TSTP Solution File: SWW248+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWW248+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:22:16 EDT 2022
% Result : Unknown 15.80s 15.66s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWW248+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 03:04:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 15.75/15.60 ----- Otter 3.3f, August 2004 -----
% 15.75/15.60 The process was started by sandbox on n027.cluster.edu,
% 15.75/15.60 Wed Jul 27 03:04:51 2022
% 15.75/15.60 The command was "./otter". The process ID is 30266.
% 15.75/15.60
% 15.75/15.60 set(prolog_style_variables).
% 15.75/15.60 set(auto).
% 15.75/15.60 dependent: set(auto1).
% 15.75/15.60 dependent: set(process_input).
% 15.75/15.60 dependent: clear(print_kept).
% 15.75/15.60 dependent: clear(print_new_demod).
% 15.75/15.60 dependent: clear(print_back_demod).
% 15.75/15.60 dependent: clear(print_back_sub).
% 15.75/15.60 dependent: set(control_memory).
% 15.75/15.60 dependent: assign(max_mem, 12000).
% 15.75/15.60 dependent: assign(pick_given_ratio, 4).
% 15.75/15.60 dependent: assign(stats_level, 1).
% 15.75/15.60 dependent: assign(max_seconds, 10800).
% 15.75/15.60 clear(print_given).
% 15.75/15.60
% 15.75/15.60 formula_list(usable).
% 15.75/15.60 all A (A=A).
% 15.75/15.60 all V_g_2 V_f_2 ((all B_x (hAPP(V_f_2,B_x)=hAPP(V_g_2,B_x)))->V_f_2=V_g_2).
% 15.75/15.60 class_Rings_Oidom(t_a)-> -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_p)).
% 15.75/15.60 class_Rings_Oidom(t_a)-> -(all B_z (B_z!=c_Groups_Ozero__class_Ozero(t_a)->hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z)=c_Groups_Ozero__class_Ozero(t_a))).
% 15.75/15.60 class_Rings_Oidom(t_a)-> -(all B_z (B_z!=c_Groups_Ozero__class_Ozero(t_a)->hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z)=c_Groups_Ozero__class_Ozero(t_a))).
% 15.75/15.60 all V_x V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),V_x)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)))).
% 15.75/15.60 all V_n T_a (class_Power_Opower(T_a)&class_Rings_Osemiring__0(T_a)-> (V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a))& (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Ozero__class_Ozero(T_a))).
% 15.75/15.60 all V_n V_m V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 15.75/15.60 all V_q V_p V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q))).
% 15.75/15.60 all V_a T_a (class_Power_Opower(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a)).
% 15.75/15.60 all V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a)).
% 15.75/15.60 all V_n_2 V_a_2 T_b (class_Power_Opower(T_b)&class_Rings_Omult__zero(T_b)&class_Rings_Ono__zero__divisors(T_b)&class_Rings_Ozero__ne_q__one(T_b)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b)&V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.60 all V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m)).
% 15.75/15.60 all V_a V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m)).
% 15.75/15.60 all V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m)).
% 15.75/15.60 all V_q V_p V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q))).
% 15.75/15.60 all V_n V_m V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n)).
% 15.75/15.60 all V_pa_2 T_b (class_Int_Oring__char__0(T_b)&class_Rings_Oidom(T_b)-> (c_Polynomial_Opoly(T_b,V_pa_2)=c_Polynomial_Opoly(T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))<->V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))).
% 15.75/15.60 all V_f_2 T_c T_b (c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)<-> (all B_x B_y (hAPP(V_f_2,B_x)=hAPP(V_f_2,B_y)))).
% 15.75/15.60 all T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))=hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.75/15.60 all V_pa_2 T_b (class_Groups_Ozero(T_b)-> (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_b,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))).
% 15.75/15.60 all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry))).
% 15.75/15.60 all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry))).
% 15.75/15.60 all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)))).
% 15.75/15.60 all V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly)).
% 15.75/15.60 all V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx))).
% 15.75/15.60 all V_ry V_rx V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry)).
% 15.75/15.60 all V_ry V_rx V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry))).
% 15.75/15.60 all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)).
% 15.75/15.60 all V_d V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))).
% 15.75/15.60 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b)).
% 15.75/15.60 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))).
% 15.75/15.60 all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d)).
% 15.75/15.60 all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d))).
% 15.75/15.60 all V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)).
% 15.75/15.60 all V_q_2 V_b_2 V_pa_2 V_a_2 T_b (class_Groups_Ozero(T_b)-> (hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2)=hAPP(hAPP(c_Polynomial_OpCons(T_b),V_b_2),V_q_2)<->V_a_2=V_b_2&V_pa_2=V_q_2)).
% 15.75/15.60 all V_q_2 V_pa_2 T_b (class_Int_Oring__char__0(T_b)&class_Rings_Oidom(T_b)-> (c_Polynomial_Opoly(T_b,V_pa_2)=c_Polynomial_Opoly(T_b,V_q_2)<->V_pa_2=V_q_2)).
% 15.75/15.60 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.60 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.60 all V_a_2 V_b_2 T_b (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)-> (V_b_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.60 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 15.75/15.60 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a).
% 15.75/15.60 all V_z_2 V_x_2 V_y_2 V_w_2 T_b (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))<->V_w_2=V_x_2|V_y_2=V_z_2)).
% 15.75/15.60 all V_b V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m)).
% 15.75/15.60 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 15.75/15.60 all V_d_2 V_ca_2 V_b_2 V_a_2 T_b (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)-> (V_a_2!=V_b_2&V_ca_2!=V_d_2<->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)))).
% 15.75/15.60 all V_z V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z))).
% 15.75/15.60 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a).
% 15.75/15.60 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a).
% 15.75/15.60 all V_n V_a T_a (class_Rings_Oring__1__no__zero__divisors(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)!=c_Groups_Ozero__class_Ozero(T_a))).
% 15.75/15.60 all V_q V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q))).
% 15.75/15.60 all V_n V_b V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))).
% 15.75/15.60 all V_n V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 15.75/15.60 all V_n T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a)).
% 15.75/15.60 all V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_x).
% 15.75/15.60 all V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_a).
% 15.75/15.60 all V_pa_2 V_a_2 T_b (class_Groups_Ozero(T_b)-> (hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))<->V_a_2=c_Groups_Ozero__class_Ozero(T_b)&V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))).
% 15.75/15.60 all T_a (class_Groups_Ozero(T_a)->hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.75/15.60 all V_q V_b V_p V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_b),V_q))=hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q))).
% 15.75/15.60 all V_x T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.60 all V_x V_q V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))).
% 15.75/15.60 all V_x V_q V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))).
% 15.75/15.60 all V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x)=c_Groups_Oone__class_Oone(T_a)).
% 15.75/15.60 all V_x V_n V_p T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n)).
% 15.75/15.60 all V_d V_c V_b V_a V_r T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_r!=c_Groups_Ozero__class_Ozero(T_a)-> (V_a=V_b&V_c!=V_d->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d))))).
% 15.75/15.60 class_Rings_Oidom(t_a)-> -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____))).
% 15.75/15.60 all V_y_2 V_x_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(T_b)<->V_x_2=c_Groups_Ozero__class_Ozero(T_b)&V_y_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.60 all T_b (class_Power_Opower(T_b)->c_Power_Opower__class_Opower(T_b)=c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b))).
% 15.75/15.60 class_Rings_Oidom(t_a)-> (exists B_k B_a (B_a!=c_Groups_Ozero__class_Ozero(t_a)& (exists B_q (hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,B_q)),B_k))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,v_cs____)& (all B_z (hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),B_a),B_q)),B_z)))))))).
% 15.75/15.60 all V_n V_m (V_m=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)->V_n=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.60 all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=V_m->V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.60 all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.60 all V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 15.75/15.60 all V_n (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=V_n).
% 15.75/15.60 all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a).
% 15.75/15.60 all V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a).
% 15.75/15.60 all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a).
% 15.75/15.60 all V_q T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.75/15.60 all V_q T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q)=V_q).
% 15.75/15.60 all V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.75/15.60 all V_p T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=V_p).
% 15.75/15.60 all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)).
% 15.75/15.60 all V_k V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))).
% 15.75/15.60 all V_r V_q V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_r)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r))).
% 15.75/15.60 all V_n_2 V_m_2 V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)<->V_m_2=V_n_2).
% 15.75/15.60 all V_n_2 V_a_2 V_times_2 V_one_2 T_b (hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2))=hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),V_n_2))).
% 15.75/15.60 all V_y V_x (hAPP(c_Nat_OSuc,V_x)=hAPP(c_Nat_OSuc,V_y)->V_x=V_y).
% 15.75/15.60 all V_nat_H_2 V_nat_2 (hAPP(c_Nat_OSuc,V_nat_2)=hAPP(c_Nat_OSuc,V_nat_H_2)<->V_nat_2=V_nat_H_2).
% 15.75/15.60 all V_n (hAPP(c_Nat_OSuc,V_n)!=V_n).
% 15.75/15.60 all V_n (V_n!=hAPP(c_Nat_OSuc,V_n)).
% 15.75/15.60 all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_m)).
% 15.75/15.60 all V_nat_H (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_nat_H)).
% 15.75/15.60 all V_m (hAPP(c_Nat_OSuc,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.60 all V_nat_H_1 (hAPP(c_Nat_OSuc,V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.60 all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_m)).
% 15.75/15.60 all V_m (hAPP(c_Nat_OSuc,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.60 all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.60 all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))).
% 15.75/15.60 all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))).
% 15.75/15.60 all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))).
% 15.75/15.60 all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))).
% 15.75/15.60 all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))).
% 15.75/15.60 all V_m_2 V_x_2 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.60 all V_n (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.60 all V_n_2 V_m_2 (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)<->V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.60 all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.60 c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.60 all V_n (hAPP(c_Nat_OSuc,V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)).
% 15.75/15.60 all V_n (hAPP(c_Nat_OSuc,V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 15.75/15.60 all V_n T_a (class_Power_Opower(T_a)&class_Rings_Osemiring__0(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.60 all V_n V_a T_a (class_Power_Opower(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 15.75/15.60 all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))).
% 15.75/15.60 all V_n V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)).
% 15.75/15.60 all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q))).
% 15.75/15.60 all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q))).
% 15.75/15.60 all V_a_2 V_times_2 V_one_2 T_b (hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_one_2).
% 15.75/15.60 all V_x_2 T_b (class_Groups_Ozero(T_b)-> (c_Groups_Ozero__class_Ozero(T_b)=V_x_2<->V_x_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.60 all V_c V_b V_a T_a (class_Groups_Oab__semigroup__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 15.75/15.60 all V_c V_b V_a T_a (class_Groups_Oab__semigroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))).
% 15.75/15.60 all V_ca_2 V_b_2 V_a_2 T_b (class_Groups_Ocancel__semigroup__add(T_b)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)<->V_b_2=V_ca_2)).
% 15.75/15.60 all V_ca_2 V_a_2 V_b_2 T_b (class_Groups_Ocancel__semigroup__add(T_b)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)<->V_b_2=V_ca_2)).
% 15.75/15.60 all V_c V_b V_a T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)->V_b=V_c)).
% 15.75/15.60 all V_c V_b V_a T_a (class_Groups_Ocancel__ab__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)->V_b=V_c)).
% 15.75/15.60 all V_c V_a V_b T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)->V_b=V_c)).
% 15.75/15.60 all V_x_2 T_b (class_Groups_Oone(T_b)-> (c_Groups_Oone__class_Oone(T_b)=V_x_2<->V_x_2=c_Groups_Oone__class_Oone(T_b))).
% 15.75/15.60 all V_n (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.60 all V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.60 all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.60 all V_n_2 V_m_2 V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)<->V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.60 all V_n_2 V_k_2 V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)<->V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.60 all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)).
% 15.75/15.60 all V_z V_y V_x (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z))).
% 15.75/15.60 all V_k V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))).
% 15.75/15.60 all V_n_2 V_m_2 V_k_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)<->V_m_2=V_n_2).
% 15.75/15.60 all V_n_2 V_k_2 V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)<->V_m_2=V_n_2).
% 15.75/15.60 all V_n V_m V_k (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))).
% 15.75/15.60 all V_k V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))).
% 15.75/15.60 all V_n (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)=V_n).
% 15.75/15.60 all V_n_2 V_m_2 (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)<->V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)&V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 15.75/15.60 all V_n (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n).
% 15.75/15.60 all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)<->V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)&V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 15.75/15.60 all V_a T_a (class_Groups_Omonoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a).
% 15.75/15.60 all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a).
% 15.75/15.60 all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (c_Groups_Ozero__class_Ozero(T_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.60 all V_a T_a (class_Groups_Omonoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 15.75/15.60 all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 15.75/15.60 all V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a).
% 15.75/15.60 class_Rings_Oidom(t_a)-> (-c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))-> (exists B_k B_a (B_a!=c_Groups_Ozero__class_Ozero(t_a)&B_k!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)& (exists B_q (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,B_q)),B_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,v_cs____)& (all B_z (hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(t_a,v_cs____),c_Groups_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),B_a),B_q)),B_z)))))))))).
% 15.75/15.60 all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Opcompose(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),V_q)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q)))).
% 15.75/15.60 all V_a_2 V_pa_2 T_b (class_Rings_Oidom(T_b)-> (hAPP(c_Polynomial_Opoly(T_b,V_pa_2),V_a_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|c_Polynomial_Oorder(T_b,V_a_2,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.60 all V_k V_j V_u V_i (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k)).
% 15.75/15.60 all V_n_2 V_m_2 V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)<->V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=V_n_2).
% 15.75/15.60 all V_b_H V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_b_H))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H))).
% 15.75/15.60 all V_y V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y))).
% 15.75/15.60 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 15.75/15.60 all V_b V_a_H V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_a_H)),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b))).
% 15.75/15.60 all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya))).
% 15.75/15.60 all V_q T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Opcompose(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.75/15.60 all V_x V_q V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),V_x)=hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))).
% 15.75/15.60 all V_b V_a T_a (class_Rings_Ono__zero__divisors(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)=c_Groups_Ozero__class_Ozero(T_a)->V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a))).
% 15.75/15.60 all V_b V_a T_a (class_Rings_Ono__zero__divisors(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a)))).
% 15.75/15.60 all V_b_2 V_a_2 T_b (class_Rings_Oring__no__zero__divisors(T_b)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b)|V_b_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.60 all V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.60 all V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.60 all V_a T_a (class_Rings_Omult__zero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.60 all V_y T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.60 all V_b T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.60 all V_a T_a (class_Rings_Omult__zero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.60 all T_a (class_Rings_Ozero__ne_q__one(T_a)->c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a)).
% 15.75/15.60 all T_a (class_Rings_Ozero__ne_q__one(T_a)->c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.60 all V_c V_b V_e V_a T_a (class_Rings_Osemiring(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c)).
% 15.75/15.60 all V_q_2 V_pa_2 T_b (class_Rings_Ocomm__semiring__0(T_b)->c_Polynomial_Opcompose(T_b,V_pa_2,V_q_2)=c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(T_b),T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBK(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBB(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),T_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))))),hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2))),V_pa_2)).
% 15.75/15.60 all V_x V_p V_n T_a (class_Rings_Ocomm__ring__1(T_a)->hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,c_Groups_Oone__class_Oone(T_a),V_n)),V_p)),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))).
% 15.75/15.60 all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.60 all V_pa_2 V_a_2 T_b V_z_2 V_f_2 T_c (class_Groups_Ozero(T_c)-> (hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_c)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c))),V_z_2)=V_z_2->c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,hAPP(hAPP(c_Polynomial_OpCons(T_c),V_a_2),V_pa_2))=hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,V_pa_2)))).
% 15.75/15.60 all V_nat (c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 15.75/15.60 all V_n V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)),V_n)=c_Groups_Oone__class_Oone(T_a)).
% 15.75/15.60 all V_pa_2 V_a_2 V_f_2 V_z_2 T_b T_c (class_Groups_Ozero(T_c)->c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,hAPP(hAPP(c_Polynomial_OpCons(T_c),V_a_2),V_pa_2))=hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),hAPP(hAPP(hAPP(c_If(T_b),hAPP(c_fe_qual(V_pa_2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c)))),V_z_2),c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,V_pa_2)))).
% 15.75/15.60 all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),V_q)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)))).
% 15.75/15.60 all V_a V_n V_m T_a (class_Groups_Ozero(T_a)-> (V_m=V_n->hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Omonom(T_a,V_a,V_m)),V_n)=V_a)& (V_m!=V_n->hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Omonom(T_a,V_a,V_m)),V_n)=c_Groups_Ozero__class_Ozero(T_a))).
% 15.75/15.60 all V_n V_b V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_n)).
% 15.75/15.60 all V_q_2 V_pa_2 T_b (class_Groups_Ozero(T_b)-> (V_pa_2=V_q_2<-> (all B_n (hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),B_n)=hAPP(c_Polynomial_Ocoeff(T_b,V_q_2),B_n))))).
% 15.75/15.60 all V_y_2 V_x_2 T_b (class_Groups_Ozero(T_b)-> (c_Polynomial_Ocoeff(T_b,V_x_2)=c_Polynomial_Ocoeff(T_b,V_y_2)<->V_x_2=V_y_2)).
% 15.75/15.60 all V_b_2 V_n_2 V_a_2 T_b (class_Groups_Ozero(T_b)-> (c_Polynomial_Omonom(T_b,V_a_2,V_n_2)=c_Polynomial_Omonom(T_b,V_b_2,V_n_2)<->V_a_2=V_b_2)).
% 15.75/15.60 all V_n V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n))).
% 15.75/15.60 all V_p V_b V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_b),V_p))=hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_p)).
% 15.75/15.60 all V_p T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),c_Groups_Oone__class_Oone(T_a)),V_p)=V_p).
% 15.75/15.60 all V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.75/15.60 all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q))).
% 15.75/15.60 all V_q V_a V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q))=hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))).
% 15.75/15.60 all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_q)=hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))).
% 15.75/15.60 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.60 all V_n T_a (class_Groups_Ozero(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_n)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.60 all V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_p)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.75/15.60 all V_pa_2 V_a_2 T_b (class_Rings_Oidom(T_b)-> (hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))<->V_a_2=c_Groups_Ozero__class_Ozero(T_b)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))).
% 15.75/15.60 all V_p V_b V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_b),V_p))=hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p))).
% 15.75/15.60 all V_p V_a T_a (class_Groups_Ozero(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_a).
% 15.75/15.60 all V_n V_p V_a T_a (class_Groups_Ozero(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),hAPP(c_Nat_OSuc,V_n))=hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)).
% 15.75/15.60 all V_x V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))).
% 15.75/15.60 all V_a V_p V_c T_a (class_Rings_Ocomm__semiring__0(T_a)-> (hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),V_p)=hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)->V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.75/15.60 all V_n V_q V_p T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n))).
% 15.75/15.60 all V_p V_b V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_p)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_b),V_p))).
% 15.75/15.60 all V_n T_a (class_Groups_Ozero(T_a)->c_Polynomial_Omonom(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.75/15.60 all V_n_2 V_a_2 T_b (class_Groups_Ozero(T_b)-> (c_Polynomial_Omonom(T_b,V_a_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.60 all V_b V_n V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_n)),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_n)).
% 15.75/15.60 all V_z V_y V_x (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z))).
% 15.75/15.60 all V_a V_p V_c T_a (class_Rings_Ocomm__semiring__0(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),V_p)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.75/15.60 all V_z V_y V_x (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z))).
% 15.75/15.60 all V_q_2 V_pa_2 T_b (class_Rings_Ocomm__semiring__0(T_b)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)=c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(T_b),T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBK(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBB(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),T_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),c_Polynomial_Osmult(T_b)),V_q_2)))),hAPP(c_Polynomial_OpCons(T_b),c_Groups_Ozero__class_Ozero(T_b)))),V_pa_2)).
% 15.75/15.60 all V_n V_a T_a (class_Groups_Ozero(T_a)->c_Polynomial_Omonom(T_a,V_a,hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Polynomial_Omonom(T_a,V_a,V_n))).
% 15.75/15.60 all V_x V_n V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))).
% 15.75/15.60 all V_a T_a (class_Groups_Ozero(T_a)->c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.75/15.60 all V_n V_b V_m V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_m)),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))).
% 15.75/15.60 all T_b V_z_2 V_f_2 T_c (class_Groups_Ozero(T_c)-> (hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_c)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c))),V_z_2)=V_z_2->c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c)))=V_z_2)).
% 15.75/15.60 all V_n T_a (class_Rings_Ocomm__semiring__1(T_a)-> (V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n)=c_Groups_Oone__class_Oone(T_a))& (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n)=c_Groups_Ozero__class_Ozero(T_a))).
% 15.75/15.60 all V_q V_a V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_q))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)))).
% 15.75/15.60 all V_h_2 V_pa_2 T_b (class_Rings_Ocomm__semiring__0(T_b)->c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_b,V_pa_2,V_h_2)=c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(T_b),T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBK(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),T_b),hAPP(c_COMBS(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b))),hAPP(c_Polynomial_Osmult(T_b),V_h_2)))),c_Polynomial_OpCons(T_b))),V_pa_2)).
% 15.75/15.60 all V_c V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)))=hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)),c_Polynomial_Osynthetic__div(T_a,V_p,V_c))).
% 15.75/15.60 all V_r V_q V_c V_p T_a (class_Rings_Ocomm__semiring__0(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),V_q))=hAPP(hAPP(c_Polynomial_OpCons(T_a),V_r),V_q)->V_r=hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)&V_q=c_Polynomial_Osynthetic__div(T_a,V_p,V_c))).
% 15.75/15.60 all V_nat (c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_nat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 15.75/15.60 all V_h V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),V_h)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_h),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)))).
% 15.75/15.60 all V_q_2 V_pa_2 T_b (class_Groups_Ocomm__monoid__add(T_b)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)=c_Polynomial_OAbs__poly(T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Oplus__class_Oplus(T_b)),c_Polynomial_Ocoeff(T_b,V_pa_2))),c_Polynomial_Ocoeff(T_b,V_q_2)))).
% 15.75/15.60 all V_pa_2 V_a_2 T_b (class_Rings_Ocomm__semiring__0(T_b)->hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_pa_2)=c_Polynomial_OAbs__poly(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2)),c_Polynomial_Ocoeff(T_b,V_pa_2)))).
% 15.75/15.60 c_HOL_Obool_Obool__size(c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.60 all V_n (c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n)=V_n).
