings_Ocomm__semiring__1(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)|c_Rings_Odvd__class_Odvd(A,C,hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B)).
% 12.72/12.62  ** KEPT (pick-wt=15): 693 [] -class_Rings_Ocomm__semiring__1(A)|B!=c_Groups_Oone__class_Oone(A)|c_Rings_Odvd__class_Odvd(A,B,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 12.72/12.62  ** KEPT (pick-wt=22): 694 [] -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)).
% 12.72/12.62  ** KEPT (pick-wt=20): 695 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C).
% 12.72/12.62  ** KEPT (pick-wt=20): 696 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,A).
% 12.72/12.62  ** KEPT (pick-wt=16): 697 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C).
% 12.72/12.62  ** KEPT (pick-wt=16): 698 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,A).
% 12.72/12.62  ** KEPT (pick-wt=15): 699 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|B!=C|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C).
% 12.72/12.62  ** KEPT (pick-wt=15): 700 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|B!=C| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,A).
% 12.72/12.62  ** KEPT (pick-wt=11): 701 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|B!=A.
% 12.72/12.62  ** KEPT (pick-wt=11): 702 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|A!=B.
% 12.72/12.62    Following clause subsumed by 702 during input processing: 0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|A!=B.
% 12.72/12.62  ** KEPT (pick-wt=16): 703 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C).
% 12.72/12.62    Following clause subsumed by 698 during input processing: 0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,A).
% 12.72/12.62  ** KEPT (pick-wt=15): 704 [] A!=B| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C).
% 12.72/12.62  ** KEPT (pick-wt=15): 705 [] A!=B| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,A).
% 12.72/12.62  ** KEPT (pick-wt=12): 706 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C).
% 12.72/12.62  ** KEPT (pick-wt=11): 707 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|A=B.
% 12.72/12.62    Following clause subsumed by 707 during input processing: 0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|A=B.
% 12.72/12.62  ** KEPT (pick-wt=11): 708 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|B!=C|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C).
% 12.72/12.62  ** KEPT (pick-wt=11): 709 [] A!=B| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C).
% 12.72/12.62    Following clause subsumed by 707 during input processing: 0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|A=B| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A).
% 12.72/12.62    Following clause subsumed by 707 during input processing: 0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|A=B.
% 12.72/12.62    Following clause subsumed by 707 during input processing: 0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|B=A.
% 12.72/12.62    Following clause subsumed by 701 during input processing: 0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|B!=A.
% 12.72/12.62  ** KEPT (pick-wt=7): 710 [] A!=B|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B).
% 12.72/12.62    Following clause subsumed by 707 during input processing: 0 [] A=B| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A).
% 12.72/12.62    Following clause subsumed by 702 during input processing: 0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|A!=B.
% 12.72/12.62    Following clause subsumed by 707 during input processing: 0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|B=A.
% 12.72/12.62    Following clause subsumed by 707 during input processing: 0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|A=B.
% 12.72/12.62    Following clause subsumed by 710 during input processing: 0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|A!=B.
% 12.72/12.62    Following clause subsumed by 710 during input processing: 0 [] A!=B|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B).
% 12.72/12.62  ** KEPT (pick-wt=7): 711 [] A!=B|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A).
% 12.72/12.62    Following clause subsumed by 707 during input processing: 0 [] A=B| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A).
% 12.72/12.62  ** KEPT (pick-wt=20): 712 [] -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,A)),B))|A!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.72/12.62  ** KEPT (pick-wt=16): 713 [] 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,A)),B))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.72/12.62  ** KEPT (pick-wt=19): 714 [] -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).
% 12.72/12.62  ** KEPT (pick-wt=15): 715 [] 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).
% 12.72/12.62  ** KEPT (pick-wt=14): 716 [] 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).
% 12.72/12.62  ** KEPT (pick-wt=23): 717 [] -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).
% 12.72/12.62  ** KEPT (pick-wt=23): 718 [] -c_Rings_Odvd__class_Odvd(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,c_Groups_Oone__class_Oone(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 12.72/12.62  ** KEPT (pick-wt=15): 719 [] -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).
% 12.72/12.62  ** KEPT (pick-wt=25): 720 [] -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)).
% 12.72/12.62  ** KEPT (pick-wt=30): 721 [] -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)).
% 12.72/12.62  ** KEPT (pick-wt=12): 722 [] -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).
% 12.72/12.62  ** KEPT (pick-wt=20): 723 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,B,C)|c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)).
% 12.72/12.62  ** KEPT (pick-wt=25): 725 [copy,724,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)).
% 12.72/12.62  ** KEPT (pick-wt=19): 727 [copy,726,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)).
% 12.72/12.62  ** KEPT (pick-wt=11): 728 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat))=B.
% 12.72/12.62  ** KEPT (pick-wt=17): 729 [] -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)).
% 12.72/12.62  ** KEPT (pick-wt=25): 730 [] -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)).
% 12.72/12.62  ** KEPT (pick-wt=17): 731 [] -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)).
% 12.72/12.62  ** KEPT (pick-wt=17): 732 [] -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)).
% 12.72/12.62  ** KEPT (pick-wt=21): 733 [] -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).
% 12.72/12.62  ** KEPT (pick-wt=21): 734 [] -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).
% 12.72/12.62  ** KEPT (pick-wt=25): 735 [] -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).
% 12.72/12.62  ** KEPT (pick-wt=23): 736 [] -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.
% 12.72/12.62  ** KEPT (pick-wt=23): 737 [] -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.
% 12.72/12.62  ** KEPT (pick-wt=12): 738 [] -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).
% 12.72/12.62  ** KEPT (pick-wt=28): 740 [copy,739,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)).
% 12.72/12.62  ** KEPT (pick-wt=20): 741 [] -class_Rings_Ocomm__semiring__1(A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C)|c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)).
% 12.72/12.62  ** KEPT (pick-wt=24): 742 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,D,E)|c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),E)).
% 12.72/12.62  ** KEPT (pick-wt=24): 743 [] -class_Rings_Ocomm__semiring__1(A)| -c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),D)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,E,C)|c_Rings_Odvd__class_Odvd(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),E),D).
% 12.72/12.62  ** KEPT (pick-wt=21): 744 [] -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)).
% 12.72/12.62  ** KEPT (pick-wt=25): 745 [] -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).
% 12.72/12.62  ** KEPT (pick-wt=22): 746 [] -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))).
% 12.72/12.62  ** KEPT (pick-wt=26): 747 [] -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))).
% 12.72/12.62  ** KEPT (pick-wt=18): 748 [] -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).
% 12.72/12.62  ** KEPT (pick-wt=18): 749 [] -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).
% 12.72/12.62  ** KEPT (pick-wt=14): 750 [] -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)).
% 12.72/12.62  ** KEPT (pick-wt=30): 751 [] -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)).
% 12.72/12.62  ** KEPT (pick-wt=25): 752 [] -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).
% 12.72/12.62  ** KEPT (pick-wt=25): 753 [] -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).
% 12.72/12.62    Following clause subsumed by 752 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).
% 12.72/12.62    Following clause subsumed by 753 during input processing: 0 [] -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)).
% 12.72/12.62  ** KEPT (pick-wt=25): 754 [] -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)).
% 12.72/12.62  ** KEPT (pick-wt=31): 755 [] -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)).
% 12.72/12.62  ** KEPT (pick-wt=30): 756 [] -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)).
% 12.72/12.62  ** KEPT (pick-wt=33): 757 [] -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.
% 12.72/12.62  ** KEPT (pick-wt=30): 758 [] -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)).
% 12.72/12.62  ** KEPT (pick-wt=25): 759 [] -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).
% 12.72/12.62    Following clause subsumed by 759 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).
% 12.72/12.62  ** KEPT (pick-wt=25): 760 [] -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).