% 15.75/15.60 all V_w V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))).
% 15.75/15.60 all V_z3 V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3))).
% 15.75/15.60 all V_z2 V_z1 V_w (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))).
% 15.75/15.60 all V_w V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)).
% 15.75/15.60 all V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z).
% 15.75/15.60 all V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)=V_z).
% 15.75/15.60 all V_x_2 T_b (class_Groups_Ozero(T_b)->c_Polynomial_OAbs__poly(T_b,c_Polynomial_Ocoeff(T_b,V_x_2))=V_x_2).
% 15.75/15.60 all V_c T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.75/15.60 all V_h T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_h)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.75/15.60 all V_h_2 V_pa_2 T_b (class_Rings_Ocomm__semiring__0(T_b)-> (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_b,V_pa_2,V_h_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))<->V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))).
% 15.75/15.60 c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.60 all T_b (class_Groups_Ozero(T_b)->c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))=c_Polynomial_OAbs__poly(T_b,hAPP(c_COMBK(T_b,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(T_b)))).
% 15.75/15.61 all V_m_2 V_a_2 T_b (class_Groups_Ozero(T_b)->c_Polynomial_Omonom(T_b,V_a_2,V_m_2)=c_Polynomial_OAbs__poly(T_b,hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b,hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_fun(T_b,T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Nat_Onat),c_If(T_b)),c_fe_qual(V_m_2))),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))).
% 15.75/15.61 all V_x V_h V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),V_x)=hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_h),V_x))).
% 15.75/15.61 all V_c V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osynthetic__div(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),V_c)=hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)),c_Polynomial_Osynthetic__div(T_a,V_p,V_c))).
% 15.75/15.61 all V_h V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h)=hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.75/15.61 c_HOL_Obool_Obool__size(c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.61 all V_p V_c T_a (class_Rings_Ocomm__ring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_c)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Osynthetic__div(T_a,V_p,V_c))),hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))=V_p).
% 15.75/15.61 all V_pa_2 V_a_2 T_b (class_Groups_Ozero(T_b)->hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2)=c_Polynomial_OAbs__poly(T_b,c_Nat_Onat_Onat__case(T_b,V_a_2,c_Polynomial_Ocoeff(T_b,V_pa_2)))).
% 15.75/15.61 all V_p V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=c_Groups_Oone__class_Oone(tc_Nat_Onat))& (V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))).
% 15.75/15.61 all V_n V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n))=V_n).
% 15.75/15.61 all V_pa_2 V_a_2 T_b (class_Groups_Ozero(T_b)->c_Polynomial_Ocoeff(T_b,hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2))=c_Nat_Onat_Onat__case(T_b,V_a_2,c_Polynomial_Ocoeff(T_b,V_pa_2))).
% 15.75/15.61 all V_n V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)))).
% 15.75/15.61 all V_p T_a (class_Groups_Ozero(T_a)-> (V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p)=hAPP(c_Nat_OSuc,c_Polynomial_Odegree(T_a,V_p)))).
% 15.75/15.61 all V_q V_b V_p V_a T_a (class_Groups_Oab__group__add(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_b),V_q))=hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),V_q))).
% 15.75/15.61 all V_p V_a T_a (class_Groups_Oab__group__add(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p))=hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_p))).
% 15.75/15.61 all V_p V_a T_b (class_Groups_Oab__group__add(T_b)->hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a),V_p))=hAPP(hAPP(c_Polynomial_OpCons(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b)),V_p))).
% 15.75/15.61 all V_x V_q V_p T_a (class_Rings_Ocomm__ring(T_a)->hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))).
% 15.75/15.61 all V_x V_p T_a (class_Rings_Ocomm__ring(T_a)->hAPP(c_Polynomial_Opoly(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_p)),V_x)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))).
% 15.75/15.61 all V_p T_a (class_Groups_Oab__group__add(T_a)->c_Polynomial_Odegree(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_p))=c_Polynomial_Odegree(T_a,V_p)).
% 15.75/15.61 all V_y V_x T_a (class_Rings_Ocomm__ring__1(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y))).
% 15.75/15.61 all V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))=V_a).
% 15.75/15.61 all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)).
% 15.75/15.61 all V_b_2 V_a_2 T_b (class_Groups_Ogroup__add(T_b)-> (V_a_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)<->V_b_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))).
% 15.75/15.61 all V_b_2 V_a_2 T_b (class_Groups_Ogroup__add(T_b)-> (hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)=V_b_2<->hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)=V_a_2)).
% 15.75/15.61 all V_b_2 V_a_2 T_b (class_Groups_Ogroup__add(T_b)-> (hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)<->V_a_2=V_b_2)).
% 15.75/15.61 all V_k V_j V_i (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j)).
% 15.75/15.61 all V_d_2 V_ca_2 V_b_2 V_a_2 T_b (class_Groups_Oab__group__add(T_b)-> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)-> (V_a_2=V_b_2<->V_ca_2=V_d_2))).
% 15.75/15.61 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)).
% 15.75/15.61 all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))).
% 15.75/15.61 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))).
% 15.75/15.61 all V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)).
% 15.75/15.61 c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.75/15.61 all V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.75/15.61 all V_w V_z (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))).
% 15.75/15.61 all V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)=V_z).
% 15.75/15.61 all V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z).
% 15.75/15.61 all V_w V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)).
% 15.75/15.61 all V_z V_y V_x (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z))).
% 15.75/15.61 all V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.75/15.61 all V_z3 V_z2 V_z1 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3))).
% 15.75/15.61 all V_b V_n V_a T_a (class_Groups_Oab__group__add(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_n)),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_n)).
% 15.75/15.61 all V_p V_b V_a T_a (class_Rings_Ocomm__ring(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_p)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_b),V_p))).
% 15.75/15.61 all V_n V_q V_p T_a (class_Groups_Oab__group__add(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_n)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n))).
% 15.75/15.61 all V_p V_a T_a (class_Rings_Ocomm__ring(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_p)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p))).
% 15.75/15.61 all V_n V_p T_a (class_Groups_Oab__group__add(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_p)),V_n)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n))).
% 15.75/15.61 all V_n V_a T_a (class_Groups_Oab__group__add(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_n))=c_Polynomial_Omonom(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_n)).
% 15.75/15.61 all V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 15.75/15.61 all V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_b_2 V_a_2 T_b (class_Groups_Oab__group__add(T_b)-> (V_a_2=V_b_2<->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.61 all V_b_2 V_a_2 T_b (class_Groups_Ogroup__add(T_b)-> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_a_2=V_b_2)).
% 15.75/15.61 all T_a (class_Groups_Ogroup__add(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_a_2 T_b (class_Groups_Ogroup__add(T_b)-> (c_Groups_Ozero__class_Ozero(T_b)=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)<->c_Groups_Ozero__class_Ozero(T_b)=V_a_2)).
% 15.75/15.61 all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (V_a_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.61 all V_a_2 T_b (class_Groups_Ogroup__add(T_b)-> (hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.61 all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)=V_a_2<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.61 all V_b_H V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_b_H))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H))).
% 15.75/15.61 all V_y V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y))).
% 15.75/15.61 all V_b V_a_H V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a_H)),V_b)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b))).
% 15.75/15.61 all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),V_ya)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya))).
% 15.75/15.61 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b)=V_a).
% 15.75/15.61 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b)=V_a).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Oring(T_a)->hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Oring(T_a)->hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)).
% 15.75/15.61 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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 15.75/15.61 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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x))).
% 15.75/15.61 all V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 15.75/15.61 all V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Oring(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Oring(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 15.75/15.61 all V_b_2 V_a_2 T_b (class_Rings_Oidom(T_b)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)<->V_a_2=V_b_2|V_a_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))).
% 15.75/15.61 all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))).
% 15.75/15.61 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))).
% 15.75/15.61 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))=V_b).
% 15.75/15.61 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=V_b).
% 15.75/15.61 all V_c V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Odegree(T_a,c_Polynomial_Osynthetic__div(T_a,V_p,V_c))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Polynomial_Odegree(T_a,V_p)),c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 15.75/15.61 all V_n (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.61 all V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 15.75/15.61 all V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.61 all V_n V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->V_m=V_n)).
% 15.75/15.61 all V_k V_n V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k)).
% 15.75/15.61 all V_n V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)).
% 15.75/15.61 all V_n V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n)=V_m).
% 15.75/15.61 all V_m V_n (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n)=V_m).
% 15.75/15.61 all V_k V_j V_i (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))).
% 15.75/15.61 all V_n V_m V_k (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)).
% 15.75/15.61 all V_n V_k V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)).
% 15.75/15.61 all V_w V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w))).
% 15.75/15.61 all V_n V_m V_k (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))).
% 15.75/15.61 all V_k V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))).
% 15.75/15.61 all T_a (class_Groups_Oab__group__add(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.75/15.61 all V_p V_a T_a (class_Rings_Ocomm__ring(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_p))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p))).
% 15.75/15.61 all V_q_2 V_pa_2 T_b (class_Groups_Oab__group__add(T_b)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)=c_Polynomial_OAbs__poly(T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),c_Polynomial_Ocoeff(T_b,V_pa_2))),c_Polynomial_Ocoeff(T_b,V_q_2)))).
% 15.75/15.61 all V_pa_2 T_b (class_Groups_Oab__group__add(T_b)->hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b)),V_pa_2)=c_Polynomial_OAbs__poly(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(T_b)),c_Polynomial_Ocoeff(T_b,V_pa_2)))).
% 15.75/15.61 all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))=hAPP(c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2))).
% 15.75/15.61 all V_h V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Odegree(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))=c_Polynomial_Odegree(T_a,V_p)).
% 15.75/15.61 all T_a (class_Groups_Ozero(T_a)->c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.61 all V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_b_2 V_a_2 T_b (class_Groups_Ogroup__add(T_b)-> (V_a_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)<->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.61 all V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_a T_a (class_Groups_Oab__group__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)=c_Groups_Ozero__class_Ozero(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)=V_b)).
% 15.75/15.61 all V_b V_a V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_a)),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_b)))).
% 15.75/15.61 all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_2 T_b (class_Rings_Oring(T_b)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)<->V_ca_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))).
% 15.75/15.61 all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_2 T_b (class_Rings_Oring(T_b)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)<->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2)=V_d_2)).
% 15.75/15.61 all V_x T_a (class_Rings_Ocomm__ring__1(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x)).
% 15.75/15.61 all V_x_2 T_b (class_Rings_Oring__1__no__zero__divisors(T_b)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)=c_Groups_Oone__class_Oone(T_b)<->V_x_2=c_Groups_Oone__class_Oone(T_b)|V_x_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)))).
% 15.75/15.61 all V_n V_a T_a (class_Groups_Ozero(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Polynomial_Odegree(T_a,c_Polynomial_Omonom(T_a,V_a,V_n))=V_n)).
% 15.75/15.61 all V_m V_n (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.61 all V_f2_2 V_f1_2 T_b (hAPP(c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_f1_2).
% 15.75/15.61 all V_nat_2 V_f2_2 V_f1_2 T_b (hAPP(c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2))=hAPP(V_f2_2,V_nat_2)).
% 15.75/15.61 all V_n V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)).
% 15.75/15.61 all V_n (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n).
% 15.75/15.61 all T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Polynomial_Odegree(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.61 all V_p V_a T_a (class_Rings_Oidom(T_a)-> (V_a=c_Groups_Ozero__class_Ozero(T_a)->c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p))=c_Polynomial_Odegree(T_a,V_p))).
% 15.75/15.61 all V_p T_a (class_Groups_Ozero(T_a)-> (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p))!=c_Groups_Ozero__class_Ozero(T_a))).
% 15.75/15.61 all V_pa_2 T_b (class_Groups_Ozero(T_b)-> (hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),c_Polynomial_Odegree(T_b,V_pa_2))=c_Groups_Ozero__class_Ozero(T_b)<->V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))).
% 15.75/15.61 all V_n V_a T_a (class_Rings_Oring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 15.75/15.61 all V_a T_a (class_Groups_Ozero(T_a)->c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.61 all V_a V_p T_a (class_Groups_Ozero(T_a)-> (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p))=hAPP(c_Nat_OSuc,c_Polynomial_Odegree(T_a,V_p)))).
% 15.75/15.61 all V_q V_p T_a (class_Rings_Oidom(T_a)-> (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))-> (V_q!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Polynomial_Odegree(T_a,V_p)),c_Polynomial_Odegree(T_a,V_q))))).
% 15.75/15.61 all V_ca_2 V_pa_2 T_b (class_Rings_Ocomm__semiring__0(T_b)-> (c_Polynomial_Osynthetic__div(T_b,V_pa_2,V_ca_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))<->c_Polynomial_Odegree(T_b,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.61 all V_a V_p T_a (class_Groups_Ozero(T_a)-> (V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p))=hAPP(c_Nat_OSuc,c_Polynomial_Odegree(T_a,V_p)))).
% 15.75/15.61 all V_q V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Polynomial_Odegree(T_a,V_p)),c_Polynomial_Odegree(T_a,V_q)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p))),hAPP(c_Polynomial_Ocoeff(T_a,V_q),c_Polynomial_Odegree(T_a,V_q)))).
% 15.75/15.61 all V_n V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=V_n)& (V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)))).
% 15.75/15.61 all V_m V_n T_a (class_Power_Opower(T_a)-> (V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=c_Groups_Oone__class_Oone(T_a))& (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))).
% 15.75/15.61 all V_y V_x T_a (class_Rings_Ocomm__ring__1(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))).
% 15.75/15.61 all V_y_2 V_x_2 T_b (class_Rings_Oidom(T_b)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))<->V_x_2=V_y_2|V_x_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2))).
% 15.75/15.61 all V_x T_a (class_Rings_Oring__1(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),c_Groups_Oone__class_Oone(T_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),c_Groups_Oone__class_Oone(T_a)))).
% 15.75/15.61 all V_b V_a V_y V_x T_a (class_Rings_Oring(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_a)),V_b))).
% 15.75/15.61 all V_y_2 V_x_2 T_b (class_Groups_Ogroup__add(T_b)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_y_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))).
% 15.75/15.61 all V_a V_p T_a (class_Rings_Oidom(T_a)-> (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p))),V_p))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(T_a,V_a,V_p)))),V_p)))).
% 15.75/15.61 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))).
% 15.75/15.61 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.75/15.61 all V_z (hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))=V_z).
% 15.75/15.61 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))))).
% 15.75/15.61 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a))).
% 15.75/15.61 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))->V_a=c_Groups_Ozero__class_Ozero(T_a))).
% 15.75/15.61 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)))).
% 15.75/15.61 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)))).
% 15.75/15.61 all V_k V_b V_a T_a (class_Rings_Odvd(T_a)-> (V_a=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)))).
% 15.75/15.61 all V_d V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))).
% 15.75/15.61 all V_b V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))).
% 15.75/15.61 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))).
% 15.75/15.61 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))))).
% 15.75/15.61 all V_z V_y V_x T_a (class_Rings_Ocomm__ring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)))))).
% 15.75/15.61 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))).
% 15.75/15.61 all V_y_2 V_x_2 T_b (class_Rings_Ocomm__ring__1(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)))).
% 15.75/15.61 all V_y_2 V_x_2 T_b (class_Rings_Ocomm__ring__1(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)))).
% 15.75/15.61 all V_n V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))))).
% 15.75/15.61 all V_w V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w)).
% 15.75/15.61 all V_w V_z (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))).
% 15.75/15.61 all V_w V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))).
% 15.75/15.61 all V_z2 V_z1 V_w (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))).
% 15.75/15.61 all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_q))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q)))).
% 15.75/15.61 all V_a V_q V_p T_a (class_Rings_Ocomm__semiring__1(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q))))).
% 15.75/15.61 all V_p T_a (class_Groups_Oab__group__add(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=V_p).
% 15.75/15.61 all V_q T_a (class_Groups_Oab__group__add(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_q)).
% 15.75/15.61 all V_q V_p V_a T_a (class_Rings_Ocomm__ring(T_a)->hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),V_q))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q))).
% 15.75/15.61 all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Oidom(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))<->V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)))).
% 15.75/15.61 all V_b_2 V_ca_2 V_a_2 T_b (class_Rings_Oidom(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)))<->V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)))).
% 15.75/15.61 all V_q V_a V_p T_a (class_Fields_Ofield(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q)))-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))))).
% 15.75/15.61 all V_a V_q V_p T_a (class_Fields_Ofield(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_q))))).
% 15.75/15.61 all V_q_2 V_pa_2 V_a_2 T_b (class_Fields_Ofield(T_b)-> (V_a_2!=c_Groups_Ozero__class_Ozero(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_q_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2))))).
% 15.75/15.61 all V_q V_p T_a (class_Rings_Oidom(T_a)-> (hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p))=hAPP(c_Polynomial_Ocoeff(T_a,V_q),c_Polynomial_Odegree(T_a,V_q))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_q),V_p))->V_p=V_q)))).
% 15.75/15.61 all V_q_2 V_pa_2 V_a_2 T_b (class_Fields_Ofield(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_pa_2)),V_q_2))<-> (V_a_2=c_Groups_Ozero__class_Ozero(T_b)->V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))& (V_a_2!=c_Groups_Ozero__class_Ozero(T_b)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2))))).
% 15.75/15.61 all V_pa_2 V_ca_2 T_b (class_Rings_Oidom(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),V_ca_2),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))))),V_pa_2))<->hAPP(c_Polynomial_Opoly(T_b,V_pa_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ca_2))=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.61 all V_ca_2 V_pa_2 T_b (class_Rings_Oidom(T_b)-> (hAPP(c_Polynomial_Opoly(T_b,V_pa_2),V_ca_2)=c_Groups_Ozero__class_Ozero(T_b)<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ca_2)),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))))),V_pa_2)))).
% 15.75/15.61 all V_p V_a T_a (class_Rings_Oidom(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p))),V_p))).
% 15.75/15.61 all V_a V_p T_a (class_Rings_Oidom(T_a)-> (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))-> -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(T_a,V_a,V_p)))),V_p)))).
% 15.75/15.61 all V_t_2 V_D_2 V_d_2 T_b (class_Rings_Ocomm__ring(T_b)&class_Rings_Odvd(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))-> (all B_x B_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))))))).
% 15.75/15.61 all V_t_2 V_D_2 V_d_2 T_b (class_Rings_Ocomm__ring(T_b)&class_Rings_Odvd(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))-> (all B_x B_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))))))).
% 15.75/15.61 all V_l_2 V_P_2 T_b (class_Rings_Odvd(T_b)&class_Rings_Osemiring__0(T_b)-> ((exists B_x hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x))))<-> (exists B_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b))))&hBOOL(hAPP(V_P_2,B_x)))))).
% 15.75/15.61 all V_pa_2 V_a_2 T_b (class_Rings_Oidom(T_b)->c_Polynomial_Oorder(T_b,V_a_2,V_pa_2)=c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot),hAPP(c_COMBC(tc_Nat_Onat,tc_Polynomial_Opoly(T_b),tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_HOL_Obool),tc_Nat_Onat),c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Polynomial_Opoly(T_b),tc_Nat_Onat),hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))))),c_Nat_OSuc))),V_pa_2)))).
% 15.75/15.61 all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))).
% 15.75/15.61 all V_k hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)).
% 15.75/15.61 all V_t_2 V_d_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d_2)),V_t_2))).
% 15.75/15.61 all V_t_2 V_d_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_t_2)))).
% 15.75/15.61 all V_n V_m V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),V_n)))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)))).
% 15.75/15.61 all V_n_2 V_k_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2))).
% 15.75/15.61 all V_n V_m V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))))).
% 15.75/15.61 all V_m_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))<->V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 15.75/15.61 all V_t_2 V_m_2 V_k_2 (V_k_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2))))).
% 15.75/15.61 all V_n V_m V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n)))-> (V_k!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)))).
% 15.75/15.61 all V_m_2 V_n_2 V_k_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2))))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2))).
% 15.75/15.61 all V_ca_2 V_t_2 V_x_2 V_d_2 V_a_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_d_2))),V_t_2))))).
% 15.75/15.61 all V_m_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))<->V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.61 all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))<->V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2))).
% 15.75/15.61 all V_n_2 V_P_2 (hBOOL(hAPP(V_P_2,V_n_2))-> (-hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))->c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2)=hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_OSuc))))).
% 15.75/15.61 all V_b V_n V_a (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b),V_n)))-> (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)))).
% 15.75/15.61 all V_b_2 V_a_2 V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a_2),V_n_2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)))).
% 15.75/15.61 all V_b_2 V_a_2 V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a_2),V_n_2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_b_2)))).
% 15.75/15.61 all V_b V_n V_a (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b),V_n)))-> (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b)))).
% 15.75/15.61 all V_d V_b V_c V_a T_a (class_Groups_Oab__group__add(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c),V_d))).
% 15.75/15.61 all V_x hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)).
% 15.75/15.61 all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))-> -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)))).
% 15.75/15.61 all V_z V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)))).
% 15.75/15.61 all V_b V_a (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))-> -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)))).
% 15.75/15.61 all V_z V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)))).
% 15.75/15.61 all V_c V_b V_a (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))-> (V_b=V_c->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)))).
% 15.75/15.61 all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))->V_y!=V_x).
% 15.75/15.61 all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))->V_x!=V_y).
% 15.75/15.61 all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))-> -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)))).
% 15.75/15.61 all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))).
% 15.75/15.61 all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))-> -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)))).
% 15.75/15.61 all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))->V_x!=V_y).
% 15.75/15.61 all V_z V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)))).
% 15.75/15.61 all V_c V_b V_a (V_a=V_b-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)))).
% 15.75/15.61 all V_z V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)))).
% 15.75/15.61 all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))->V_x=V_y)).
% 15.75/15.61 all V_n V_m (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))->V_m=V_n)).
% 15.75/15.61 all V_c V_b V_a (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))-> (V_b=V_c->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)))).
% 15.75/15.61 all V_c V_b V_a (V_a=V_b-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)))).
% 15.75/15.61 all V_b V_a (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))-> (V_a!=V_b->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)))).
% 15.75/15.61 all V_y V_x (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))|V_x=V_y).
% 15.75/15.61 all V_x_2 V_y_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))<->V_x_2=V_y_2)).
% 15.75/15.61 all V_y V_x (V_x=V_y->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))).
% 15.75/15.61 all V_b V_a (V_a!=V_b-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)))).
% 15.75/15.61 all V_y_2 V_x_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))&V_x_2!=V_y_2).
% 15.75/15.61 all V_y_2 V_x_2 (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))|V_x_2=V_y_2).
% 15.75/15.61 all V_y_2 V_x_2 (V_x_2=V_y_2<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))&hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))).
% 15.75/15.61 all V_x hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.61 all V_x hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x)).
% 15.75/15.61 all V_y V_x T_a (class_Fields_Ofield(T_a)-> (V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))&V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)))=c_Groups_Ozero__class_Ozero(T_a))& (-(V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))&V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))->hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)))=c_Groups_Oone__class_Oone(T_a))).
% 15.75/15.61 all V_k_2 V_P_2 T_b (class_Orderings_Owellorder(T_b)-> (hBOOL(hAPP(V_P_2,V_k_2))->hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))))).
% 15.75/15.61 all V_x V_n T_a (class_Groups_Omonoid__mult(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))).
% 15.75/15.61 all V_x_2 V_A_2 T_c T_b (class_Groups_Ouminus(T_b)->hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2))).
% 15.75/15.61 all V_x_2 V_B_2 V_A_2 T_c T_b (class_Groups_Ominus(T_b)->hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2))).
% 15.75/15.61 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.61 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,hAPP(c_Nat_OSuc,V_m),hAPP(c_Nat_OSuc,V_n))).
% 15.75/15.61 all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(c_Nat_OSuc,V_n)).
% 15.75/15.61 all V_y V_x T_a (class_Fields_Ofield(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),V_x))).
% 15.75/15.61 all V_y V_x T_a (class_Fields_Ofield(T_a)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),V_y))).
% 15.75/15.61 all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)).
% 15.75/15.61 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))))).
% 15.75/15.61 all V_n V_m V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))).
% 15.75/15.61 all V_y_2 V_x_2 V_b_2 T_b (class_Rings_Olinordered__semidom(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),V_b_2)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2)))).
% 15.75/15.61 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 15.75/15.61 all V_b V_a T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,V_a,V_b)=c_Polynomial_Opoly__gcd(T_a,V_b,V_a)).
% 15.75/15.61 all V_c V_a V_b T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,V_b,c_Polynomial_Opoly__gcd(T_a,V_a,V_c))=c_Polynomial_Opoly__gcd(T_a,V_a,c_Polynomial_Opoly__gcd(T_a,V_b,V_c))).
% 15.75/15.61 all V_c V_b V_a T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,c_Polynomial_Opoly__gcd(T_a,V_a,V_b),V_c)=c_Polynomial_Opoly__gcd(T_a,V_a,c_Polynomial_Opoly__gcd(T_a,V_b,V_c))).
% 15.75/15.61 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (V_x!=V_y->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 15.75/15.61 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 15.75/15.61 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 15.75/15.61 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 15.75/15.61 all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))).
% 15.75/15.61 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))).
% 15.75/15.61 all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_b)->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))).
% 15.75/15.61 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))).
% 15.75/15.61 all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> -c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 15.75/15.61 all V_b V_a T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> -c_Orderings_Oord__class_Oless(T_a,V_b,V_a))).
% 15.75/15.61 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_y!=V_x)).
% 15.75/15.61 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)).
% 15.75/15.61 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 15.75/15.61 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 15.75/15.61 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)).
% 15.75/15.61 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 15.75/15.61 all V_x_2 V_y_2 T_b (class_Orderings_Olinorder(T_b)-> (-c_Orderings_Oord__class_Oless(T_b,V_y_2,V_x_2)-> (-c_Orderings_Oord__class_Oless(T_b,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 15.75/15.61 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x)).
% 15.75/15.61 all V_y_2 V_x_2 T_b (class_Orderings_Olinorder(T_b)-> (-c_Orderings_Oord__class_Oless(T_b,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_b,V_y_2,V_x_2)|V_x_2=V_y_2)).
% 15.75/15.61 all V_y_2 V_x_2 T_b (class_Orderings_Olinorder(T_b)-> (V_x_2!=V_y_2<->c_Orderings_Oord__class_Oless(T_b,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_b,V_y_2,V_x_2))).
% 15.75/15.61 all V_x T_a (class_Orderings_Opreorder(T_a)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_x)).
% 15.75/15.61 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 15.75/15.61 all V_n_2 V_m_2 (V_m_2!=V_n_2<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)).
% 15.75/15.61 all V_y V_x (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x))).
% 15.75/15.61 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 15.75/15.61 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)->V_m!=V_n).
% 15.75/15.61 all V_t V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)->V_s!=V_t).
% 15.75/15.61 all V_P_2 V_n_2 V_m_2 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))-> ((V_m_2=V_n_2->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))-> ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))))).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m)))).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n),V_k)).
% 15.75/15.61 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k)).
% 15.75/15.61 all V_n V_m V_l V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))).
% 15.75/15.61 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.75/15.61 all V_i V_j (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_i)).
% 15.75/15.61 all V_j V_i (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_i)).
% 15.75/15.61 all V_n_2 V_m_2 (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,V_m_2))).
% 15.75/15.61 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2).
% 15.75/15.61 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.75/15.61 all V_m_2 V_n_2 (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,V_m_2))<->V_n_2=V_m_2)).
% 15.75/15.61 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,hAPP(c_Nat_OSuc,V_m))->V_m=V_n)).
% 15.75/15.61 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,hAPP(c_Nat_OSuc,V_n))).
% 15.75/15.61 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)-> (hAPP(c_Nat_OSuc,V_m)!=V_n->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n))).
% 15.75/15.61 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,hAPP(c_Nat_OSuc,V_i),V_k))).
% 15.75/15.61 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n))-> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->V_m=V_n)).
% 15.75/15.61 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)).
% 15.75/15.61 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),hAPP(c_Nat_OSuc,V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)).
% 15.75/15.61 all V_n (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)).
% 15.75/15.61 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.61 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.61 all V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 15.75/15.61 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.61 all V_a_2 V_b_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2))).
% 15.75/15.61 all V_b_2 V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2),V_b_2)<->c_Orderings_Oord__class_Oless(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2),V_a_2))).
% 15.75/15.61 all V_b_2 V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))<->c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))).
% 15.75/15.61 all V_d_2 V_ca_2 V_b_2 V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)-> (c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless(T_b,V_ca_2,V_d_2)))).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))))).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))).
% 15.75/15.61 all V_b_2 V_a_2 V_ca_2 T_b (class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2))).
% 15.75/15.61 all V_b_2 V_ca_2 V_a_2 T_b (class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2))).
% 15.75/15.61 all V_P_2 V_k_2 T_b (class_Orderings_Owellorder(T_b)-> (c_Orderings_Oord__class_Oless(T_b,V_k_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))-> -hBOOL(hAPP(V_P_2,V_k_2)))).
% 15.75/15.61 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))).
% 15.75/15.61 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 15.75/15.61 all T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.75/15.61 all V_y_2 V_x_2 T_b (class_Fields_Ofield(T_b)-> (c_Polynomial_Opoly__gcd(T_b,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))<->V_x_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))&V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))).
% 15.75/15.61 all V_y_2 V_x_2 V_k_2 T_b (class_Fields_Ofield(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_k_2),c_Polynomial_Opoly__gcd(T_b,V_x_2,V_y_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_k_2),V_x_2))&hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_k_2),V_y_2)))).
% 15.75/15.61 all V_y V_x V_k T_a (class_Fields_Ofield(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k),V_x))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k),V_y))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k),c_Polynomial_Opoly__gcd(T_a,V_x,V_y)))))).
% 15.75/15.61 all V_y V_x T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_x),V_y)=c_Polynomial_Opoly__gcd(T_a,V_x,V_y)).
% 15.75/15.61 all V_y V_x T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,V_x,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_y))=c_Polynomial_Opoly__gcd(T_a,V_x,V_y)).
% 15.75/15.61 all V_y T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)),V_y)=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))).
% 15.75/15.61 all V_x T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))).
% 15.75/15.61 all V_a T_a (class_Rings_Olinordered__ring(T_a)-> -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a))).
% 15.75/15.61 all V_b_2 V_ca_2 V_a_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)&c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))&c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2))).
% 15.75/15.61 all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)&c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))&c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2))).
% 15.75/15.61 all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)))).
% 15.75/15.61 all V_a V_b T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)))).
% 15.75/15.61 all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2)))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))).
% 15.75/15.61 all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))).
% 15.75/15.61 all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 15.75/15.61 all V_c V_b V_a T_a (class_Rings_Olinordered__comm__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 15.75/15.61 all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))).
% 15.75/15.61 all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 15.75/15.61 all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2),c_Groups_Ozero__class_Ozero(T_b))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)))).
% 15.75/15.61 all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2))).
% 15.75/15.61 all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2),c_Groups_Ozero__class_Ozero(T_b))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)))).
% 15.75/15.61 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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))))).
% 15.75/15.61 all V_b_2 V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))).
% 15.75/15.61 all T_a (class_Rings_Olinordered__semidom(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))).
% 15.75/15.61 all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))).
% 15.75/15.61 all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)))).
% 15.75/15.61 all V_a_2 T_b (class_Groups_Olinordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2),V_a_2)<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2))).
% 15.75/15.61 all V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2))).
% 15.75/15.61 all V_a_2 T_b (class_Groups_Oordered__ab__group__add(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)))).
% 15.75/15.61 all V_n V_m T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))))).
% 15.75/15.61 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))).
% 15.75/15.61 all V_a T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,V_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))).
% 15.75/15.61 all V_n_2 V_m_2 V_a_2 T_b (class_Rings_Olinordered__semidom(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),V_a_2)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2)=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)<->V_m_2=V_n_2))).
% 15.75/15.61 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=hAPP(c_Nat_OSuc,B_m)))).
% 15.75/15.61 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.61 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| (exists B_j (V_m_2=hAPP(c_Nat_OSuc,B_j)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)))).
% 15.75/15.61 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m))).
% 15.75/15.61 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)-> -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)))).
% 15.75/15.61 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 15.75/15.61 all V_m V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m))).
% 15.75/15.61 all V_m V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i))).
% 15.75/15.61 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)<-> (exists B_k (V_n_2=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k))))).
% 15.75/15.61 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))).
% 15.75/15.61 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))).
% 15.75/15.61 all V_n_2 V_k_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.75/15.61 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.75/15.61 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 15.75/15.61 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))).
% 15.75/15.61 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)<->V_m_2=V_n_2)).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_m))).
% 15.75/15.61 all V_m_2 V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.75/15.61 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.75/15.61 all V_n V_m c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),hAPP(c_Nat_OSuc,V_m)).
% 15.75/15.61 all V_n V_m (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))=V_m).
% 15.75/15.61 all V_k_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),V_j_2)).
% 15.75/15.61 all V_n V_m V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 15.75/15.61 all V_n_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.61 all V_p V_q T_a (class_Groups_Ocomm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),c_Polynomial_Odegree(T_a,V_p))->c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q))=c_Polynomial_Odegree(T_a,V_p))).
% 15.75/15.61 all V_q V_p T_a (class_Groups_Ocomm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))->c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q))=c_Polynomial_Odegree(T_a,V_q))).
% 15.75/15.61 all V_q V_n V_p T_a (class_Groups_Ocomm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_n)))).
% 15.75/15.61 all V_q V_n V_p T_a (class_Groups_Oab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_n)))).
% 15.75/15.61 all V_y V_x T_a (class_Rings_Olinordered__ring(T_a)-> -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a))).
% 15.75/15.61 all V_y_2 V_x_2 T_b (class_Rings_Olinordered__ring__strict(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)))<->V_x_2!=c_Groups_Ozero__class_Ozero(T_b)|V_y_2!=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.61 all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))).
% 15.75/15.61 all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_2 T_b (class_Rings_Oordered__ring(T_b)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))<->c_Orderings_Oord__class_Oless(T_b,V_ca_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)))).
% 15.75/15.61 all V_d_2 V_b_2 V_ca_2 V_e_2 V_a_2 T_b (class_Rings_Oordered__ring(T_b)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))<->c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2),V_d_2))).
% 15.75/15.61 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 15.75/15.61 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 15.75/15.61 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),hAPP(c_Nat_OSuc,V_n))))).
% 15.75/15.61 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))).
% 15.75/15.61 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)))).
% 15.75/15.61 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))).
% 15.75/15.61 all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i)),V_n)).
% 15.75/15.61 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)))).
% 15.75/15.61 all V_n V_m V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)))-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)))).
% 15.75/15.61 all V_b_2 V_a_2 V_P_2 (hBOOL(hAPP(V_P_2,hAPP(hAPP(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=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)& -hBOOL(hAPP(V_P_2,B_d)))))).
% 15.75/15.61 all V_b_2 V_a_2 V_P_2 (hBOOL(hAPP(V_P_2,hAPP(hAPP(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=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)->hBOOL(hAPP(V_P_2,B_d))))).
% 15.75/15.61 all V_a T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)=V_a).
% 15.75/15.61 all V_x T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)=V_x).
% 15.75/15.61 all V_b V_a T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 15.75/15.61 all V_x_2 V_B_2 V_A_2 T_c T_b (class_Groups_Ominus(T_b)->hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2))).
% 15.75/15.61 all V_n V_p T_a (class_Groups_Ozero(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)->hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)=c_Groups_Ozero__class_Ozero(T_a))).
% 15.75/15.61 all V_y_2 V_x_2 T_b (class_Lattices_Oboolean__algebra(T_b)-> (hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)<->V_x_2=V_y_2)).
% 15.75/15.61 all V_x_2 V_A_2 T_c T_b (class_Groups_Ouminus(T_b)->hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2))).
% 15.75/15.61 all V_x T_a (class_Lattices_Oboolean__algebra(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))=V_x).
% 15.75/15.61 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 15.75/15.61 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),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(T_a))))).
% 15.75/15.61 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)->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))))).
% 15.75/15.61 all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->V_n=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 15.75/15.61 all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=V_n).
% 15.75/15.61 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_m_2))<->V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 15.75/15.61 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_m_2)),V_m_2))<->V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 15.75/15.61 all V_P_2 T_b (class_Orderings_Owellorder(T_b)-> ((exists B_x1 hBOOL(hAPP(V_P_2,B_x1)))->hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))))).
% 15.75/15.61 all V_n_2 V_x_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)).
% 15.75/15.61 all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))->V_x=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.61 all V_y V_x V_d T_a (class_Fields_Ofield(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_x))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_y))-> ((all B_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),B_k),V_x))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),B_k),V_y))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),B_k),V_d)))))-> ((V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))&V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))=c_Groups_Ozero__class_Ozero(T_a))& (-(V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))&V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))->hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))=c_Groups_Oone__class_Oone(T_a))->c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d))))).
% 15.75/15.61 all V_y_2 V_x_2 V_f_2 T_b (class_Orderings_Oorder(T_b)-> (c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))& -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))->c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2))))).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))).
% 15.75/15.61 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 15.75/15.61 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)->c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)))).
% 15.75/15.61 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)|V_w_2=V_z_2).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.75/15.61 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)-> -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)))).
% 15.75/15.61 all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 15.75/15.61 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint)<->V_m_2=c_Groups_Oone__class_Oone(tc_Int_Oint)&V_n_2=c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 15.75/15.61 all V_f_2 T_b (class_Orderings_Oorder(T_b)-> (c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)->c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2))).
% 15.75/15.61 all V_r_2 V_q_2 V_y_2 V_x_2 T_b (class_Fields_Ofield(T_b)-> (c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)<->V_x_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2),V_y_2)),V_r_2)& (V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))->V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))& (V_y_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))->V_r_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_b,V_r_2),c_Polynomial_Odegree(T_b,V_y_2))))).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))).
% 15.75/15.61 all V_y V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x)).
% 15.75/15.61 all V_x T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opdivmod__rel(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)).
% 15.75/15.61 all V_y T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.75/15.61 all V_r_2 V_q_2 V_x_2 T_b (class_Fields_Ofield(T_b)-> (c_Polynomial_Opdivmod__rel(T_b,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),V_q_2,V_r_2)<->V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))&V_r_2=V_x_2)).
% 15.75/15.61 all V_r_2 V_q_2 V_y_2 T_b (class_Fields_Ofield(T_b)-> (c_Polynomial_Opdivmod__rel(T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),V_y_2,V_q_2,V_r_2)<->V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))&V_r_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))).
% 15.75/15.61 all V_a V_r V_q V_y V_x T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)->c_Polynomial_Opdivmod__rel(T_a,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_x),V_y,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_r)))).
% 15.75/15.61 all V_r2 V_q2 V_r1 V_q1 V_y V_x T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)->V_q1=V_q2))).
% 15.75/15.61 all V_r2 V_q2 V_r1 V_q1 V_y V_x T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)->V_r1=V_r2))).
% 15.75/15.61 all V_r2 V_q2 V_r1 V_q1 V_y V_x T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)->V_q1=V_q2&V_r1=V_r2))).
% 15.75/15.61 all V_r_H V_q_H V_z V_r V_q V_y V_x T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)-> (c_Polynomial_Opdivmod__rel(T_a,V_q,V_z,V_q_H,V_r_H)->c_Polynomial_Opdivmod__rel(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z),V_q_H,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_r_H)),V_r))))).
% 15.75/15.61 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))).
% 15.75/15.61 all V_a V_b V_r V_q V_y V_x T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)-> (V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))-> (V_b=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_r)),c_Polynomial_Odegree(T_a,V_y))),hAPP(c_Polynomial_Ocoeff(T_a,V_y),c_Polynomial_Odegree(T_a,V_y)))->c_Polynomial_Opdivmod__rel(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_x),V_y,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_b),V_q),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_r)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_b),V_y))))))).
% 15.75/15.61 all V_pa_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Polynomial_Opos__poly(T_b,V_pa_2)<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),c_Polynomial_Odegree(T_b,V_pa_2))))).
% 15.75/15.61 all V_pa_2 V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Polynomial_Opos__poly(T_b,hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2))<->c_Polynomial_Opos__poly(T_b,V_pa_2)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))&c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2))).
% 15.75/15.61 all V_y V_x T_a (class_RealVector_Oreal__normed__field(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Odivision__ring(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)).
% 15.75/15.61 all V_c V_b V_a T_a (class_Rings_Odivision__ring(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))).
% 15.75/15.61 all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__field(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),V_ya)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_ya)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_ya))).
% 15.75/15.61 all V_n V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))).
% 15.75/15.61 all V_a T_a (class_Rings_Odivision__ring(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a).
% 15.75/15.61 all V_c V_b V_a T_a (class_Rings_Odivision__ring(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))).
% 15.75/15.61 all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__field(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_ya)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_ya))).
% 15.75/15.61 all V_c V_b V_a T_a (class_Rings_Odivision__ring(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)).
% 15.75/15.61 all V_a T_a (class_Rings_Odivision__ring(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_y T_a (class_RealVector_Oreal__normed__field(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_n V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n)).
% 15.75/15.61 all V_n V_a V_b T_a (class_Fields_Ofield(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))).
% 15.75/15.61 all V_a V_b T_a (class_Rings_Odivision__ring(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)))).
% 15.75/15.61 all V_a V_b T_a (class_Rings_Odivision__ring(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b))).
% 15.75/15.61 all V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)-> (V_a=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a))& (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a)=c_Groups_Oone__class_Oone(T_a))).
% 15.75/15.61 all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a)=c_Groups_Oone__class_Oone(T_a))).
% 15.75/15.61 all V_a_2 V_b_2 T_b (class_Rings_Odivision__ring(T_b)-> (V_b_2!=c_Groups_Ozero__class_Ozero(T_b)-> (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)=c_Groups_Oone__class_Oone(T_b)<->V_a_2=V_b_2))).
% 15.75/15.61 all V_b_2 V_a_2 V_ca_2 T_b (class_Rings_Odivision__ring(T_b)-> (V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)-> (V_a_2=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)<->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)=V_b_2))).
% 15.75/15.61 all V_a_2 V_b_2 V_ca_2 T_b (class_Rings_Odivision__ring(T_b)-> (V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)-> (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)=V_a_2<->V_b_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)))).
% 15.75/15.61 all V_a V_b V_c T_a (class_Rings_Odivision__ring(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)=V_a))).
% 15.75/15.61 all V_b V_a V_c T_a (class_Rings_Odivision__ring(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)=V_b->V_a=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)))).
% 15.75/15.61 all T_a (class_Rings_Olinordered__idom(T_a)-> -c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.75/15.61 all V_q V_p T_a (class_Rings_Olinordered__idom(T_a)-> (c_Polynomial_Opos__poly(T_a,V_p)-> (c_Polynomial_Opos__poly(T_a,V_q)->c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q))))).
% 15.75/15.61 all V_q V_p T_a (class_Rings_Olinordered__idom(T_a)-> (c_Polynomial_Opos__poly(T_a,V_p)-> (c_Polynomial_Opos__poly(T_a,V_q)->c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))))).
% 15.75/15.61 all V_y_2 V_x_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_b),V_x_2,V_y_2)<->c_Polynomial_Opos__poly(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_b)),V_y_2),V_x_2)))).
% 15.75/15.61 all V_h V_d V_c V_b V_a T_a (class_RealVector_Oreal__field(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))),V_h)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d)),V_h))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c)),V_h)),V_d))).
% 15.75/15.61 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,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_p))).
% 15.75/15.61 all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_b))).
% 15.75/15.61 all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,V_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))))).
% 15.75/15.61 all V_y V_x V_z T_a (class_Fields_Ofield(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z))).
% 15.75/15.61 all V_w V_z V_y V_x T_a (class_Fields_Ofield__inverse__zero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_z),V_w))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w))).
% 15.75/15.61 all V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))).
% 15.75/15.61 all V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)).
% 15.75/15.61 all V_c V_a V_b T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))))).
% 15.75/15.61 all V_c V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))))).
% 15.75/15.61 all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))))).
% 15.75/15.61 all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.75/15.61 all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.75/15.61 all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))))).
% 15.75/15.61 all V_b_2 V_a_2 T_b (class_Fields_Olinordered__field__inverse__zero(T_b)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_b))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2)&c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b))&c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_b_2))).
% 15.75/15.61 all V_b_2 V_a_2 T_b (class_Fields_Olinordered__field__inverse__zero(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2)&c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b))&c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ozero__class_Ozero(T_b)))).
% 15.75/15.61 all V_w_2 V_x_2 V_z_2 V_y_2 T_b (class_Fields_Ofield(T_b)-> (V_y_2!=c_Groups_Ozero__class_Ozero(T_b)-> (V_z_2!=c_Groups_Ozero__class_Ozero(T_b)-> (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2)<->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2))))).