% 12.72/12.62  ** KEPT (pick-wt=14): 761 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 12.72/12.62    Following clause subsumed by 660 during input processing: 0 [] -class_Rings_Oidom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),c_Polynomial_Oorder(A,C,B)),B).
% 12.72/12.62  ** KEPT (pick-wt=33): 762 [] -class_Rings_Oidom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),c_Nat_OSuc(c_Polynomial_Oorder(A,C,B))),B).
% 12.72/12.62    Following clause subsumed by 762 during input processing: 0 [] -class_Rings_Oidom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),c_Polynomial_OpCons(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),c_Nat_OSuc(c_Polynomial_Oorder(A,C,B))),B).
% 12.72/12.62  ** KEPT (pick-wt=10): 763 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B)).
% 12.72/12.62  ** KEPT (pick-wt=21): 764 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,B,A)|A=B.
% 12.72/12.62  ** KEPT (pick-wt=22): 765 [] A=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,B,C)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)).
% 12.72/12.62  ** KEPT (pick-wt=22): 766 [] A=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,B,C)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)).
% 12.72/12.62  ** KEPT (pick-wt=11): 767 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint))|c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.72/12.62  ** KEPT (pick-wt=11): 768 [] c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint))|c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.72/12.62  ** KEPT (pick-wt=16): 769 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)))|c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B).
% 12.72/12.62  ** KEPT (pick-wt=16): 770 [] c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C)))| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B).
% 12.72/12.62  ** KEPT (pick-wt=26): 771 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,D))|c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),E),B)),D)).
% 12.72/12.62  ** KEPT (pick-wt=26): 772 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,D))| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),E),B)),D)).
% 12.72/12.62  ** KEPT (pick-wt=15): 773 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,B,A)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)=c_Groups_Oabs__class_Oabs(tc_Int_Oint,B).
% 12.72/12.62    Following clause subsumed by 766 during input processing: 0 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))|A=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,B,C).
% 12.72/12.62  ** KEPT (pick-wt=13): 774 [] -c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B).
% 12.72/12.62  ** KEPT (pick-wt=13): 775 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,B,A).
% 12.72/12.62  ** KEPT (pick-wt=16): 776 [] A=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,B,A)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,B),c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)).
% 12.72/12.62  ** KEPT (pick-wt=19): 777 [] A=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),A)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.72/12.62  ** KEPT (pick-wt=19): 778 [] A=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),A)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,B)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.72/12.62  ** KEPT (pick-wt=19): 779 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.72/12.62  ** KEPT (pick-wt=14): 780 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.72/12.62  ** KEPT (pick-wt=15): 781 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.72/12.62  ** KEPT (pick-wt=10): 782 [] A!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,A)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.72/12.62  ** KEPT (pick-wt=15): 783 [] A=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Groups_Osgn__class_Osgn(tc_Int_Oint,A)=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.72/12.62  ** KEPT (pick-wt=5): 784 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.72/12.62  ** KEPT (pick-wt=11): 785 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A),A)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.72/12.62  ** KEPT (pick-wt=10): 786 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A).
% 12.72/12.62  ** KEPT (pick-wt=10): 787 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A).
% 12.72/12.62  ** KEPT (pick-wt=8): 788 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B).
% 12.72/12.62  ** KEPT (pick-wt=7): 789 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|A!=B.
% 12.72/12.62  ** KEPT (pick-wt=11): 790 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B)|A=B.
% 12.72/12.62  ** KEPT (pick-wt=12): 791 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B).
% 12.72/12.62  ** KEPT (pick-wt=12): 792 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A,B).
% 12.72/12.62  ** KEPT (pick-wt=11): 793 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint))|A=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.72/12.62  ** KEPT (pick-wt=11): 794 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,A),c_Groups_Oone__class_Oone(tc_Int_Oint))|A!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.72/12.63  ** KEPT (pick-wt=12): 795 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)),B)|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 12.72/12.63  ** KEPT (pick-wt=12): 796 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)),B)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 12.72/12.63  ** KEPT (pick-wt=17): 797 [] -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),A),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.72/12.63  ** KEPT (pick-wt=17): 798 [] 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),A),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.72/12.63  ** KEPT (pick-wt=14): 799 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|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),A)).