% 15.75/15.61 all V_b V_a V_c T_a (class_Fields_Ofield__inverse__zero(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b))).
% 15.75/15.61 all V_b V_a V_c T_a (class_Fields_Ofield__inverse__zero(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b))).
% 15.75/15.61 all V_a_2 V_ca_2 V_b_2 T_b (class_Fields_Ofield__inverse__zero(T_b)-> (hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)=V_a_2<-> (V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)->V_b_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))& (V_ca_2=c_Groups_Ozero__class_Ozero(T_b)->V_a_2=c_Groups_Ozero__class_Ozero(T_b)))).
% 15.75/15.61 all V_ca_2 V_b_2 V_a_2 T_b (class_Fields_Ofield__inverse__zero(T_b)-> (V_a_2=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)<-> (V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)=V_b_2)& (V_ca_2=c_Groups_Ozero__class_Ozero(T_b)->V_a_2=c_Groups_Ozero__class_Ozero(T_b)))).
% 15.75/15.61 all V_c V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)))))).
% 15.75/15.61 all V_c V_a V_b T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)))))).
% 15.75/15.61 all V_a_2 V_b_2 V_ca_2 T_b (class_Fields_Olinordered__field(T_b)-> (c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2),V_a_2)<->c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)))).
% 15.75/15.61 all V_b_2 V_a_2 V_ca_2 T_b (class_Fields_Olinordered__field(T_b)-> (c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))-> (c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))<->c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))))).
% 15.75/15.61 all V_x V_z V_y T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y),V_x)->c_Orderings_Oord__class_Oless(T_a,V_z,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))))).
% 15.75/15.61 all V_z V_x V_y T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y),V_z)))).
% 15.75/15.61 all V_a_2 V_b_2 V_ca_2 T_b (class_Fields_Olinordered__field(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2),V_a_2)<->c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))))).
% 15.75/15.61 all V_b_2 V_a_2 V_ca_2 T_b (class_Fields_Olinordered__field(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))<->c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)))).
% 15.75/15.61 all V_a_2 V_ca_2 V_b_2 T_b (class_Fields_Olinordered__field__inverse__zero(T_b)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2),V_a_2)<-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)->c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)))& (-c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))->c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2))))).
% 15.75/15.61 all V_ca_2 V_b_2 V_a_2 T_b (class_Fields_Olinordered__field__inverse__zero(T_b)-> (c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))<-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)->c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)-> (c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))->c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)))& (-c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))->c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)))))).
% 15.75/15.61 all V_w V_x V_z V_y T_a (class_Fields_Ofield(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z))))).
% 15.75/15.61 all V_y V_x V_z T_a (class_Fields_Ofield(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z))).
% 15.75/15.61 all V_z V_x V_y T_a (class_Fields_Ofield__inverse__zero(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y))).
% 15.75/15.61 all V_y V_x V_z T_a (class_Fields_Ofield(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z))).
% 15.75/15.61 all V_x V_z V_y T_a (class_Fields_Ofield__inverse__zero(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y))).
% 15.75/15.61 all V_w V_x V_z V_y T_a (class_Fields_Ofield(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z))))).
% 15.75/15.61 all V_y V_x V_z T_a (class_Fields_Ofield(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z))).
% 15.75/15.61 all V_x V_a V_y T_a (class_Fields_Ofield(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_x),V_y)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))),hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))),c_Polynomial_Odegree(T_a,V_y))),hAPP(c_Polynomial_Ocoeff(T_a,V_y),c_Polynomial_Odegree(T_a,V_y)))),V_y)))).
% 15.75/15.61 all V_e_2 V_g_2 V_d_2 V_x_2 V_f_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_d_2)-> (c_Deriv_Oderiv(T_b,V_g_2,V_x_2,V_e_2)-> (hAPP(V_g_2,V_x_2)!=c_Groups_Ozero__class_Ozero(T_b)->c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_g_2),V_x_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_d_2),hAPP(V_g_2,V_x_2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_e_2),hAPP(V_f_2,V_x_2)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(V_g_2,V_x_2)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))))).
% 15.75/15.61 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)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))))).
% 15.75/15.61 all V_y V_x T_a (class_Fields_Ofield(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_x),c_Polynomial_Odegree(T_a,V_y))->c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)=V_x)).
% 15.75/15.61 all V_x V_y T_a (class_Fields_Ofield(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=c_Polynomial_Opoly__gcd(T_a,V_y,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)))).
% 15.75/15.61 all V_r V_q V_y V_x T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)->c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)=V_r)).
% 15.75/15.61 all V_y V_x V_a T_a (class_Fields_Ofield(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_y))=c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))).
% 15.75/15.61 all V_y V_x T_a (class_Fields_Ofield(T_a)->c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_y))=c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.75/15.61 all V_y V_x T_a (class_Fields_Ofield(T_a)->c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_x),V_y)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))).
% 15.75/15.61 all T_a (class_Groups_Osgn__if(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Groups_Osgn__class_Osgn(T_b,V_a_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.61 all V_x_2 T_b (class_RealVector_Oreal__normed__vector(T_b)-> (c_Groups_Osgn__class_Osgn(T_b,V_x_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_x_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b))).
% 15.75/15.61 all V_y V_x T_a (class_RealVector_Oreal__normed__div__algebra(T_a)->c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y))).
% 15.75/15.61 all V_x_2 V_k_2 T_b (class_RealVector_Oreal__normed__field(T_b)->c_Deriv_Oderiv(T_b,hAPP(c_COMBK(T_b,T_b),V_k_2),V_x_2,c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.61 all T_a (class_RealVector_Oreal__normed__algebra__1(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a)).
% 15.75/15.61 all V_y V_x V_a T_a (class_Fields_Ofield(T_a)->c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_x),V_y)=hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))).
% 15.75/15.61 all V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a))=c_Groups_Osgn__class_Osgn(T_a,V_a)).
% 15.75/15.61 all V_x_2 V_ca_2 T_b (class_RealVector_Oreal__normed__field(T_b)->c_Deriv_Oderiv(T_b,hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_x_2,V_ca_2)).
% 15.75/15.61 all V_E_2 V_D_2 V_x_2 V_f_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)-> (c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_E_2)->V_D_2=V_E_2))).
% 15.75/15.61 all V_Y_2 V_X_2 V_x_2 V_f_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_X_2)-> (V_X_2=V_Y_2->c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_Y_2)))).
% 15.75/15.61 all V_E_2 V_D_2 V_x_2 V_f_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)-> (V_D_2=V_E_2->c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_E_2)))).
% 15.75/15.61 all V_D_2 V_x_2 V_f_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)->c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,T_b),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2),V_x_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_D_2)))).
% 15.75/15.61 all V_x_2 T_b (class_RealVector_Oreal__normed__field(T_b)->c_Deriv_Oderiv(T_b,c_COMBI(T_b),V_x_2,c_Groups_Oone__class_Oone(T_b))).
% 15.75/15.61 all V_E_2 V_g_2 V_D_2 V_x_2 V_f_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)-> (c_Deriv_Oderiv(T_b,V_g_2,V_x_2,V_E_2)->c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2),V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_D_2),V_E_2))))).
% 15.75/15.61 all V_x T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Groups_Osgn__class_Osgn(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x))).
% 15.75/15.61 all V_E_2 V_g_2 V_D_2 V_x_2 V_f_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)-> (c_Deriv_Oderiv(T_b,V_g_2,V_x_2,V_E_2)->c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2),V_x_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_D_2),V_E_2))))).
% 15.75/15.61 all V_Db_2 V_Da_2 V_x_2 V_g_2 V_f_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (c_Deriv_Oderiv(T_b,V_f_2,hAPP(V_g_2,V_x_2),V_Da_2)-> (c_Deriv_Oderiv(T_b,V_g_2,V_x_2,V_Db_2)->c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,T_b),V_f_2),V_g_2),V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_Da_2),V_Db_2))))).
% 15.75/15.61 all V_E_2 V_g_2 V_D_2 V_x_2 V_f_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)-> (c_Deriv_Oderiv(T_b,V_g_2,hAPP(V_f_2,V_x_2),V_E_2)->c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,T_b),V_g_2),V_f_2),V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_E_2),V_D_2))))).
% 15.75/15.61 all V_ca_2 V_D_2 V_x_2 V_f_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)->c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2)),V_f_2),V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_D_2)))).
% 15.75/15.61 all V_ca_2 V_D_2 V_x_2 V_f_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)->c_Deriv_Oderiv(T_b,hAPP(c_COMBC(T_b,T_b,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_ca_2),V_x_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_D_2),V_ca_2)))).
% 15.75/15.61 all V_E_2 V_g_2 V_D_2 V_x_2 V_f_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)-> (c_Deriv_Oderiv(T_b,V_g_2,V_x_2,V_E_2)->c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2),V_x_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_f_2,V_x_2)),V_E_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_D_2),hAPP(V_g_2,V_x_2))))))).
% 15.75/15.61 all V_Db_2 V_g_2 V_Da_2 V_x_2 V_f_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_Da_2)-> (c_Deriv_Oderiv(T_b,V_g_2,V_x_2,V_Db_2)->c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2),V_x_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_Da_2),hAPP(V_g_2,V_x_2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_Db_2),hAPP(V_f_2,V_x_2))))))).
% 15.75/15.61 all V_E_2 V_g_2 V_D_2 V_x_2 V_f_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)-> (c_Deriv_Oderiv(T_b,V_g_2,V_x_2,V_E_2)->c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(T_b,T_b,T_b),c_Groups_Ouminus__class_Ouminus(T_b)),V_g_2)),V_x_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_D_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_E_2)))))).
% 15.75/15.61 all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2))).
% 15.75/15.61 all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Osgn__class_Osgn(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)))).
% 15.75/15.61 all V_x V_y T_a (class_Fields_Ofield(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)),c_Polynomial_Odegree(T_a,V_y)))).
% 15.75/15.61 all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Groups_Osgn__class_Osgn(T_b,V_a_2)=c_Groups_Oone__class_Oone(T_b)<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2))).
% 15.75/15.61 all V_a T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Groups_Osgn__class_Osgn(T_a,V_a)=c_Groups_Oone__class_Oone(T_a))).
% 15.75/15.61 all V_E_2 V_g_2 V_D_2 V_x_2 V_f_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)-> (c_Deriv_Oderiv(T_b,V_g_2,V_x_2,V_E_2)-> (hAPP(V_g_2,V_x_2)!=c_Groups_Ozero__class_Ozero(T_b)->c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_g_2),V_x_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_D_2),hAPP(V_g_2,V_x_2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_f_2,V_x_2)),V_E_2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(V_g_2,V_x_2)))))))).
% 15.75/15.61 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)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))))).
% 15.75/15.61 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)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)))).
% 15.75/15.61 all V_a_2 T_b (class_Rings_Olinordered__idom(T_b)-> (c_Groups_Osgn__class_Osgn(T_b,V_a_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)))).
% 15.75/15.61 all V_b_2 V_a_2 T_b (class_Divides_Osemiring__div(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))<->c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2)=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.61 all V_b V_a T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))->c_Divides_Odiv__class_Omod(T_a,V_b,V_a)=c_Groups_Ozero__class_Ozero(T_a))).
% 15.75/15.61 all V_n V_m (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)).
% 15.75/15.61 all V_n V_m ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=V_m)& (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n))).
% 15.75/15.61 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=V_m).
% 15.75/15.61 all V_a V_b (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))).
% 15.75/15.61 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_n)).
% 15.75/15.61 all V_a V_b (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b)).
% 15.75/15.61 all V_b V_a ((c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))& (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b))).
% 15.75/15.61 all V_b V_a ((c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))& (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))).
% 15.75/15.61 all V_m V_n V_k (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)).
% 15.75/15.61 all V_m V_x (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_x),V_m)).
% 15.75/15.61 all V_b V_a (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))).
% 15.75/15.61 all V_b V_a (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b))).
% 15.75/15.61 all V_m V_y V_x (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m)).
% 15.75/15.61 all V_y V_m V_x (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m)).
% 15.75/15.61 all V_d_2 V_m_2 (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<-> (exists B_q (V_m_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q)))).
% 15.75/15.61 all V_m V_n V_k (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)).
% 15.75/15.61 all V_l V_k (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.75/15.61 all V_l V_k (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.75/15.61 all V_n V_m (c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)).
% 15.75/15.61 all V_y V_m V_x (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m)).
% 15.75/15.61 all V_k V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))).
% 15.75/15.61 all V_n V_m V_k (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))).
% 15.75/15.61 all V_c V_b V_a (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c)).
% 15.75/15.61 all V_c V_b V_a (c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)).
% 15.75/15.61 all V_a (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.75/15.61 all V_b (c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.75/15.61 all V_d_2 V_m_2 (c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<-> (exists B_q (V_m_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q)))).
% 15.75/15.61 all V_m (c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.61 all V_n V_m ((hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))=V_n->c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))!=V_n->c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)=hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))).
% 15.75/15.61 all V_n V_m V_k (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)))).
% 15.75/15.61 all V_n V_m V_f (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))))).
% 15.75/15.61 all V_y_2 V_n_2 V_x_2 (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_n_2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_n_2)<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x_2),V_y_2)))).
% 15.75/15.61 all V_q V_b V_r V_c (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_c)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_r,V_b)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)))).
% 15.75/15.61 all V_k_2 V_n_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))<-> (V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hBOOL(hAPP(V_P_2,V_n_2)))& (V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (all B_i B_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2)-> (V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)->hBOOL(hAPP(V_P_2,B_j))))))).
% 15.75/15.61 all V_m V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_k)->c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k)=c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 15.75/15.61 all V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b)).
% 15.75/15.61 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)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))).
% 15.75/15.61 all V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 15.75/15.61 all V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)).
% 15.75/15.61 all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c)).
% 15.75/15.61 all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)).
% 15.75/15.61 all V_b V_a V_c T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))).
% 15.75/15.61 all V_b V_c V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c)).
% 15.75/15.61 all V_b V_c V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)).
% 15.75/15.61 all V_b_H V_b V_a_H V_c V_a T_a (class_Divides_Osemiring__div(T_a)-> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c)=c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)-> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c)=c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c)))).
% 15.75/15.61 all V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b)).
% 15.75/15.61 all V_a V_b T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b)).
% 15.75/15.61 all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)).
% 15.75/15.61 all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c)).
% 15.75/15.61 all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)).
% 15.75/15.61 all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)).
% 15.75/15.61 all V_b V_c V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)).
% 15.75/15.61 all V_b_H V_b V_a_H V_c V_a T_a (class_Divides_Osemiring__div(T_a)-> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c)=c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)-> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c)=c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c)))).
% 15.75/15.61 all V_b_H V_b V_a_H V_c V_a T_a (class_Divides_Oring__div(T_a)-> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c)=c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)-> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c)=c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c)))).
% 15.75/15.61 all V_c V_b V_a T_a (class_Divides_Oring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)).
% 15.75/15.61 all V_c V_b V_a T_a (class_Divides_Oring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c)).
% 15.75/15.61 all V_c V_b V_a T_a (class_Divides_Oring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)).
% 15.75/15.61 all V_b V_a T_a (class_Divides_Oring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b)=c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b)).
% 15.75/15.61 all V_a_H V_b V_a T_a (class_Divides_Oring__div(T_a)-> (c_Divides_Odiv__class_Omod(T_a,V_a,V_b)=c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)->c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b)=c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_H),V_b))).
% 15.75/15.61 all V_m_2 V_n_2 V_k_2 T_b (class_Divides_Osemiring__div(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2))))).
% 15.75/15.61 all V_a V_b V_c T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))->c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,V_a,V_c))).
% 15.75/15.61 all V_n V_m V_k T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))))).
% 15.75/15.61 all V_n V_m V_k T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))))).
% 15.75/15.61 all V_a V_b T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_b V_c V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b)).
% 15.75/15.61 all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b)).
% 15.75/15.61 all V_d_2 V_x_2 V_f_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_d_2)-> (hAPP(V_f_2,V_x_2)!=c_Groups_Ozero__class_Ozero(T_b)->c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,T_b),c_Rings_Oinverse__class_Oinverse(T_b)),V_f_2),V_x_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_d_2),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))))))))).
% 15.75/15.61 all V_k V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))).
% 15.75/15.61 all V_m V_n (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))).
% 15.75/15.61 all V_n V_m (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n)),V_n))).
% 15.75/15.61 all V_b V_a (V_a=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))).
% 15.75/15.61 all V_c V_b V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c))).
% 15.75/15.61 all V_k V_a V_b (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k)).
% 15.75/15.61 all V_k V_b V_a (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k)).
% 15.75/15.61 all V_c V_b V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c))).
% 15.75/15.61 all V_b V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.75/15.61 all V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)&c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_a).
% 15.75/15.61 all V_x V_y T_a (class_Divides_Oring__div(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))->c_Divides_Odiv__class_Odiv(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x),V_y)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)))).
% 15.75/15.61 all V_x V_y T_a (class_Divides_Oring__div(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))->c_Divides_Odiv__class_Odiv(T_a,V_x,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)))).
% 15.75/15.61 all V_n V_x V_y T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),V_n)=c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)))).
% 15.75/15.61 all V_ca_2 V_b_2 V_a_2 T_b (class_Divides_Osemiring__div(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ca_2))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2)),c_Divides_Odiv__class_Odiv(T_b,V_ca_2,V_a_2)))<->hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_ca_2)))))).
% 15.75/15.61 all V_a (V_a!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a)=c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 15.75/15.61 all V_b (c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.75/15.61 all V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a).
% 15.75/15.61 all V_y V_x V_z T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y),V_z)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_z)),c_Divides_Odiv__class_Odiv(T_a,V_y,V_z))))).
% 15.75/15.61 all V_w V_z V_x V_y T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),c_Divides_Odiv__class_Odiv(T_a,V_w,V_z))=c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z))))).
% 15.75/15.61 all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_c)=c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c),V_a))).
% 15.75/15.61 all V_b V_a T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_a)=V_b)).
% 15.75/15.61 all V_a V_b V_c T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_c))=c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c))).
% 15.75/15.61 all V_b V_a T_a (class_Divides_Osemiring__div(T_a)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a))=V_b)).
% 15.75/15.61 all V_a T_a (class_Divides_Osemiring__div(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,V_a,V_a)=c_Groups_Oone__class_Oone(T_a))).
% 15.75/15.61 all V_m V_n (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n))=V_m).
% 15.75/15.61 all V_b V_a V_c T_a (class_Divides_Osemiring__div(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))).
% 15.75/15.61 all V_b V_a V_c T_a (class_Divides_Osemiring__div(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))).
% 15.75/15.61 all V_a V_b T_a (class_Divides_Osemiring__div(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b)=V_a)).
% 15.75/15.61 all V_a V_b T_a (class_Divides_Osemiring__div(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b)=V_a)).
% 15.75/15.61 all V_b V_a V_c T_a (class_Divides_Osemiring__div(T_a)-> (V_c=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=c_Groups_Ozero__class_Ozero(T_a))& (V_c!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))).
% 15.75/15.61 all V_b V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)).
% 15.75/15.61 all V_b V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)).
% 15.75/15.61 all V_a_2 V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))).
% 15.75/15.61 all V_a_2 V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2))).
% 15.75/15.61 all V_b V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))).
% 15.75/15.61 all V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_a)).
% 15.75/15.61 all V_b V_a T_a (class_Fields_Ofield(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))).
% 15.75/15.61 all T_a (class_Fields_Ofield__inverse__zero(T_a)->hAPP(c_Rings_Oinverse__class_Oinverse(T_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))).
% 15.75/15.61 all V_x_2 T_b (class_Fields_Ofield__inverse__zero(T_b)-> (hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_x_2)=c_Groups_Oone__class_Oone(T_b)<->V_x_2=c_Groups_Oone__class_Oone(T_b))).
% 15.75/15.61 all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 15.75/15.61 all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 15.75/15.61 all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))))).
% 15.75/15.61 all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a))))).
% 15.75/15.61 all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a))))).
% 15.75/15.61 all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))).
% 15.75/15.61 all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a))-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)))).
% 15.75/15.61 all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)))).
% 15.75/15.61 all V_a_2 T_b (class_Fields_Olinordered__field__inverse__zero(T_b)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))<->c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)))).
% 15.75/15.61 all V_a_2 T_b (class_Fields_Olinordered__field__inverse__zero(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2))).
% 15.75/15.61 all V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)-> (hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)=hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)->V_a=V_b)).
% 15.75/15.61 all V_b_2 V_a_2 T_b (class_Rings_Odivision__ring__inverse__zero(T_b)-> (hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2)=hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_b_2)<->V_a_2=V_b_2)).
% 15.75/15.61 all V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a))=V_a).
% 15.75/15.61 all V_n V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),V_n)).
% 15.75/15.61 all T_a (class_Rings_Odivision__ring(T_a)->hAPP(c_Rings_Oinverse__class_Oinverse(T_a),c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a)).
% 15.75/15.61 all T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->hAPP(c_Rings_Oinverse__class_Oinverse(T_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.61 all V_a_2 T_b (class_Rings_Odivision__ring__inverse__zero(T_b)-> (hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2)=c_Groups_Ozero__class_Ozero(T_b)<->V_a_2=c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.61 all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)!=c_Groups_Ozero__class_Ozero(T_a))).
% 15.75/15.61 all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a))=V_a)).
% 15.75/15.61 all V_a T_a (class_Rings_Odivision__ring(T_a)-> (hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)->V_a=c_Groups_Ozero__class_Ozero(T_a))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)=hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->V_a=V_b)))).
% 15.75/15.61 all V_n V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),V_n))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)=c_Groups_Oone__class_Oone(T_a)->hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)=V_b)).
% 15.75/15.61 all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a))))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Odivision__ring(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))).
% 15.75/15.61 all V_a T_a (class_Fields_Ofield(T_a)->hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)).
% 15.75/15.61 all V_a T_a (class_Rings_Odivision__ring(T_a)->hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))))).
% 15.75/15.61 all V_b V_a T_a (class_Fields_Ofield(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a))),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))))).
% 15.75/15.61 all V_x_2 T_b (class_Fields_Olinordered__field__inverse__zero(T_b)-> (c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_x_2))<->c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_x_2)&c_Orderings_Oord__class_Oless(T_b,V_x_2,c_Groups_Oone__class_Oone(T_b)))).
% 15.75/15.61 all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a))))).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a))),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))))).
% 15.75/15.61 all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),V_a)=c_Groups_Oone__class_Oone(T_a))).
% 15.75/15.61 all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a))=c_Groups_Oone__class_Oone(T_a))).
% 15.75/15.61 all V_a T_a (class_Fields_Ofield(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),V_a)=c_Groups_Oone__class_Oone(T_a))).
% 15.75/15.61 all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))).
% 15.75/15.61 all V_k V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x))).
% 15.75/15.61 all V_b V_a V_c (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c)).
% 15.75/15.61 all V_r V_q V_y V_x V_a T_a (class_Fields_Ofield(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)->c_Polynomial_Opdivmod__rel(T_a,V_x,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_y),hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),V_q),V_r)))).
% 15.75/15.61 all V_c V_a V_b T_a (class_Divides_Osemiring__div(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))).
% 15.75/15.61 all V_c V_a V_b T_a (class_Divides_Osemiring__div(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))).
% 15.75/15.61 all V_a V_b T_a (class_Divides_Osemiring__div(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Groups_Oone__class_Oone(T_a)))).
% 15.75/15.61 all V_a V_b T_a (class_Divides_Osemiring__div(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Groups_Oone__class_Oone(T_a)))).
% 15.75/15.61 all V_d_2 V_b_2 V_ca_2 V_a_2 T_b (class_Divides_Osemiring__div(T_b)-> (V_a_2!=c_Groups_Ozero__class_Ozero(T_b)-> (V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_ca_2),V_d_2))-> (c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2)=c_Divides_Odiv__class_Odiv(T_b,V_d_2,V_ca_2)<->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2))))))).
% 15.75/15.61 all V_ca_2 V_b_2 V_a_2 T_b (class_Divides_Osemiring__div(T_b)-> (V_a_2!=c_Groups_Ozero__class_Ozero(T_b)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))-> (c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2)=V_ca_2<->V_b_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2))))).
% 15.75/15.61 all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)).
% 15.75/15.61 all V_c V_a V_b T_a (class_Divides_Osemiring__div(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)).
% 15.75/15.61 all V_b V_a T_a (class_Divides_Osemiring__div(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))=V_a).
% 15.75/15.61 all V_a V_b T_a (class_Divides_Osemiring__div(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))=V_a).
% 15.75/15.61 all V_b V_a T_a (class_Divides_Osemiring__div(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b))=V_a).
% 15.75/15.61 all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)))))).
% 15.75/15.61 all V_b V_a V_c (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)->c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))).
% 15.75/15.61 all V_a V_b (V_b!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)-> (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)))& (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)))).
% 15.75/15.61 all V_a V_b (V_b!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)-> (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)))& (c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)))).
% 15.75/15.61 all V_D_2 V_x_2 V_f_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)-> (hAPP(V_f_2,V_x_2)!=c_Groups_Ozero__class_Ozero(T_b)->c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,T_b),c_Rings_Oinverse__class_Oinverse(T_b)),V_f_2),V_x_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),hAPP(V_f_2,V_x_2))),V_D_2)),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),hAPP(V_f_2,V_x_2)))))))).
% 15.75/15.61 all V_h V_b V_a T_a (class_RealVector_Oreal__normed__field(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))),V_h)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_h))),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)))))).
% 15.75/15.61 all V_x T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_x),c_Polynomial_Odegree(T_a,V_x)))),V_x)).
% 15.75/15.61 all V_x_2 T_b (class_RealVector_Oreal__normed__field(T_b)-> (V_x_2!=c_Groups_Ozero__class_Ozero(T_b)->c_Deriv_Oderiv(T_b,c_Rings_Oinverse__class_Oinverse(T_b),V_x_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_x_2)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))).
% 15.75/15.61 all V_x V_y T_a (class_Fields_Ofield(T_a)-> (V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_x),c_Polynomial_Odegree(T_a,V_x)))),V_x))& (V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=c_Polynomial_Opoly__gcd(T_a,V_y,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)))).
% 15.75/15.61 all V_n_2 V_P_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))<-> (all B_i B_j (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j)&c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))&V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)->hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)))))).
% 15.75/15.61 all V_n_2 V_P_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)-> (hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))<-> (all B_i B_j (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j)&c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)&V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)->hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)))))).
% 15.75/15.61 all V_x T_a (class_Orderings_Opreorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x)).
% 15.75/15.61 all V_c V_b V_a (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_b,V_c))),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c)),V_c))).
% 15.75/15.61 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)))).
% 15.75/15.61 all V_k 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_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k),V_m)).
% 15.75/15.61 all V_m (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=V_m).
% 15.75/15.61 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y)))).
% 15.75/15.61 all V_c V_b V_a (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c)).
% 15.75/15.61 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.61 all V_y V_x T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))).
% 15.75/15.61 all V_a_2 T_b (class_Fields_Olinordered__field__inverse__zero(T_b)-> (c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2))<->c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2))).
% 15.75/15.61 all V_a_2 T_b (class_Fields_Olinordered__field__inverse__zero(T_b)-> (c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))<->c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)))).
% 15.75/15.61 all V_r V_q V_y V_x T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)->c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)=V_q)).
% 15.75/15.61 all V_z V_y V_x T_a (class_Fields_Ofield(T_a)->c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z))=c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z)).
% 15.75/15.61 all V_y V_x T_a (class_Fields_Ofield(T_a)->c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_x),V_y)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y))).
% 15.75/15.61 all V_y V_x T_a (class_Fields_Ofield(T_a)->c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_y))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y))).
% 15.75/15.61 all V_y V_x V_a T_a (class_Fields_Ofield(T_a)->c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_x),V_y)=hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y))).
% 15.75/15.61 all V_n V_m V_k ((V_k=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (V_k!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n))).
% 15.75/15.61 all V_y_2 V_x_2 V_f_2 T_b (class_Orderings_Oorder(T_b)-> (c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))->c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2))))).
% 15.75/15.61 all V_n V_m V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)).
% 15.75/15.61 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n)=V_m).
% 15.75/15.61 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n)=V_m).
% 15.75/15.61 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)-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))-> (hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))->V_m=V_n)))).
% 15.75/15.61 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)))).
% 15.75/15.61 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)))).
% 15.75/15.61 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))))))).
% 15.75/15.61 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))))))).
% 15.75/15.61 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))))).
% 15.75/15.61 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))))).
% 15.75/15.61 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))))).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Groups_Ocancel__ab__semigroup__add(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Rings_Oring__1__no__zero__divisors(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Rings_Oring__no__zero__divisors(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Groups_Ocancel__semigroup__add(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Groups_Oab__semigroup__mult(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Groups_Ocomm__monoid__mult(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Groups_Oab__semigroup__add(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Rings_Ono__zero__divisors(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Groups_Ocomm__monoid__add(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Rings_Ocomm__semiring__1(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Rings_Ocomm__semiring__0(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Rings_Ocomm__semiring(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Groups_Oab__group__add(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Rings_Ozero__ne_q__one(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Groups_Omonoid__mult(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Rings_Ocomm__ring__1(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Groups_Omonoid__add(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Rings_Osemiring__0(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Groups_Ogroup__add(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Rings_Omult__zero(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Rings_Ocomm__ring(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Rings_Osemiring(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Groups_Ouminus(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Rings_Oring__1(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Groups_Ominus(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Power_Opower(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Groups_Ozero(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Rings_Oring(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Groups_Oone(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Rings_Odvd(T)).
% 15.75/15.61 all T (class_Rings_Oidom(T)->class_Groups_Ocancel__comm__monoid__add(T)).
% 15.75/15.61 all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 15.75/15.61 class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat).
% 15.75/15.61 class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint).
% 15.75/15.61 all T_2 T_1 (class_Lattices_Oboolean__algebra(T_1)->class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))).
% 15.75/15.61 all T_2 T_1 (class_Orderings_Opreorder(T_1)->class_Orderings_Opreorder(tc_fun(T_2,T_1))).
% 15.75/15.61 all T_2 T_1 (class_Orderings_Oorder(T_1)->class_Orderings_Oorder(tc_fun(T_2,T_1))).
% 15.75/15.61 all T_2 T_1 (class_Orderings_Oord(T_1)->class_Orderings_Oord(tc_fun(T_2,T_1))).
% 15.75/15.61 all T_2 T_1 (class_Groups_Ouminus(T_1)->class_Groups_Ouminus(tc_fun(T_2,T_1))).
% 15.75/15.61 all T_2 T_1 (class_Groups_Ominus(T_1)->class_Groups_Ominus(tc_fun(T_2,T_1))).
% 15.75/15.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 15.75/15.61 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 15.75/15.61 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 15.75/15.61 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 15.75/15.61 class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 15.75/15.61 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 15.75/15.61 class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 15.75/15.61 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 15.75/15.61 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 15.75/15.61 class_Rings_Oordered__cancel__semiring(tc_Int_Oint).
% 15.75/15.61 class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 15.75/15.61 class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 15.75/15.61 class_Rings_Oordered__comm__semiring(tc_Int_Oint).
% 15.75/15.61 class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 15.75/15.61 class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 15.75/15.61 class_Rings_Olinordered__semidom(tc_Int_Oint).
% 15.75/15.61 class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 15.75/15.61 class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 15.75/15.61 class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 15.75/15.61 class_Rings_Oordered__semiring(tc_Int_Oint).
% 15.75/15.61 class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 15.75/15.61 class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 15.75/15.61 class_Rings_Olinordered__ring(tc_Int_Oint).
% 15.75/15.61 class_Rings_Olinordered__idom(tc_Int_Oint).
% 15.75/15.61 class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 15.75/15.61 class_Rings_Ocomm__semiring__0(tc_Int_Oint).
% 15.75/15.61 class_Divides_Osemiring__div(tc_Int_Oint).
% 15.75/15.61 class_Rings_Ocomm__semiring(tc_Int_Oint).
% 15.75/15.61 class_Groups_Oab__group__add(tc_Int_Oint).
% 15.75/15.61 class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 15.75/15.61 class_Rings_Oordered__ring(tc_Int_Oint).
% 15.75/15.61 class_Orderings_Opreorder(tc_Int_Oint).
% 15.75/15.61 class_Orderings_Olinorder(tc_Int_Oint).
% 15.75/15.61 class_Groups_Omonoid__mult(tc_Int_Oint).
% 15.75/15.61 class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 15.75/15.61 class_Groups_Omonoid__add(tc_Int_Oint).
% 15.75/15.61 class_Rings_Osemiring__0(tc_Int_Oint).
% 15.75/15.61 class_Groups_Ogroup__add(tc_Int_Oint).
% 15.75/15.61 class_Divides_Oring__div(tc_Int_Oint).
% 15.75/15.61 class_Rings_Omult__zero(tc_Int_Oint).
% 15.75/15.61 class_Rings_Ocomm__ring(tc_Int_Oint).
% 15.75/15.61 class_Orderings_Oorder(tc_Int_Oint).
% 15.75/15.61 class_Int_Oring__char__0(tc_Int_Oint).
% 15.75/15.61 class_Rings_Osemiring(tc_Int_Oint).
% 15.75/15.61 class_Orderings_Oord(tc_Int_Oint).
% 15.75/15.61 class_Groups_Ouminus(tc_Int_Oint).
% 15.75/15.61 class_Groups_Osgn__if(tc_Int_Oint).
% 15.75/15.61 class_Rings_Oring__1(tc_Int_Oint).
% 15.75/15.61 class_Groups_Ominus(tc_Int_Oint).
% 15.75/15.61 class_Power_Opower(tc_Int_Oint).
% 15.75/15.61 class_Groups_Ozero(tc_Int_Oint).
% 15.75/15.61 class_Rings_Oring(tc_Int_Oint).
% 15.75/15.61 class_Rings_Oidom(tc_Int_Oint).
% 15.75/15.61 class_Groups_Oone(tc_Int_Oint).
% 15.75/15.61 class_Rings_Odvd(tc_Int_Oint).
% 15.75/15.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 15.75/15.61 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 15.75/15.61 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 15.75/15.61 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 15.75/15.61 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 15.75/15.61 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 15.75/15.61 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 15.75/15.61 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 15.75/15.61 class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 15.75/15.61 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 15.75/15.61 class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 15.75/15.61 class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 15.75/15.61 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 15.75/15.61 class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 15.75/15.61 class_Rings_Oordered__semiring(tc_Nat_Onat).
% 15.75/15.61 class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 15.75/15.61 class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 15.75/15.61 class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 15.75/15.61 class_Rings_Ocomm__semiring__0(tc_Nat_Onat).
% 15.75/15.61 class_Divides_Osemiring__div(tc_Nat_Onat).
% 15.75/15.61 class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 15.75/15.61 class_Orderings_Owellorder(tc_Nat_Onat).
% 15.75/15.61 class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 15.75/15.61 class_Orderings_Opreorder(tc_Nat_Onat).
% 15.75/15.61 class_Orderings_Olinorder(tc_Nat_Onat).
% 15.75/15.61 class_Groups_Omonoid__mult(tc_Nat_Onat).
% 15.75/15.61 class_Groups_Omonoid__add(tc_Nat_Onat).
% 15.75/15.61 class_Rings_Osemiring__0(tc_Nat_Onat).
% 15.75/15.61 class_Rings_Omult__zero(tc_Nat_Onat).
% 15.75/15.61 class_Orderings_Oorder(tc_Nat_Onat).
% 15.75/15.61 class_Rings_Osemiring(tc_Nat_Onat).
% 15.75/15.61 class_Orderings_Oord(tc_Nat_Onat).
% 15.75/15.61 class_Groups_Ominus(tc_Nat_Onat).
% 15.75/15.61 class_Power_Opower(tc_Nat_Onat).
% 15.75/15.61 class_Groups_Ozero(tc_Nat_Onat).
% 15.75/15.61 class_Groups_Oone(tc_Nat_Onat).
% 15.75/15.61 class_Rings_Odvd(tc_Nat_Onat).
% 15.75/15.61 class_Lattices_Oboolean__algebra(tc_HOL_Obool).
% 15.75/15.61 class_Orderings_Opreorder(tc_HOL_Obool).
% 15.75/15.61 class_Orderings_Oorder(tc_HOL_Obool).
% 15.75/15.61 class_Orderings_Oord(tc_HOL_Obool).
% 15.75/15.61 class_Groups_Ouminus(tc_HOL_Obool).
% 15.75/15.61 class_Groups_Ominus(tc_HOL_Obool).
% 15.75/15.61 all T_1 (class_Rings_Oidom(T_1)->class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Oidom(T_1)->class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Fields_Ofield(T_1)->class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Fields_Ofield(T_1)->class_Divides_Oring__div(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Oorder(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Osemiring(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Oord(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ouminus(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Oring__1(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ominus(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Power_Opower(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Groups_Ozero(T_1)->class_Groups_Ozero(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Oring(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oidom(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Oone(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Odvd(tc_Polynomial_Opoly(T_1))).
% 15.75/15.62 all V_P T_a (hAPP(c_COMBI(T_a),V_P)=V_P).
% 15.75/15.62 all V_Q V_P T_b T_a (hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q)=V_P).
% 15.75/15.62 all V_R_2 V_Q_2 V_P_2 T_d T_b T_c (hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_P_2),V_Q_2),V_R_2)=hAPP(V_P_2,hAPP(V_Q_2,V_R_2))).
% 15.75/15.62 all V_R_2 V_Q_2 V_P_2 T_b T_d T_c (hAPP(hAPP(c_COMBC(T_c,T_d,T_b,V_P_2),V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),V_Q_2)).
% 15.75/15.62 all V_R_2 V_Q_2 V_P_2 T_b T_d T_c (hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2))).
% 15.75/15.62 all V_y_2 V_x_2 (-hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2))|V_x_2=V_y_2).
% 15.75/15.62 all V_y_2 V_x_2 (V_x_2!=V_y_2|hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2))).
% 15.75/15.62 -hBOOL(c_fFalse).
% 15.75/15.62 hBOOL(c_fTrue).
% 15.75/15.62 all V_P_2 (-hBOOL(hAPP(c_fNot,V_P_2))| -hBOOL(V_P_2)).
% 15.75/15.62 all V_P_2 (-(-hBOOL(V_P_2))|hBOOL(hAPP(c_fNot,V_P_2))).
% 15.75/15.62 all V_Q_2 V_P_2 (-hBOOL(V_P_2)| -hBOOL(V_Q_2)|hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))).
% 15.75/15.62 all V_Q_2 V_P_2 (-hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))|hBOOL(V_P_2)).
% 15.75/15.62 all V_Q_2 V_P_2 (-hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))|hBOOL(V_Q_2)).
% 15.75/15.62 -(exists B_k B_a (B_a!=c_Groups_Ozero__class_Ozero(t_a)&B_k!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)& (exists B_q (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,B_q)),B_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____))& (all B_z (hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),B_z)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),c_Groups_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),B_k)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),B_a),B_q)),B_z))))))))).
% 15.75/15.62 class_Rings_Oidom(t_a).
% 15.75/15.62 end_of_list.
% 15.75/15.62
% 15.75/15.62 -------> usable clausifies to:
% 15.75/15.62
% 15.75/15.62 list(usable).
% 15.75/15.62 0 [] A=A.
% 15.75/15.62 0 [] hAPP(V_f_2,$f1(V_g_2,V_f_2))!=hAPP(V_g_2,$f1(V_g_2,V_f_2))|V_f_2=V_g_2.
% 15.75/15.62 0 [] -class_Rings_Oidom(t_a)| -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_p)).
% 15.75/15.62 0 [] -class_Rings_Oidom(t_a)|$c1!=c_Groups_Ozero__class_Ozero(t_a).
% 15.75/15.62 0 [] -class_Rings_Oidom(t_a)|hAPP(c_Polynomial_Opoly(t_a,v_cs____),$c1)!=c_Groups_Ozero__class_Ozero(t_a).
% 15.75/15.62 0 [] -class_Rings_Oidom(t_a)|$c2!=c_Groups_Ozero__class_Ozero(t_a).
% 15.75/15.62 0 [] -class_Rings_Oidom(t_a)|hAPP(c_Polynomial_Opoly(t_a,v_cs____),$c2)!=c_Groups_Ozero__class_Ozero(t_a).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),V_x)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))).
% 15.75/15.62 0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.62 0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)).
% 15.75/15.62 0 [] -class_Power_Opower(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.62 0 [] -class_Power_Opower(T_b)| -class_Rings_Omult__zero(T_b)| -class_Rings_Ono__zero__divisors(T_b)| -class_Rings_Ozero__ne_q__one(T_b)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Power_Opower(T_b)| -class_Rings_Omult__zero(T_b)| -class_Rings_Ono__zero__divisors(T_b)| -class_Rings_Ozero__ne_q__one(T_b)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] -class_Power_Opower(T_b)| -class_Rings_Omult__zero(T_b)| -class_Rings_Ono__zero__divisors(T_b)| -class_Rings_Ozero__ne_q__one(T_b)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)).
% 15.75/15.62 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n).
% 15.75/15.62 0 [] -class_Int_Oring__char__0(T_b)| -class_Rings_Oidom(T_b)|c_Polynomial_Opoly(T_b,V_pa_2)!=c_Polynomial_Opoly(T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.62 0 [] -class_Int_Oring__char__0(T_b)| -class_Rings_Oidom(T_b)|c_Polynomial_Opoly(T_b,V_pa_2)=c_Polynomial_Opoly(T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.62 0 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)|hAPP(V_f_2,B_x)=hAPP(V_f_2,B_y).
% 15.75/15.62 0 [] c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(T_b,T_c,V_f_2)|hAPP(V_f_2,$f3(V_f_2,T_c,T_b))!=hAPP(V_f_2,$f2(V_f_2,T_c,T_b)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))=hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_b,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_b,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2)!=hAPP(hAPP(c_Polynomial_OpCons(T_b),V_b_2),V_q_2)|V_a_2=V_b_2.
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2)!=hAPP(hAPP(c_Polynomial_OpCons(T_b),V_b_2),V_q_2)|V_pa_2=V_q_2.
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2)=hAPP(hAPP(c_Polynomial_OpCons(T_b),V_b_2),V_q_2)|V_a_2!=V_b_2|V_pa_2!=V_q_2.
% 15.75/15.62 0 [] -class_Int_Oring__char__0(T_b)| -class_Rings_Oidom(T_b)|c_Polynomial_Opoly(T_b,V_pa_2)!=c_Polynomial_Opoly(T_b,V_q_2)|V_pa_2=V_q_2.
% 15.75/15.62 0 [] -class_Int_Oring__char__0(T_b)| -class_Rings_Oidom(T_b)|c_Polynomial_Opoly(T_b,V_pa_2)=c_Polynomial_Opoly(T_b,V_q_2)|V_pa_2!=V_q_2.
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|V_b_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|V_b_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 15.75/15.62 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))|V_w_2=V_x_2|V_y_2=V_z_2.
% 15.75/15.62 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))|V_w_2!=V_x_2.
% 15.75/15.62 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))|V_y_2!=V_z_2.
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 15.75/15.62 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|V_a_2=V_b_2|V_ca_2=V_d_2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)).
% 15.75/15.62 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|V_a_2!=V_b_2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)).
% 15.75/15.62 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)|V_ca_2!=V_d_2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a.
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a.
% 15.75/15.62 0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)!=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)).
% 15.75/15.62 0 [] -class_Groups_Ocomm__monoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)).
% 15.75/15.62 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 15.75/15.62 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_x.
% 15.75/15.62 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_a.
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_a_2!=c_Groups_Ozero__class_Ozero(T_b)|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_a)|hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.75/15.62 0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_b),V_q))=hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x)=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n).
% 15.75/15.62 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_r=c_Groups_Ozero__class_Ozero(T_a)|V_a!=V_b|V_c=V_d|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)).
% 15.75/15.62 0 [] -class_Rings_Oidom(t_a)| -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____))).
% 15.75/15.62 0 [] -class_Rings_Olinordered__ring__strict(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(T_b)|V_x_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Rings_Olinordered__ring__strict(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(T_b)|V_y_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Rings_Olinordered__ring__strict(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(T_b)|V_x_2!=c_Groups_Ozero__class_Ozero(T_b)|V_y_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Power_Opower(T_b)|c_Power_Opower__class_Opower(T_b)=c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b)).
% 15.75/15.62 0 [] -class_Rings_Oidom(t_a)|$c4!=c_Groups_Ozero__class_Ozero(t_a).
% 15.75/15.62 0 [] -class_Rings_Oidom(t_a)|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,$c3)),$c5))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,v_cs____).