% 12.72/12.63  ** KEPT (pick-wt=18): 800 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|A=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.72/12.63  ** KEPT (pick-wt=18): 801 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|B=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.72/12.63  ** KEPT (pick-wt=22): 802 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)=c_Groups_Oone__class_Oone(tc_Int_Oint)|A!=c_Groups_Oone__class_Oone(tc_Int_Oint)|B!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.72/12.63    Following clause subsumed by 796 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)),B).
% 12.72/12.63  ** KEPT (pick-wt=23): 803 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)).
% 12.72/12.63  ** KEPT (pick-wt=18): 804 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,C,D)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,D)).
% 12.72/12.63  ** KEPT (pick-wt=17): 805 [] c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))!=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,A)=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 12.72/12.63  ** KEPT (pick-wt=14): 806 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)).
% 12.72/12.63  ** KEPT (pick-wt=18): 807 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),C)|B=C.
% 12.72/12.63    Following clause subsumed by 534 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),C)|B!=C.
% 12.72/12.63  ** KEPT (pick-wt=15): 808 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|A=B.
% 12.72/12.63  ** KEPT (pick-wt=12): 809 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 12.72/12.63  ** KEPT (pick-wt=11): 810 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)))|A!=B.
% 12.72/12.63  ** KEPT (pick-wt=5): 812 [copy,811,flip.1] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.72/12.63    Following clause subsumed by 812 during input processing: 0 [flip.1] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.72/12.63    Following clause subsumed by 812 during input processing: 0 [] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.72/12.63    Following clause subsumed by 812 during input processing: 0 [] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.72/12.63    Following clause subsumed by 812 during input processing: 0 [flip.1] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.72/12.63    Following clause subsumed by 812 during input processing: 0 [] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.72/12.63  ** KEPT (pick-wt=9): 813 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Nat_OSuc(A)).
% 12.72/12.63  ** KEPT (pick-wt=12): 814 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B.
% 12.72/12.63  ** KEPT (pick-wt=9): 815 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.72/12.63  ** KEPT (pick-wt=8): 816 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A!=B.
% 12.72/12.63  ** KEPT (pick-wt=10): 817 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.72/12.63    Following clause subsumed by 763 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.72/12.63    Following clause subsumed by 814 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A=B.
% 12.72/12.63    Following clause subsumed by 816 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A!=B.
% 12.72/12.63  ** KEPT (pick-wt=12): 818 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|B=A.
% 12.72/12.63    Following clause subsumed by 815 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B)).
% 12.72/12.63  ** KEPT (pick-wt=13): 819 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Nat_OSuc(A)=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),B).
% 12.72/12.63  ** KEPT (pick-wt=13): 820 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),C).
% 12.72/12.63    Following clause subsumed by 814 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B.
% 12.72/12.63  ** KEPT (pick-wt=9): 821 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.72/12.63    Following clause subsumed by 817 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.72/12.63  ** KEPT (pick-wt=5): 822 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A),A).
% 12.72/12.63  ** KEPT (pick-wt=9): 823 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(B),A).
% 12.72/12.63  ** KEPT (pick-wt=13): 824 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=c_Nat_OSuc(B).
% 12.72/12.63  ** KEPT (pick-wt=9): 825 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Nat_OSuc(B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 12.72/12.63    Following clause subsumed by 383 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Nat_OSuc(B))|A!=c_Nat_OSuc(B).
% 12.72/12.63  ** KEPT (pick-wt=10): 826 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 12.72/12.63  ** KEPT (pick-wt=10): 827 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 12.72/12.63    Following clause subsumed by 825 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Nat_OSuc(B)).