% 15.75/15.62 0 [] -class_Rings_Oidom(t_a)|hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),$c5)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),$c4),$c3)),B_z)).
% 15.75/15.62 0 [] V_m!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)|V_n=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)!=V_m|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=V_n.
% 15.75/15.62 0 [] -class_Groups_Ocomm__monoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a.
% 15.75/15.62 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a.
% 15.75/15.62 0 [] -class_Groups_Ocomm__monoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a.
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.75/15.62 0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q)=V_q.
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.75/15.62 0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=V_p.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_r)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)|V_m_2=V_n_2.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)|V_m_2!=V_n_2.
% 15.75/15.62 0 [] hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2))=hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),V_n_2)).
% 15.75/15.62 0 [] hAPP(c_Nat_OSuc,V_x)!=hAPP(c_Nat_OSuc,V_y)|V_x=V_y.
% 15.75/15.62 0 [] hAPP(c_Nat_OSuc,V_nat_2)!=hAPP(c_Nat_OSuc,V_nat_H_2)|V_nat_2=V_nat_H_2.
% 15.75/15.62 0 [] hAPP(c_Nat_OSuc,V_nat_2)=hAPP(c_Nat_OSuc,V_nat_H_2)|V_nat_2!=V_nat_H_2.
% 15.75/15.62 0 [] hAPP(c_Nat_OSuc,V_n)!=V_n.
% 15.75/15.62 0 [] V_n!=hAPP(c_Nat_OSuc,V_n).
% 15.75/15.62 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_m).
% 15.75/15.62 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_nat_H).
% 15.75/15.62 0 [] hAPP(c_Nat_OSuc,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(c_Nat_OSuc,V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_m).
% 15.75/15.62 0 [] hAPP(c_Nat_OSuc,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_x_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.62 0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.62 0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.62 0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.62 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.62 0 [] hAPP(c_Nat_OSuc,V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n).
% 15.75/15.62 0 [] hAPP(c_Nat_OSuc,V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 15.75/15.62 0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n))=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Power_Opower(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)).
% 15.75/15.62 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_one_2.
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|c_Groups_Ozero__class_Ozero(T_b)!=V_x_2|V_x_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|c_Groups_Ozero__class_Ozero(T_b)=V_x_2|V_x_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Oab__semigroup__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 15.75/15.62 0 [] -class_Groups_Oab__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)).
% 15.75/15.62 0 [] -class_Groups_Ocancel__semigroup__add(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)|V_b_2=V_ca_2.
% 15.75/15.62 0 [] -class_Groups_Ocancel__semigroup__add(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)|V_b_2!=V_ca_2.
% 15.75/15.62 0 [] -class_Groups_Ocancel__semigroup__add(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)|V_b_2=V_ca_2.
% 15.75/15.62 0 [] -class_Groups_Ocancel__semigroup__add(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)|V_b_2!=V_ca_2.
% 15.75/15.62 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)|V_b=V_c.
% 15.75/15.62 0 [] -class_Groups_Ocancel__ab__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)|V_b=V_c.
% 15.75/15.62 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)|V_b=V_c.
% 15.75/15.62 0 [] -class_Groups_Oone(T_b)|c_Groups_Oone__class_Oone(T_b)!=V_x_2|V_x_2=c_Groups_Oone__class_Oone(T_b).
% 15.75/15.62 0 [] -class_Groups_Oone(T_b)|c_Groups_Oone__class_Oone(T_b)=V_x_2|V_x_2!=c_Groups_Oone__class_Oone(T_b).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2!=V_n_2.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)|V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)|V_m_2!=V_n_2.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2=V_n_2.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2!=V_n_2.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)|V_m_2=V_n_2.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)|V_m_2!=V_n_2.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)=V_n.
% 15.75/15.62 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.62 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.62 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.62 0 [] -class_Groups_Omonoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 15.75/15.62 0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 15.75/15.62 0 [] -class_Groups_Olinordered__ab__group__add(T_b)|c_Groups_Ozero__class_Ozero(T_b)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Olinordered__ab__group__add(T_b)|c_Groups_Ozero__class_Ozero(T_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Omonoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 15.75/15.62 0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 15.75/15.62 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a.
% 15.75/15.62 0 [] -class_Rings_Oidom(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))|$c7!=c_Groups_Ozero__class_Ozero(t_a).
% 15.75/15.62 0 [] -class_Rings_Oidom(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))|$c8!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] -class_Rings_Oidom(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,$c6)),$c8)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,v_cs____).
% 15.75/15.62 0 [] -class_Rings_Oidom(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))|hAPP(c_Polynomial_Opoly(t_a,v_cs____),B_z)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(t_a,v_cs____),c_Groups_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),B_z),$c8)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),$c7),$c6)),B_z))).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Opcompose(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),V_q)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q))).
% 15.75/15.62 0 [] -class_Rings_Oidom(T_b)|hAPP(c_Polynomial_Opoly(T_b,V_pa_2),V_a_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|c_Polynomial_Oorder(T_b,V_a_2,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] -class_Rings_Oidom(T_b)|hAPP(c_Polynomial_Opoly(T_b,V_pa_2),V_a_2)=c_Groups_Ozero__class_Ozero(T_b)|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.62 0 [] -class_Rings_Oidom(T_b)|hAPP(c_Polynomial_Opoly(T_b,V_pa_2),V_a_2)=c_Groups_Ozero__class_Ozero(T_b)|c_Polynomial_Oorder(T_b,V_a_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=V_n_2.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2!=V_n_2.
% 15.75/15.62 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_b_H))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)).
% 15.75/15.62 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 15.75/15.62 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_a_H)),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)).
% 15.75/15.62 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Opcompose(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),V_x)=hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)).
% 15.75/15.62 0 [] -class_Rings_Ono__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Rings_Ono__zero__divisors(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Rings_Oring__no__zero__divisors(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)|V_b_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Rings_Oring__no__zero__divisors(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Rings_Oring__no__zero__divisors(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_b)|V_b_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Rings_Omult__zero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Rings_Omult__zero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.62 0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Rings_Osemiring(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_b)|c_Polynomial_Opcompose(T_b,V_pa_2,V_q_2)=c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(T_b),T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBK(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBB(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),T_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))))),hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2))),V_pa_2).
% 15.75/15.62 0 [] -class_Rings_Ocomm__ring__1(T_a)|hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,c_Groups_Oone__class_Oone(T_a),V_n)),V_p)),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)).
% 15.75/15.62 0 [] -class_Groups_Olinordered__ab__group__add(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Olinordered__ab__group__add(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_c)|hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_c)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c))),V_z_2)!=V_z_2|c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,hAPP(hAPP(c_Polynomial_OpCons(T_c),V_a_2),V_pa_2))=hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,V_pa_2)).
% 15.75/15.62 0 [] c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)),V_n)=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_c)|c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,hAPP(hAPP(c_Polynomial_OpCons(T_c),V_a_2),V_pa_2))=hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),hAPP(hAPP(hAPP(c_If(T_b),hAPP(c_fe_qual(V_pa_2),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c)))),V_z_2),c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,V_pa_2))).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),V_q)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_a)|V_m!=V_n|hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Omonom(T_a,V_a,V_m)),V_n)=V_a.
% 15.75/15.62 0 [] -class_Groups_Ozero(T_a)|V_m=V_n|hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Omonom(T_a,V_a,V_m)),V_n)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_n).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|V_pa_2!=V_q_2|hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),B_n)=hAPP(c_Polynomial_Ocoeff(T_b,V_q_2),B_n).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|V_pa_2=V_q_2|hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),$f4(V_q_2,V_pa_2,T_b))!=hAPP(c_Polynomial_Ocoeff(T_b,V_q_2),$f4(V_q_2,V_pa_2,T_b)).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|c_Polynomial_Ocoeff(T_b,V_x_2)!=c_Polynomial_Ocoeff(T_b,V_y_2)|V_x_2=V_y_2.
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|c_Polynomial_Ocoeff(T_b,V_x_2)=c_Polynomial_Ocoeff(T_b,V_y_2)|V_x_2!=V_y_2.
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|c_Polynomial_Omonom(T_b,V_a_2,V_n_2)!=c_Polynomial_Omonom(T_b,V_b_2,V_n_2)|V_a_2=V_b_2.
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|c_Polynomial_Omonom(T_b,V_a_2,V_n_2)=c_Polynomial_Omonom(T_b,V_b_2,V_n_2)|V_a_2!=V_b_2.
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_b),V_p))=hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_p).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),c_Groups_Oone__class_Oone(T_a)),V_p)=V_p.
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q))=hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_q)=hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 15.75/15.62 0 [] c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_n)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_p)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.75/15.62 0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_a_2=c_Groups_Ozero__class_Ozero(T_b)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.62 0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_b),V_p))=hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_a.
% 15.75/15.62 0 [] -class_Groups_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),hAPP(c_Nat_OSuc,V_n))=hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),V_p)!=hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.75/15.62 0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_p)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_b),V_p)).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|c_Polynomial_Omonom(T_b,V_a_2,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|c_Polynomial_Omonom(T_b,V_a_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_n)),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_n).
% 15.75/15.62 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),V_p)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p))!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)=c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(T_b),T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBK(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBB(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),T_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b))),hAPP(c_COMBC(T_b,tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),c_Polynomial_Osmult(T_b)),V_q_2)))),hAPP(c_Polynomial_OpCons(T_b),c_Groups_Ozero__class_Ozero(T_b)))),V_pa_2).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,V_a,hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Polynomial_Omonom(T_a,V_a,V_n)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_m)),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_c)|hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_c)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c))),V_z_2)!=V_z_2|c_Polynomial_Opoly__rec(T_b,T_c,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_c)))=V_z_2.
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n)=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_q))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_b)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_b,V_pa_2,V_h_2)=c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(T_b),T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b))),T_b),c_COMBK(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),T_b),hAPP(c_COMBS(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b))),hAPP(c_Polynomial_Osmult(T_b),V_h_2)))),c_Polynomial_OpCons(T_b))),V_pa_2).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)))=hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),V_q))!=hAPP(hAPP(c_Polynomial_OpCons(T_a),V_r),V_q)|V_r=hAPP(c_Polynomial_Opoly(T_a,V_p),V_c).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_c),V_q))!=hAPP(hAPP(c_Polynomial_OpCons(T_a),V_r),V_q)|V_q=c_Polynomial_Osynthetic__div(T_a,V_p,V_c).
% 15.75/15.62 0 [] c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_nat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_Nat_Onat,V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),V_h)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_h),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))).
% 15.75/15.62 0 [] -class_Groups_Ocomm__monoid__add(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)=c_Polynomial_OAbs__poly(T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Oplus__class_Oplus(T_b)),c_Polynomial_Ocoeff(T_b,V_pa_2))),c_Polynomial_Ocoeff(T_b,V_q_2))).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_b)|hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_pa_2)=c_Polynomial_OAbs__poly(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2)),c_Polynomial_Ocoeff(T_b,V_pa_2))).
% 15.75/15.62 0 [] c_HOL_Obool_Obool__size(c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n)=V_n.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)=V_z.
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|c_Polynomial_OAbs__poly(T_b,c_Polynomial_Ocoeff(T_b,V_x_2))=V_x_2.
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_h)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_b)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_b,V_pa_2,V_h_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_b)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_b,V_pa_2,V_h_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.62 0 [] c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))=c_Polynomial_OAbs__poly(T_b,hAPP(c_COMBK(T_b,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|c_Polynomial_Omonom(T_b,V_a_2,V_m_2)=c_Polynomial_OAbs__poly(T_b,hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b,hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_fun(T_b,T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Nat_Onat),c_If(T_b)),c_fe_qual(V_m_2))),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),V_x)=hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_h),V_x)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osynthetic__div(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p),V_c)=hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h)=hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.75/15.62 0 [] c_HOL_Obool_Obool__size(c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] -class_Rings_Ocomm__ring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_c)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Osynthetic__div(T_a,V_p,V_c))),hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))=V_p.
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2)=c_Polynomial_OAbs__poly(T_b,c_Nat_Onat_Onat__case(T_b,V_a_2,c_Polynomial_Ocoeff(T_b,V_pa_2))).
% 15.75/15.62 0 [] V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.62 0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n))=V_n.
% 15.75/15.62 0 [] -class_Groups_Ozero(T_b)|c_Polynomial_Ocoeff(T_b,hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2))=c_Nat_Onat_Onat__case(T_b,V_a_2,c_Polynomial_Ocoeff(T_b,V_pa_2)).
% 15.75/15.62 0 [] V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_a)|V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p)=hAPP(c_Nat_OSuc,c_Polynomial_Odegree(T_a,V_p)).
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_b),V_q))=hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p))=hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_p)).
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_b)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a),V_p))=hAPP(hAPP(c_Polynomial_OpCons(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b)),V_p)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__ring(T_a)|hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__ring(T_a)|hAPP(c_Polynomial_Opoly(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_p)),V_x)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)).
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_a)|c_Polynomial_Odegree(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_p))=c_Polynomial_Odegree(T_a,V_p).
% 15.75/15.62 0 [] -class_Rings_Ocomm__ring__1(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))=V_a.
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_b)|V_a_2!=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)|V_b_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_b)|V_a_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)|V_b_2!=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_b)|hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)!=V_b_2|hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)=V_a_2.
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_b)|hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)=V_b_2|hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)!=V_a_2.
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_b)|hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)!=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)|V_a_2=V_b_2.
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_b)|hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)|V_a_2!=V_b_2.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j).
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_b)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)|V_a_2!=V_b_2|V_ca_2=V_d_2.
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_b)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)|V_a_2=V_b_2|V_ca_2!=V_d_2.
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b).
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a).
% 15.75/15.62 0 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.75/15.62 0 [] hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)=V_z.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)).
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_n)),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_n).
% 15.75/15.62 0 [] -class_Rings_Ocomm__ring(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_p)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_b),V_p)).
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_n)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__ring(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_p)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)).
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_p)),V_n)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)).
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_n))=c_Polynomial_Omonom(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_n).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_b)|V_a_2!=V_b_2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_b)|V_a_2=V_b_2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_b)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=V_b_2.
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_b)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=V_b_2.
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_b)|c_Groups_Ozero__class_Ozero(T_b)!=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)|c_Groups_Ozero__class_Ozero(T_b)=V_a_2.
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_b)|c_Groups_Ozero__class_Ozero(T_b)=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)|c_Groups_Ozero__class_Ozero(T_b)!=V_a_2.
% 15.75/15.62 0 [] -class_Groups_Olinordered__ab__group__add(T_b)|V_a_2!=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Olinordered__ab__group__add(T_b)|V_a_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_b)|hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_b)|hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Olinordered__ab__group__add(T_b)|hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)!=V_a_2|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Olinordered__ab__group__add(T_b)|hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)=V_a_2|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_b_H))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)).
% 15.75/15.62 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)).
% 15.75/15.62 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a_H)),V_b)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)).
% 15.75/15.62 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),V_ya)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b)=V_a.
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b)=V_a.
% 15.75/15.62 0 [] -class_Rings_Oring(T_a)|hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)).
% 15.75/15.62 0 [] -class_Rings_Oring(T_a)|hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b).
% 15.75/15.62 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 15.75/15.62 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)).
% 15.75/15.62 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 15.75/15.62 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)).
% 15.75/15.62 0 [] -class_Rings_Oring(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)).
% 15.75/15.62 0 [] -class_Rings_Oring(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b).
% 15.75/15.62 0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)|V_a_2=V_b_2|V_a_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2).
% 15.75/15.62 0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)|V_a_2!=V_b_2.
% 15.75/15.62 0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)|V_a_2!=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2).
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))=V_b.
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))=V_b.
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Odegree(T_a,c_Polynomial_Osynthetic__div(T_a,V_p,V_c))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Polynomial_Odegree(T_a,V_p)),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m=V_n.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n)=V_m.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n)=V_m.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)).
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__ring(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_p))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)).
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_b)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)=c_Polynomial_OAbs__poly(T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),c_Polynomial_Ocoeff(T_b,V_pa_2))),c_Polynomial_Ocoeff(T_b,V_q_2))).
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_b)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b)),V_pa_2)=c_Polynomial_OAbs__poly(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(T_b)),c_Polynomial_Ocoeff(T_b,V_pa_2))).
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))=hAPP(c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2)).
% 15.75/15.62 0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Odegree(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))=c_Polynomial_Odegree(T_a,V_p).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_b)|V_a_2!=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_b)|V_a_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.62 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)=V_b.
% 15.75/15.62 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_a)),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_b))).
% 15.75/15.62 0 [] -class_Rings_Oring(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)|V_ca_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2).
% 15.75/15.62 0 [] -class_Rings_Oring(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)|V_ca_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2).
% 15.75/15.62 0 [] -class_Rings_Oring(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2)=V_d_2.
% 15.75/15.62 0 [] -class_Rings_Oring(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2)!=V_d_2.
% 15.75/15.62 0 [] -class_Rings_Ocomm__ring__1(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x).
% 15.75/15.62 0 [] -class_Rings_Oring__1__no__zero__divisors(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)!=c_Groups_Oone__class_Oone(T_b)|V_x_2=c_Groups_Oone__class_Oone(T_b)|V_x_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)).
% 15.75/15.62 0 [] -class_Rings_Oring__1__no__zero__divisors(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)=c_Groups_Oone__class_Oone(T_b)|V_x_2!=c_Groups_Oone__class_Oone(T_b).
% 15.75/15.62 0 [] -class_Rings_Oring__1__no__zero__divisors(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)=c_Groups_Oone__class_Oone(T_b)|V_x_2!=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)).
% 15.75/15.62 0 [] -class_Groups_Ozero(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Polynomial_Odegree(T_a,c_Polynomial_Omonom(T_a,V_a,V_n))=V_n.
% 15.75/15.62 0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] hAPP(c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_f1_2.
% 15.75/15.63 0 [] hAPP(c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2))=hAPP(V_f2_2,V_nat_2).
% 15.75/15.63 0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n).
% 15.75/15.63 0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Polynomial_Odegree(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_a)|V_a!=c_Groups_Ozero__class_Ozero(T_a)|c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p))=c_Polynomial_Odegree(T_a,V_p).
% 15.75/15.63 0 [] -class_Groups_Ozero(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p))!=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_Groups_Ozero(T_b)|hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),c_Polynomial_Odegree(T_b,V_pa_2))!=c_Groups_Ozero__class_Ozero(T_b)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.63 0 [] -class_Groups_Ozero(T_b)|hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),c_Polynomial_Odegree(T_b,V_pa_2))=c_Groups_Ozero__class_Ozero(T_b)|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.63 0 [] -class_Rings_Oring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(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),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 15.75/15.63 0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] -class_Groups_Ozero(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p))=hAPP(c_Nat_OSuc,c_Polynomial_Odegree(T_a,V_p)).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_q=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Polynomial_Odegree(T_a,V_p)),c_Polynomial_Odegree(T_a,V_q)).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__0(T_b)|c_Polynomial_Osynthetic__div(T_b,V_pa_2,V_ca_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|c_Polynomial_Odegree(T_b,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__0(T_b)|c_Polynomial_Osynthetic__div(T_b,V_pa_2,V_ca_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|c_Polynomial_Odegree(T_b,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] -class_Groups_Ozero(T_a)|V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] -class_Groups_Ozero(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_p))=hAPP(c_Nat_OSuc,c_Polynomial_Odegree(T_a,V_p)).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Polynomial_Odegree(T_a,V_p)),c_Polynomial_Odegree(T_a,V_q)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p))),hAPP(c_Polynomial_Ocoeff(T_a,V_q),c_Polynomial_Odegree(T_a,V_q))).
% 15.75/15.63 0 [] V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=V_n.
% 15.75/15.63 0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)).
% 15.75/15.63 0 [] -class_Power_Opower(T_a)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.63 0 [] -class_Power_Opower(T_a)|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 15.75/15.63 0 [] -class_Rings_Ocomm__ring__1(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))!=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x_2=V_y_2|V_x_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x_2!=V_y_2.
% 15.75/15.63 0 [] -class_Rings_Oidom(T_b)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x_2!=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2).
% 15.75/15.63 0 [] -class_Rings_Oring__1(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),c_Groups_Oone__class_Oone(T_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),c_Groups_Oone__class_Oone(T_a))).
% 15.75/15.63 0 [] -class_Rings_Oring(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_a)),V_b)).
% 15.75/15.63 0 [] -class_Groups_Ogroup__add(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_y_2=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2).
% 15.75/15.63 0 [] -class_Groups_Ogroup__add(T_b)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)=c_Groups_Ozero__class_Ozero(T_b)|V_y_2!=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p))),V_p)).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(T_a,V_a,V_p)))),V_p)).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))).
% 15.75/15.63 0 [] hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.75/15.63 0 [] hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))=V_z.
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))|V_a=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)).
% 15.75/15.63 0 [] -class_Rings_Odvd(T_a)|V_a!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))).
% 15.75/15.63 0 [] -class_Rings_Ocomm__ring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)).
% 15.75/15.63 0 [] -class_Rings_Ocomm__ring__1(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)).
% 15.75/15.63 0 [] -class_Rings_Ocomm__ring__1(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)).
% 15.75/15.63 0 [] -class_Rings_Ocomm__ring__1(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)).
% 15.75/15.63 0 [] -class_Rings_Ocomm__ring__1(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))).
% 15.75/15.63 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w).
% 15.75/15.63 0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)).
% 15.75/15.63 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)).
% 15.75/15.63 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_q))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q))).
% 15.75/15.63 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=V_p.
% 15.75/15.63 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_q).
% 15.75/15.63 0 [] -class_Rings_Ocomm__ring(T_a)|hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),V_q))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q)).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))|V_ca_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)))|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)))|V_ca_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q)))|V_a=c_Groups_Ozero__class_Ozero(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))|V_a=c_Groups_Ozero__class_Ozero(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_p)),V_q)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_q_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_q_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p))!=hAPP(c_Polynomial_Ocoeff(T_a,V_q),c_Polynomial_Odegree(T_a,V_q))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_q),V_p))|V_p=V_q.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_pa_2)),V_q_2))|V_a_2!=c_Groups_Ozero__class_Ozero(T_b)|V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_pa_2)),V_q_2))|V_a_2=c_Groups_Ozero__class_Ozero(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_pa_2)),V_q_2))|V_a_2=c_Groups_Ozero__class_Ozero(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_pa_2)),V_q_2))|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_Osmult(T_b),V_a_2),V_pa_2)),V_q_2))|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_pa_2),V_q_2)).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),V_ca_2),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))))),V_pa_2))|hAPP(c_Polynomial_Opoly(T_b,V_pa_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ca_2))=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),V_ca_2),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))))),V_pa_2))|hAPP(c_Polynomial_Opoly(T_b,V_pa_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ca_2))!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_b)|hAPP(c_Polynomial_Opoly(T_b,V_pa_2),V_ca_2)!=c_Groups_Ozero__class_Ozero(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ca_2)),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))))),V_pa_2)).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_b)|hAPP(c_Polynomial_Opoly(T_b,V_pa_2),V_ca_2)=c_Groups_Ozero__class_Ozero(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ca_2)),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))))),V_pa_2)).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p))),V_p)).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(T_a,V_a,V_p)))),V_p)).