% 12.72/12.63    Following clause subsumed by 824 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=c_Nat_OSuc(B).
% 12.72/12.63  ** KEPT (pick-wt=9): 828 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A),B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 12.72/12.63  ** KEPT (pick-wt=4): 830 [copy,829,flip.1] c_Nat_OSuc(A)!=A.
% 12.72/12.63    Following clause subsumed by 830 during input processing: 0 [] c_Nat_OSuc(A)!=A.
% 12.72/12.63  ** KEPT (pick-wt=8): 831 [] c_Nat_OSuc(A)!=c_Nat_OSuc(B)|A=B.
% 12.72/12.63  ** KEPT (pick-wt=8): 832 [] c_Nat_OSuc(A)=c_Nat_OSuc(B)|A!=B.
% 12.72/12.63    Following clause subsumed by 831 during input processing: 0 [] c_Nat_OSuc(A)!=c_Nat_OSuc(B)|A=B.
% 12.72/12.63  ** KEPT (pick-wt=12): 834 [copy,833,flip.2] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A)=c_Groups_Oabs__class_Oabs(tc_Int_Oint,A).
% 12.72/12.63  ** KEPT (pick-wt=15): 835 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),c_Nat_OSuc(B))=c_Groups_Ozero__class_Ozero(A).
% 12.72/12.63  ** KEPT (pick-wt=21): 836 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 12.72/12.63    Following clause subsumed by 836 during input processing: 0 [flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 12.72/12.63  ** KEPT (pick-wt=21): 837 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C)).
% 12.72/12.63  ** KEPT (pick-wt=21): 838 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B).
% 12.72/12.63  ** KEPT (pick-wt=21): 839 [] -class_Power_Opower(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 12.72/12.63  ** KEPT (pick-wt=15): 841 [copy,840,flip.3] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nat_OSuc($f28(B,A))=A.
% 12.72/12.63  ** KEPT (pick-wt=15): 842 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f28(B,A),B).
% 12.72/12.63  ** KEPT (pick-wt=9): 843 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.72/12.63  ** KEPT (pick-wt=13): 844 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A!=c_Nat_OSuc(C)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,B).
% 12.72/12.63  ** KEPT (pick-wt=10): 845 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.72/12.63    Following clause subsumed by 843 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.72/12.63  ** KEPT (pick-wt=10): 847 [copy,846,flip.2] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero
% 12.72/12.63  Search stopped in tp_alloc by max_mem option.
% 12.72/12.63  (tc_Nat_Onat),A)|c_Nat_OSuc($f29(A))=A.
% 12.72/12.63  ** KEPT (pick-wt=9): 848 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|A!=c_Nat_OSuc(B).
% 12.72/12.63  ** KEPT (pick-wt=11): 849 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|A=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.72/12.63    Following clause subsumed by 710 during input processing: 0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|A!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.72/12.63  
% 12.72/12.63  Search stopped in tp_alloc by max_mem option.
% 12.72/12.63  
% 12.72/12.63  ============ end of search ============
% 12.72/12.63  
% 12.72/12.63  -------------- statistics -------------
% 12.72/12.63  clauses given                  0
% 12.72/12.63  clauses generated              0
% 12.72/12.63  clauses kept                 806
% 12.72/12.63  clauses forward subsumed     170
% 12.72/12.63  clauses back subsumed          0
% 12.72/12.63  Kbytes malloced            11718
% 12.72/12.63  
% 12.72/12.63  ----------- times (seconds) -----------
% 12.72/12.63  user CPU time          0.19          (0 hr, 0 min, 0 sec)
% 12.72/12.63  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 12.72/12.63  wall-clock time       13             (0 hr, 0 min, 13 sec)
% 12.72/12.63  
% 12.72/12.63  Process 4047 finished Wed Jul 27 03:03:33 2022
% 12.72/12.63  Otter interrupted
% 12.72/12.63  PROOF NOT FOUND
%------------------------------------------------------------------------------