% 15.75/15.63 0 [] -class_Rings_Ocomm__ring(T_b)| -class_Rings_Odvd(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))).
% 15.75/15.63 0 [] -class_Rings_Ocomm__ring(T_b)| -class_Rings_Odvd(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))).
% 15.75/15.63 0 [] -class_Rings_Ocomm__ring(T_b)| -class_Rings_Odvd(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))).
% 15.75/15.63 0 [] -class_Rings_Ocomm__ring(T_b)| -class_Rings_Odvd(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))).
% 15.75/15.63 0 [] -class_Rings_Odvd(T_b)| -class_Rings_Osemiring__0(T_b)| -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),$f5(V_l_2,V_P_2,T_b)),c_Groups_Ozero__class_Ozero(T_b)))).
% 15.75/15.63 0 [] -class_Rings_Odvd(T_b)| -class_Rings_Osemiring__0(T_b)| -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))|hBOOL(hAPP(V_P_2,$f5(V_l_2,V_P_2,T_b))).
% 15.75/15.63 0 [] -class_Rings_Odvd(T_b)| -class_Rings_Osemiring__0(T_b)|hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),$f6(V_l_2,V_P_2,T_b))))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),X1),c_Groups_Ozero__class_Ozero(T_b))))| -hBOOL(hAPP(V_P_2,X1)).
% 15.75/15.63 0 [] -class_Rings_Oidom(T_b)|c_Polynomial_Oorder(T_b,V_a_2,V_pa_2)=c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot),hAPP(c_COMBC(tc_Nat_Onat,tc_Polynomial_Opoly(T_b),tc_HOL_Obool,hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(T_b),tc_fun(tc_Polynomial_Opoly(T_b),tc_HOL_Obool),tc_Nat_Onat),c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Polynomial_Opoly(T_b),tc_Nat_Onat),hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Polynomial_OpCons(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),hAPP(hAPP(c_Polynomial_OpCons(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))))),c_Nat_OSuc))),V_pa_2))).
% 15.75/15.63 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)).
% 15.75/15.63 0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d_2)),V_t_2)).
% 15.75/15.63 0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d_2)),V_t_2)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_t_2))).
% 15.75/15.63 0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_t_2))).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),V_n)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)).
% 15.75/15.63 0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.63 0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|V_m_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.63 0 [] V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2))).
% 15.75/15.63 0 [] V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2))).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n)))|V_k=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2))))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2)).
% 15.75/15.63 0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2))))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_d_2))),V_t_2))).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_d_2))),V_t_2))).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.63 0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_m_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)).
% 15.75/15.63 0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)).
% 15.75/15.63 0 [] -hBOOL(hAPP(V_P_2,V_n_2))|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2)=hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_OSuc))).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b),V_n)))|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)).
% 15.75/15.63 0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a_2),V_n_2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)).
% 15.75/15.63 0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a_2),V_n_2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)).
% 15.75/15.63 0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a_2),V_n_2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_b_2)).
% 15.75/15.63 0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a_2),V_n_2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_b_2)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b),V_n)))|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b)).
% 15.75/15.63 0 [] -class_Groups_Oab__group__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c),V_d)).
% 15.75/15.63 0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))|V_b!=V_c|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))|V_b!=V_c| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))|V_y!=V_x.
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))|V_x!=V_y.
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))|V_x!=V_y.
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)).
% 15.75/15.63 0 [] V_a!=V_b| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)).
% 15.75/15.63 0 [] V_a!=V_b| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))|V_x=V_y.
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))|V_m=V_n.
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))|V_b!=V_c|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)).
% 15.75/15.63 0 [] V_a!=V_b| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))|V_a=V_b| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))|V_x=V_y.
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))|V_x_2=V_y_2.
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))|V_x_2!=V_y_2.
% 15.75/15.63 0 [] V_x!=V_y|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)).
% 15.75/15.63 0 [] V_a=V_b| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))|V_x_2!=V_y_2.
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))|V_x_2=V_y_2.
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))|V_x_2=V_y_2.
% 15.75/15.63 0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))|V_x_2!=V_y_2.
% 15.75/15.63 0 [] V_x_2!=V_y_2|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)).
% 15.75/15.63 0 [] V_x_2!=V_y_2|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)).
% 15.75/15.63 0 [] V_x_2=V_y_2| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)).
% 15.75/15.63 0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.63 0 [] hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|V_x!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)))=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)))=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)))=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.63 0 [] -class_Orderings_Owellorder(T_b)| -hBOOL(hAPP(V_P_2,V_k_2))|hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))).
% 15.75/15.63 0 [] -class_Groups_Omonoid__mult(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n).
% 15.75/15.63 0 [] -class_Groups_Ouminus(T_b)|hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)).
% 15.75/15.63 0 [] -class_Groups_Ominus(T_b)|hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),hAPP(c_Nat_OSuc,V_n)).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(c_Nat_OSuc,V_n)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),V_x)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),V_y)).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semidom(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semidom(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),V_b_2)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_a)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,V_a,V_b)=c_Polynomial_Opoly__gcd(T_a,V_b,V_a).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,V_b,c_Polynomial_Opoly__gcd(T_a,V_a,V_c))=c_Polynomial_Opoly__gcd(T_a,V_a,c_Polynomial_Opoly__gcd(T_a,V_b,V_c)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,c_Polynomial_Opoly__gcd(T_a,V_a,V_b),V_c)=c_Polynomial_Opoly__gcd(T_a,V_a,c_Polynomial_Opoly__gcd(T_a,V_b,V_c)).
% 15.75/15.63 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 15.75/15.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 15.75/15.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 15.75/15.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 15.75/15.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_c,V_a).
% 15.75/15.63 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_a,V_c).
% 15.75/15.63 0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_c,V_b)|c_Orderings_Oord__class_Oless(T_a,V_c,V_a).
% 15.75/15.63 0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_c).
% 15.75/15.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 15.75/15.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 15.75/15.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_y!=V_x.
% 15.75/15.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 15.75/15.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 15.75/15.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 15.75/15.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 15.75/15.63 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 15.75/15.63 0 [] -class_Orderings_Olinorder(T_b)|c_Orderings_Oord__class_Oless(T_b,V_y_2,V_x_2)|c_Orderings_Oord__class_Oless(T_b,V_x_2,V_y_2)|V_x_2=V_y_2.
% 15.75/15.63 0 [] -class_Orderings_Olinorder(T_b)|c_Orderings_Oord__class_Oless(T_b,V_y_2,V_x_2)| -c_Orderings_Oord__class_Oless(T_b,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 15.75/15.63 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 15.75/15.63 0 [] -class_Orderings_Olinorder(T_b)|c_Orderings_Oord__class_Oless(T_b,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_b,V_y_2,V_x_2)|V_x_2=V_y_2.
% 15.75/15.63 0 [] -class_Orderings_Olinorder(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_b,V_y_2,V_x_2).
% 15.75/15.63 0 [] -class_Orderings_Olinorder(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 15.75/15.63 0 [] -class_Orderings_Olinorder(T_b)|V_x_2=V_y_2|c_Orderings_Oord__class_Oless(T_b,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_b,V_y_2,V_x_2).
% 15.75/15.63 0 [] -class_Orderings_Olinorder(T_b)|V_x_2!=V_y_2| -c_Orderings_Oord__class_Oless(T_b,V_x_2,V_y_2).
% 15.75/15.63 0 [] -class_Orderings_Olinorder(T_b)|V_x_2!=V_y_2| -c_Orderings_Oord__class_Oless(T_b,V_y_2,V_x_2).
% 15.75/15.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_x).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 15.75/15.63 0 [] V_m_2=V_n_2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 15.75/15.63 0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.75/15.63 0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 15.75/15.63 0 [] V_x=V_y|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)|V_m!=V_n.
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)|V_s!=V_t.
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)|hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)).
% 15.75/15.63 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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n),V_k).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 15.75/15.63 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_i).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_i).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,V_m_2)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,V_m_2)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2.
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))|V_m_2!=V_n_2.
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,V_m_2))|V_n_2=V_m_2.
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,V_m_2))|V_n_2!=V_m_2.
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(c_Nat_OSuc,V_m))|V_m=V_n.
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|hAPP(c_Nat_OSuc,V_m)=V_n|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n).
% 15.75/15.63 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,hAPP(c_Nat_OSuc,V_i),V_k).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_m=V_n.
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),hAPP(c_Nat_OSuc,V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 15.75/15.63 0 [] V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.63 0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 15.75/15.63 0 [] V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2),V_b_2)|c_Orderings_Oord__class_Oless(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2),V_a_2).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2),V_a_2).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))|c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__group__add(T_b)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,V_d_2).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__group__add(T_b)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,V_d_2).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 15.75/15.63 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)).
% 15.75/15.63 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)).
% 15.75/15.63 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.75/15.63 0 [] -class_Orderings_Owellorder(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_k_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))| -hBOOL(hAPP(V_P_2,V_k_2)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opoly__gcd(T_b,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_x_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opoly__gcd(T_b,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opoly__gcd(T_b,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_x_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_y_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_k_2),c_Polynomial_Opoly__gcd(T_b,V_x_2,V_y_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_k_2),V_x_2)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_k_2),c_Polynomial_Opoly__gcd(T_b,V_x_2,V_y_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_k_2),V_y_2)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_k_2),c_Polynomial_Opoly__gcd(T_b,V_x_2,V_y_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_k_2),V_x_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_b)),V_k_2),V_y_2)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k),c_Polynomial_Opoly__gcd(T_a,V_x,V_y))).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_x),V_y)=c_Polynomial_Opoly__gcd(T_a,V_x,V_y).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_y))=c_Polynomial_Opoly__gcd(T_a,V_x,V_y).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)),V_y)=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))|c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_b,V_b_2,V_a_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__comm__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2),c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Groups_Olinordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.63 0 [] -class_Groups_Olinordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.63 0 [] -class_Groups_Olinordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Groups_Olinordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2),c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)).
% 15.75/15.63 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.63 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Groups_Olinordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2),V_a_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.63 0 [] -class_Groups_Olinordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__group__add(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Groups_Oordered__ab__group__add(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semidom(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),V_a_2)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2)!=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)|V_m_2=V_n_2.
% 15.75/15.63 0 [] -class_Rings_Olinordered__semidom(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),V_a_2)|hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2)=hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)|V_m_2!=V_n_2.
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)|V_n_2=hAPP(c_Nat_OSuc,$f7(V_n_2)).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)|V_n_2!=hAPP(c_Nat_OSuc,B_m).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=hAPP(c_Nat_OSuc,$f8(V_n_2,V_m_2)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f8(V_n_2,V_m_2),V_n_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))|V_m_2!=hAPP(c_Nat_OSuc,B_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m).
% 15.75/15.63 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)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m))).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i))).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),$f9(V_n_2,V_m_2))).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2!=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2=V_n_2.
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2!=V_n_2.
% 15.75/15.63 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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_m).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),hAPP(c_Nat_OSuc,V_m)).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))=V_m.
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),V_j_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),V_j_2).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] -class_Groups_Ocomm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),c_Polynomial_Odegree(T_a,V_p))|c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q))=c_Polynomial_Odegree(T_a,V_p).
% 15.75/15.63 0 [] -class_Groups_Ocomm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))|c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q))=c_Polynomial_Odegree(T_a,V_q).
% 15.75/15.63 0 [] -class_Groups_Ocomm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_n).
% 15.75/15.63 0 [] -class_Groups_Oab__group__add(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_n).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)))|V_x_2!=c_Groups_Ozero__class_Ozero(T_b)|V_y_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)))|V_x_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Rings_Olinordered__ring__strict(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)))|V_y_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))).
% 15.75/15.63 0 [] -class_Rings_Oordered__ring(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))|c_Orderings_Oord__class_Oless(T_b,V_ca_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)).
% 15.75/15.63 0 [] -class_Rings_Oordered__ring(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)).
% 15.75/15.63 0 [] -class_Rings_Oordered__ring(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2),V_d_2).
% 15.75/15.63 0 [] -class_Rings_Oordered__ring(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2),V_d_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 15.75/15.63 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 15.75/15.63 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),hAPP(c_Nat_OSuc,V_n))).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n.
% 15.75/15.63 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,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i)),V_n).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)).
% 15.75/15.63 0 [] -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.63 0 [] -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))|V_a_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 15.75/15.63 0 [] hBOOL(hAPP(V_P_2,hAPP(hAPP(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=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),$f10(V_b_2,V_a_2,V_P_2)).
% 15.75/15.63 0 [] hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)| -hBOOL(hAPP(V_P_2,$f10(V_b_2,V_a_2,V_P_2))).
% 15.75/15.63 0 [] hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),$f10(V_b_2,V_a_2,V_P_2)).
% 15.75/15.63 0 [] hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f10(V_b_2,V_a_2,V_P_2))).
% 15.75/15.63 0 [] -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.75/15.63 0 [] -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))|V_a_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 15.75/15.63 0 [] hBOOL(hAPP(V_P_2,hAPP(hAPP(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=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),$f11(V_b_2,V_a_2,V_P_2)).
% 15.75/15.63 0 [] hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)| -hBOOL(hAPP(V_P_2,$f11(V_b_2,V_a_2,V_P_2))).
% 15.75/15.63 0 [] hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),$f11(V_b_2,V_a_2,V_P_2)).
% 15.75/15.63 0 [] hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f11(V_b_2,V_a_2,V_P_2))).
% 15.75/15.63 0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)=V_a.
% 15.75/15.63 0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)=V_x.
% 15.75/15.63 0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b).
% 15.75/15.63 0 [] -class_Groups_Ominus(T_b)|hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)).
% 15.75/15.63 0 [] -class_Groups_Ozero(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)|hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_Lattices_Oboolean__algebra(T_b)|hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)!=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)|V_x_2=V_y_2.
% 15.75/15.63 0 [] -class_Lattices_Oboolean__algebra(T_b)|hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)|V_x_2!=V_y_2.
% 15.75/15.63 0 [] -class_Groups_Ouminus(T_b)|hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)).
% 15.75/15.63 0 [] -class_Lattices_Oboolean__algebra(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))=V_x.
% 15.75/15.63 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 15.75/15.63 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),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(T_a)).
% 15.75/15.63 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)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))).
% 15.75/15.63 0 [] -class_Rings_Ocomm__semiring__1(T_a)|V_x!=c_Groups_Oone__class_Oone(T_a)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|V_n=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=V_n.
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_m_2))|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_m_2))|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_m_2)),V_m_2))|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_m_2)),V_m_2))|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.63 0 [] -class_Orderings_Owellorder(T_b)| -hBOOL(hAPP(V_P_2,B_x1))|hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),$f12(V_y,V_x,V_d,T_a)),V_x))|V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),$f12(V_y,V_x,V_d,T_a)),V_x))|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),$f12(V_y,V_x,V_d,T_a)),V_x))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Ozero__class_Ozero(T_a)|V_x!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),$f12(V_y,V_x,V_d,T_a)),V_x))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),$f12(V_y,V_x,V_d,T_a)),V_y))|V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),$f12(V_y,V_x,V_d,T_a)),V_y))|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),$f12(V_y,V_x,V_d,T_a)),V_y))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Ozero__class_Ozero(T_a)|V_x!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_y))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),$f12(V_y,V_x,V_d,T_a)),V_y))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),$f12(V_y,V_x,V_d,T_a)),V_d))|V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),$f12(V_y,V_x,V_d,T_a)),V_d))|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),$f12(V_y,V_x,V_d,T_a)),V_d))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Ozero__class_Ozero(T_a)|V_x!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_y))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),$f12(V_y,V_x,V_d,T_a)),V_d))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.75/15.63 0 [] -class_Orderings_Oorder(T_b)| -c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))|c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k)).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)|V_w_2=V_z_2.
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))|V_w_2!=V_z_2.
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.75/15.63 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)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_m_2=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_n_2=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_m_2!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_n_2!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.75/15.63 0 [] -class_Orderings_Oorder(T_b)| -c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)|c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)| -c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2),V_y_2)),V_r_2).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)| -c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)|V_y_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)| -c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)|V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_r_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_b,V_r_2),c_Polynomial_Odegree(T_b,V_y_2)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2),V_y_2)),V_r_2)|V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_r_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2),V_y_2)),V_r_2)|V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_b,V_r_2),c_Polynomial_Odegree(T_b,V_y_2)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2),V_y_2)),V_r_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_y_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2),V_y_2)),V_r_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_r_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opdivmod__rel(T_b,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_b)),V_q_2),V_y_2)),V_r_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_b,V_r_2),c_Polynomial_Odegree(T_b,V_y_2)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opdivmod__rel(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)| -c_Polynomial_Opdivmod__rel(T_b,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),V_q_2,V_r_2)|V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)| -c_Polynomial_Opdivmod__rel(T_b,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),V_q_2,V_r_2)|V_r_2=V_x_2.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opdivmod__rel(T_b,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),V_q_2,V_r_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_r_2!=V_x_2.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)| -c_Polynomial_Opdivmod__rel(T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),V_y_2,V_q_2,V_r_2)|V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)| -c_Polynomial_Opdivmod__rel(T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),V_y_2,V_q_2,V_r_2)|V_r_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|c_Polynomial_Opdivmod__rel(T_b,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),V_y_2,V_q_2,V_r_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))|V_r_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)|c_Polynomial_Opdivmod__rel(T_a,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_x),V_y,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_q),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_r)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)|V_q1=V_q2.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)|V_r1=V_r2.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)|V_q1=V_q2.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)|V_r1=V_r2.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)| -c_Polynomial_Opdivmod__rel(T_a,V_q,V_z,V_q_H,V_r_H)|c_Polynomial_Opdivmod__rel(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z),V_q_H,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_r_H)),V_r)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_b!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_r)),c_Polynomial_Odegree(T_a,V_y))),hAPP(c_Polynomial_Ocoeff(T_a,V_y),c_Polynomial_Odegree(T_a,V_y)))|c_Polynomial_Opdivmod__rel(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_x),V_y,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_b),V_q),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_r)),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_b),V_y))).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)| -c_Polynomial_Opos__poly(T_b,V_pa_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),c_Polynomial_Odegree(T_b,V_pa_2))).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)|c_Polynomial_Opos__poly(T_b,V_pa_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(c_Polynomial_Ocoeff(T_b,V_pa_2),c_Polynomial_Odegree(T_b,V_pa_2))).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)| -c_Polynomial_Opos__poly(T_b,hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2))|c_Polynomial_Opos__poly(T_b,V_pa_2)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)| -c_Polynomial_Opos__poly(T_b,hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2))|c_Polynomial_Opos__poly(T_b,V_pa_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)|c_Polynomial_Opos__poly(T_b,hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2))| -c_Polynomial_Opos__poly(T_b,V_pa_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)|c_Polynomial_Opos__poly(T_b,hAPP(hAPP(c_Polynomial_OpCons(T_b),V_a_2),V_pa_2))|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)).
% 15.75/15.63 0 [] -class_Rings_Odivision__ring(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b).
% 15.75/15.63 0 [] -class_Rings_Odivision__ring(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),V_ya)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_ya)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_ya)).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)).
% 15.75/15.63 0 [] -class_Rings_Odivision__ring(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a.
% 15.75/15.63 0 [] -class_Rings_Odivision__ring(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_ya)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_ya)).
% 15.75/15.63 0 [] -class_Rings_Odivision__ring(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c).
% 15.75/15.63 0 [] -class_Rings_Odivision__ring(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)).
% 15.75/15.63 0 [] -class_Rings_Odivision__ring(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)).
% 15.75/15.63 0 [] -class_Rings_Odivision__ring(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b).
% 15.75/15.63 0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|V_a!=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a)=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.63 0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a)=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.63 0 [] -class_Rings_Odivision__ring(T_b)|V_b_2=c_Groups_Ozero__class_Ozero(T_b)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)!=c_Groups_Oone__class_Oone(T_b)|V_a_2=V_b_2.
% 15.75/15.63 0 [] -class_Rings_Odivision__ring(T_b)|V_b_2=c_Groups_Ozero__class_Ozero(T_b)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)=c_Groups_Oone__class_Oone(T_b)|V_a_2!=V_b_2.
% 15.75/15.63 0 [] -class_Rings_Odivision__ring(T_b)|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)=V_b_2.
% 15.75/15.63 0 [] -class_Rings_Odivision__ring(T_b)|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)!=V_b_2.
% 15.75/15.63 0 [] -class_Rings_Odivision__ring(T_b)|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)!=V_a_2|V_b_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2).
% 15.75/15.63 0 [] -class_Rings_Odivision__ring(T_b)|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)=V_a_2|V_b_2!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2).
% 15.75/15.63 0 [] -class_Rings_Odivision__ring(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|V_b!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)=V_a.
% 15.75/15.63 0 [] -class_Rings_Odivision__ring(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)!=V_b|V_a=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,V_p)| -c_Polynomial_Opos__poly(T_a,V_q)|c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,V_p)| -c_Polynomial_Opos__poly(T_a,V_q)|c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)| -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_b),V_x_2,V_y_2)|c_Polynomial_Opos__poly(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_b)),V_y_2),V_x_2)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)|c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_b),V_x_2,V_y_2)| -c_Polynomial_Opos__poly(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_b)),V_y_2),V_x_2)).
% 15.75/15.63 0 [] -class_RealVector_Oreal__field(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))),V_h)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d)),V_h))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c)),V_h)),V_d)).
% 15.75/15.63 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,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_p)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_b).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,V_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_z),V_w))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y),c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y),c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_b_2).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_b_2).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_b_2).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2)|c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_b_2).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_b_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|V_y_2=c_Groups_Ozero__class_Ozero(T_b)|V_z_2=c_Groups_Ozero__class_Ozero(T_b)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2)!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_b)|V_y_2=c_Groups_Ozero__class_Ozero(T_b)|V_z_2=c_Groups_Ozero__class_Ozero(T_b)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_b)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)!=V_a_2|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|V_b_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_b)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)!=V_a_2|V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_b)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)=V_a_2|V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_b)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)=V_a_2|V_b_2!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)|V_ca_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_b)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)=V_a_2|V_b_2!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_b)|V_a_2!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)=V_b_2.
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_b)|V_a_2!=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)|V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_b)|V_a_2=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)|V_ca_2!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_b)|V_a_2=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)!=V_b_2|V_ca_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_b)|V_a_2=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)!=V_b_2|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y),V_x)|c_Orderings_Oord__class_Oless(T_a,V_z,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y),V_z).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2),V_a_2)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_ca_2).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)|c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,V_ca_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,V_a_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_b,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|V_y=c_Groups_Ozero__class_Ozero(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_y=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z).
% 15.75/15.63 0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_y=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|V_y=c_Groups_Ozero__class_Ozero(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),V_x),V_y)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))),hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Polynomial_OpCons(T_a),V_a),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))),c_Polynomial_Odegree(T_a,V_y))),hAPP(c_Polynomial_Ocoeff(T_a,V_y),c_Polynomial_Odegree(T_a,V_y)))),V_y)).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)| -c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_d_2)| -c_Deriv_Oderiv(T_b,V_g_2,V_x_2,V_e_2)|hAPP(V_g_2,V_x_2)=c_Groups_Ozero__class_Ozero(T_b)|c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_g_2),V_x_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_d_2),hAPP(V_g_2,V_x_2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_e_2),hAPP(V_f_2,V_x_2)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(V_g_2,V_x_2)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_a)|V_x!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_a)|V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))| -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)|c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x)=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)).
% 15.75/15.63 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)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_x),c_Polynomial_Odegree(T_a,V_y))|c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)=V_x.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=c_Polynomial_Opoly__gcd(T_a,V_y,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)|c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)=V_r.
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_y))=c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_y))=c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_x),V_y)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.75/15.63 0 [] -class_Groups_Osgn__if(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_a_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_a_2)=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__vector(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_x_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_x_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__vector(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_x_2)=c_Groups_Ozero__class_Ozero(T_b)|V_x_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__div__algebra(T_a)|c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y)).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)|c_Deriv_Oderiv(T_b,hAPP(c_COMBK(T_b,T_b),V_k_2),V_x_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__algebra__1(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_x),V_y)=hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a))=c_Groups_Osgn__class_Osgn(T_a,V_a).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)|c_Deriv_Oderiv(T_b,hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_x_2,V_ca_2).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)| -c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)| -c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_E_2)|V_D_2=V_E_2.
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)| -c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_X_2)|V_X_2!=V_Y_2|c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_Y_2).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)| -c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)|V_D_2!=V_E_2|c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_E_2).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)| -c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)|c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,T_b),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2),V_x_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_D_2)).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)|c_Deriv_Oderiv(T_b,c_COMBI(T_b),V_x_2,c_Groups_Oone__class_Oone(T_b)).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)| -c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)| -c_Deriv_Oderiv(T_b,V_g_2,V_x_2,V_E_2)|c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2),V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_D_2),V_E_2)).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Osgn__class_Osgn(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)| -c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)| -c_Deriv_Oderiv(T_b,V_g_2,V_x_2,V_E_2)|c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2),V_x_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_D_2),V_E_2)).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)| -c_Deriv_Oderiv(T_b,V_f_2,hAPP(V_g_2,V_x_2),V_Da_2)| -c_Deriv_Oderiv(T_b,V_g_2,V_x_2,V_Db_2)|c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,T_b),V_f_2),V_g_2),V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_Da_2),V_Db_2)).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)| -c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)| -c_Deriv_Oderiv(T_b,V_g_2,hAPP(V_f_2,V_x_2),V_E_2)|c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,T_b),V_g_2),V_f_2),V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_E_2),V_D_2)).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)| -c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)|c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2)),V_f_2),V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_D_2)).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)| -c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)|c_Deriv_Oderiv(T_b,hAPP(c_COMBC(T_b,T_b,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_ca_2),V_x_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_D_2),V_ca_2)).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)| -c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)| -c_Deriv_Oderiv(T_b,V_g_2,V_x_2,V_E_2)|c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2),V_x_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_f_2,V_x_2)),V_E_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_D_2),hAPP(V_g_2,V_x_2)))).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)| -c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_Da_2)| -c_Deriv_Oderiv(T_b,V_g_2,V_x_2,V_Db_2)|c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2),V_x_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_Da_2),hAPP(V_g_2,V_x_2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_Db_2),hAPP(V_f_2,V_x_2)))).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)| -c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)| -c_Deriv_Oderiv(T_b,V_g_2,V_x_2,V_E_2)|c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(T_b,T_b,T_b),c_Groups_Ouminus__class_Ouminus(T_b)),V_g_2)),V_x_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_D_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_E_2))).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Osgn__class_Osgn(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Osgn__class_Osgn(T_b,V_a_2),c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Fields_Ofield(T_a)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)),c_Polynomial_Odegree(T_a,V_y)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_a_2)!=c_Groups_Oone__class_Oone(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_a_2)=c_Groups_Oone__class_Oone(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Groups_Osgn__class_Osgn(T_a,V_a)=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)| -c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)| -c_Deriv_Oderiv(T_b,V_g_2,V_x_2,V_E_2)|hAPP(V_g_2,V_x_2)=c_Groups_Ozero__class_Ozero(T_b)|c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_g_2),V_x_2,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_D_2),hAPP(V_g_2,V_x_2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_f_2,V_x_2)),V_E_2))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_g_2,V_x_2)),hAPP(V_g_2,V_x_2)))).
% 15.75/15.63 0 [] -class_Groups_Osgn__if(T_a)|V_x!=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_Groups_Osgn__if(T_a)|V_x=c_Groups_Ozero__class_Ozero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)|c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.63 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)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)).
% 15.75/15.63 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)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_a_2)!=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Rings_Olinordered__idom(T_b)|c_Groups_Osgn__class_Osgn(T_b,V_a_2)=hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))|c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2)=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_b)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))|c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2)!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))|c_Divides_Odiv__class_Omod(T_a,V_b,V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=V_m.
% 15.75/15.63 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=V_m.
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_n).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_x),V_m).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_m_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),$f13(V_d_2,V_m_2)).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_m_2!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m).
% 15.75/15.63 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)).
% 15.75/15.63 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),$f14(V_d_2,V_m_2)).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))!=V_n|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))=V_n|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)=hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_n_2)!=c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_n_2)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x_2),V_y_2))).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_n_2)=c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_n_2)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x_2),V_y_2))).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_c)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_r,V_b)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)).
% 15.75/15.63 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(V_P_2,V_n_2)).
% 15.75/15.63 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2)|V_n_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)|hBOOL(hAPP(V_P_2,B_j)).
% 15.75/15.63 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f15(V_k_2,V_n_2,V_P_2),V_k_2).
% 15.75/15.63 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),$f16(V_k_2,V_n_2,V_P_2))),$f15(V_k_2,V_n_2,V_P_2)).
% 15.75/15.63 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(V_P_2,$f15(V_k_2,V_n_2,V_P_2))).
% 15.75/15.63 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,V_n_2))|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.63 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f15(V_k_2,V_n_2,V_P_2),V_k_2).
% 15.75/15.63 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,V_n_2))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),$f16(V_k_2,V_n_2,V_P_2))),$f15(V_k_2,V_n_2,V_P_2)).
% 15.75/15.63 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,V_n_2))| -hBOOL(hAPP(V_P_2,$f15(V_k_2,V_n_2,V_P_2))).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_k)|c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k)=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b).
% 15.75/15.63 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).
% 15.75/15.63 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).
% 15.75/15.63 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)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,V_a,V_c)!=c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)|c_Divides_Odiv__class_Omod(T_a,V_b,V_c)!=c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,V_a,V_c)!=c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)|c_Divides_Odiv__class_Omod(T_a,V_b,V_c)!=c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c).
% 15.75/15.63 0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,V_a,V_c)!=c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)|c_Divides_Odiv__class_Omod(T_a,V_b,V_c)!=c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c).
% 15.75/15.63 0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c).
% 15.75/15.63 0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c).
% 15.75/15.63 0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c).
% 15.75/15.63 0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b)=c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b).
% 15.75/15.63 0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,V_a,V_b)!=c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)|c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b)=c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_H),V_b).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))|c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,V_a,V_c).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b).
% 15.75/15.63 0 [] -class_RealVector_Oreal__normed__field(T_b)| -c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_d_2)|hAPP(V_f_2,V_x_2)=c_Groups_Ozero__class_Ozero(T_b)|c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,T_b),c_Rings_Oinverse__class_Oinverse(T_b)),V_f_2),V_x_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_d_2),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))).
% 15.75/15.63 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 15.75/15.63 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n)),V_n)).
% 15.75/15.63 0 [] V_a=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)).
% 15.75/15.63 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k).
% 15.75/15.63 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c))),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_a.
% 15.75/15.63 0 [] -class_Divides_Oring__div(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))|c_Divides_Odiv__class_Odiv(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x),V_y)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)).
% 15.75/15.63 0 [] -class_Divides_Oring__div(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))|c_Divides_Odiv__class_Odiv(T_a,V_x,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),V_n)=c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ca_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2)),c_Divides_Odiv__class_Odiv(T_b,V_ca_2,V_a_2)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_ca_2)).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ca_2))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2)),c_Divides_Odiv__class_Odiv(T_b,V_ca_2,V_a_2)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_ca_2)).
% 15.75/15.63 0 [] V_a=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a)=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a.
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y),V_z)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_z)),c_Divides_Odiv__class_Odiv(T_a,V_y,V_z)).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),c_Divides_Odiv__class_Odiv(T_a,V_w,V_z))=c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_c)=c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c),V_a).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_a)=V_b.
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_c))=c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a))=V_b.
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,V_a,V_a)=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.63 0 [] -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n))=V_m.
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b)=V_a.
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b)=V_a.
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|V_c!=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.63 0 [] -class_Divides_Osemiring__div(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))=c_Divides_Odiv__class_Odiv(T_a,V_a,V_b).
% 15.75/15.63 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b).
% 15.75/15.64 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.75/15.64 0 [] -class_Fields_Ofield__inverse__zero(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b))=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_a).
% 15.75/15.64 0 [] -class_Fields_Ofield(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)).
% 15.75/15.64 0 [] -class_Fields_Ofield__inverse__zero(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.64 0 [] -class_Fields_Ofield__inverse__zero(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)).
% 15.75/15.64 0 [] -class_Fields_Ofield__inverse__zero(T_b)|hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_x_2)!=c_Groups_Oone__class_Oone(T_b)|V_x_2=c_Groups_Oone__class_Oone(T_b).
% 15.75/15.64 0 [] -class_Fields_Ofield__inverse__zero(T_b)|hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_x_2)=c_Groups_Oone__class_Oone(T_b)|V_x_2!=c_Groups_Oone__class_Oone(T_b).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a))|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)!=hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)|V_a=V_b.
% 15.75/15.64 0 [] -class_Rings_Odivision__ring__inverse__zero(T_b)|hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2)!=hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_b_2)|V_a_2=V_b_2.
% 15.75/15.64 0 [] -class_Rings_Odivision__ring__inverse__zero(T_b)|hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2)=hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_b_2)|V_a_2!=V_b_2.
% 15.75/15.64 0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a))=V_a.
% 15.75/15.64 0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),V_n).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring__inverse__zero(T_b)|hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2)!=c_Groups_Ozero__class_Ozero(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring__inverse__zero(T_b)|hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2)=c_Groups_Ozero__class_Ozero(T_b)|V_a_2!=c_Groups_Ozero__class_Ozero(T_b).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)!=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a))=V_a.
% 15.75/15.64 0 [] -class_Rings_Odivision__ring(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)!=c_Groups_Ozero__class_Ozero(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)!=hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|V_a=V_b.
% 15.75/15.64 0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),V_n).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)!=c_Groups_Oone__class_Oone(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)=V_b.
% 15.75/15.64 0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)).
% 15.75/15.64 0 [] -class_Fields_Ofield(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)).
% 15.75/15.64 0 [] -class_Fields_Ofield(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a))),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_x_2))|c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_x_2).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_x_2))|c_Orderings_Oord__class_Oless(T_b,V_x_2,c_Groups_Oone__class_Oone(T_b)).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless(T_b,c_Groups_Oone__class_Oone(T_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_x_2))| -c_Orderings_Oord__class_Oless(T_b,c_Groups_Ozero__class_Ozero(T_b),V_x_2)| -c_Orderings_Oord__class_Oless(T_b,V_x_2,c_Groups_Oone__class_Oone(T_b)).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a))),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b)).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),V_a)=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a))=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.64 0 [] -class_Fields_Ofield(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),V_a)=c_Groups_Oone__class_Oone(T_a).
% 15.75/15.64 0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)=hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c).
% 15.75/15.64 0 [] -class_Fields_Ofield(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)|c_Polynomial_Opdivmod__rel(T_a,V_x,hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_y),hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),V_q),V_r).
% 15.75/15.64 0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)).
% 15.75/15.64 0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)).
% 15.75/15.64 0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Groups_Oone__class_Oone(T_a)).
% 15.75/15.64 0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Groups_Oone__class_Oone(T_a)).
% 15.75/15.64 0 [] -class_Divides_Osemiring__div(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_ca_2),V_d_2))|c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2)!=c_Divides_Odiv__class_Odiv(T_b,V_d_2,V_ca_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2).
% 15.75/15.64 0 [] -class_Divides_Osemiring__div(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)|V_ca_2=c_Groups_Ozero__class_Ozero(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_ca_2),V_d_2))|c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2)=c_Divides_Odiv__class_Odiv(T_b,V_d_2,V_ca_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2).
% 15.75/15.64 0 [] -class_Divides_Osemiring__div(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))|c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2)!=V_ca_2|V_b_2=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2).
% 15.75/15.64 0 [] -class_Divides_Osemiring__div(T_b)|V_a_2=c_Groups_Ozero__class_Ozero(T_b)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))|c_Divides_Odiv__class_Odiv(T_b,V_b_2,V_a_2)=V_ca_2|V_b_2!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2).
% 15.75/15.64 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c).
% 15.75/15.64 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c).
% 15.75/15.64 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))=V_a.
% 15.75/15.64 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))=V_a.
% 15.75/15.64 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b))=V_a.
% 15.75/15.64 0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)).
% 15.75/15.64 0 [] V_b=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)).
% 15.75/15.64 0 [] V_b=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 15.75/15.64 0 [] V_b=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)).
% 15.75/15.64 0 [] V_b=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 15.75/15.64 0 [] -class_RealVector_Oreal__normed__field(T_b)| -c_Deriv_Oderiv(T_b,V_f_2,V_x_2,V_D_2)|hAPP(V_f_2,V_x_2)=c_Groups_Ozero__class_Ozero(T_b)|c_Deriv_Oderiv(T_b,hAPP(hAPP(c_COMBB(T_b,T_b,T_b),c_Rings_Oinverse__class_Oinverse(T_b)),V_f_2),V_x_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),hAPP(V_f_2,V_x_2))),V_D_2)),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),hAPP(V_f_2,V_x_2))))).
% 15.75/15.64 0 [] -class_RealVector_Oreal__normed__field(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))),V_h)=hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_h))),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),V_b))).
% 15.75/15.64 0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_x),c_Polynomial_Odegree(T_a,V_x)))),V_x).
% 15.75/15.64 0 [] -class_RealVector_Oreal__normed__field(T_b)|V_x_2=c_Groups_Ozero__class_Ozero(T_b)|c_Deriv_Oderiv(T_b,c_Rings_Oinverse__class_Oinverse(T_b),V_x_2,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_x_2)),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))).
% 15.75/15.64 0 [] -class_Fields_Ofield(T_a)|V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=hAPP(hAPP(c_Polynomial_Osmult(T_a),hAPP(c_Rings_Oinverse__class_Oinverse(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_x),c_Polynomial_Odegree(T_a,V_x)))),V_x).
% 15.75/15.64 0 [] -class_Fields_Ofield(T_a)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=c_Polynomial_Opoly__gcd(T_a,V_y,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|V_n_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)|hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,$f17(V_n_2,V_P_2,V_k_2)).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f17(V_n_2,V_P_2,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f18(V_n_2,V_P_2,V_k_2))),$f17(V_n_2,V_P_2,V_k_2)).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(hAPP(V_P_2,$f18(V_n_2,V_P_2,V_k_2)),$f17(V_n_2,V_P_2,V_k_2))).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)| -hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)|V_n_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)|hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),$f19(V_n_2,V_P_2,V_k_2)).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,$f19(V_n_2,V_P_2,V_k_2),V_k_2).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f20(V_n_2,V_P_2,V_k_2))),$f19(V_n_2,V_P_2,V_k_2)).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)|hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(hAPP(V_P_2,$f20(V_n_2,V_P_2,V_k_2)),$f19(V_n_2,V_P_2,V_k_2))).
% 15.75/15.64 0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x).
% 15.75/15.64 0 [] c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_b,V_c))),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c)),V_c)).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)).
% 15.75/15.64 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_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k),V_m).
% 15.75/15.64 0 [] c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=V_m.
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y)).
% 15.75/15.64 0 [] c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2))|c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b),hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2))| -c_Orderings_Oord__class_Oless__e_q(T_b,c_Groups_Ozero__class_Ozero(T_b),V_a_2).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))|c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.64 0 [] -class_Fields_Olinordered__field__inverse__zero(T_b)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(c_Rings_Oinverse__class_Oinverse(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))| -c_Orderings_Oord__class_Oless__e_q(T_b,V_a_2,c_Groups_Ozero__class_Ozero(T_b)).
% 15.75/15.64 0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)|c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)=V_q.
% 15.75/15.64 0 [] -class_Fields_Ofield(T_a)|c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z))=c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z).
% 15.75/15.64 0 [] -class_Fields_Ofield(T_a)|c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_x),V_y)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.75/15.64 0 [] -class_Fields_Ofield(T_a)|c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),V_y))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a)),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.75/15.64 0 [] -class_Fields_Ofield(T_a)|c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),V_x),V_y)=hAPP(hAPP(c_Polynomial_Osmult(T_a),V_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.75/15.64 0 [] V_k!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 0 [] V_k=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n).
% 15.75/15.64 0 [] -class_Orderings_Oorder(T_b)| -c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n).
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n)=V_m.
% 15.75/15.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n)=V_m.
% 15.75/15.64 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)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))|V_m=V_n.
% 15.75/15.64 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)).
% 15.75/15.64 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)).
% 15.75/15.64 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)).
% 15.75/15.64 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)).
% 15.75/15.64 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)).
% 15.75/15.64 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)).
% 15.75/15.64 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)).
% 15.75/15.64 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)).
% 15.75/15.64 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)).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Groups_Ocancel__ab__semigroup__add(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Rings_Oring__1__no__zero__divisors(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Rings_Oring__no__zero__divisors(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Groups_Ocancel__semigroup__add(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Groups_Oab__semigroup__mult(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Groups_Ocomm__monoid__mult(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Groups_Oab__semigroup__add(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Rings_Ono__zero__divisors(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Groups_Ocomm__monoid__add(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Rings_Ocomm__semiring__1(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Rings_Ocomm__semiring__0(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Rings_Ocomm__semiring(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Groups_Oab__group__add(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Rings_Ozero__ne_q__one(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Groups_Omonoid__mult(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Rings_Ocomm__ring__1(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Groups_Omonoid__add(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Rings_Osemiring__0(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Groups_Ogroup__add(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Rings_Omult__zero(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Rings_Ocomm__ring(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Rings_Osemiring(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Groups_Ouminus(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Rings_Oring__1(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Groups_Ominus(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Power_Opower(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Groups_Ozero(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Rings_Oring(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Groups_Oone(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Rings_Odvd(T).
% 15.75/15.64 0 [] -class_Rings_Oidom(T)|class_Groups_Ocancel__comm__monoid__add(T).
% 15.75/15.64 0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint).
% 15.75/15.64 0 [] -class_Lattices_Oboolean__algebra(T_1)|class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)).
% 15.75/15.64 0 [] -class_Orderings_Opreorder(T_1)|class_Orderings_Opreorder(tc_fun(T_2,T_1)).
% 15.75/15.64 0 [] -class_Orderings_Oorder(T_1)|class_Orderings_Oorder(tc_fun(T_2,T_1)).
% 15.75/15.64 0 [] -class_Orderings_Oord(T_1)|class_Orderings_Oord(tc_fun(T_2,T_1)).
% 15.75/15.64 0 [] -class_Groups_Ouminus(T_1)|class_Groups_Ouminus(tc_fun(T_2,T_1)).
% 15.75/15.64 0 [] -class_Groups_Ominus(T_1)|class_Groups_Ominus(tc_fun(T_2,T_1)).
% 15.75/15.64 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Oordered__cancel__semiring(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Oordered__comm__semiring(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Olinordered__semidom(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Oordered__semiring(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Olinordered__ring(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Olinordered__idom(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Ocomm__semiring__0(tc_Int_Oint).
% 15.75/15.64 0 [] class_Divides_Osemiring__div(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Ocomm__semiring(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Oab__group__add(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Oordered__ring(tc_Int_Oint).
% 15.75/15.64 0 [] class_Orderings_Opreorder(tc_Int_Oint).
% 15.75/15.64 0 [] class_Orderings_Olinorder(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Omonoid__mult(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Omonoid__add(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Osemiring__0(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Ogroup__add(tc_Int_Oint).
% 15.75/15.64 0 [] class_Divides_Oring__div(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Omult__zero(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Ocomm__ring(tc_Int_Oint).
% 15.75/15.64 0 [] class_Orderings_Oorder(tc_Int_Oint).
% 15.75/15.64 0 [] class_Int_Oring__char__0(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Osemiring(tc_Int_Oint).
% 15.75/15.64 0 [] class_Orderings_Oord(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Ouminus(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Osgn__if(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Oring__1(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Ominus(tc_Int_Oint).
% 15.75/15.64 0 [] class_Power_Opower(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Ozero(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Oring(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Oidom(tc_Int_Oint).
% 15.75/15.64 0 [] class_Groups_Oone(tc_Int_Oint).
% 15.75/15.64 0 [] class_Rings_Odvd(tc_Int_Oint).
% 15.75/15.64 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Rings_Oordered__semiring(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Rings_Ocomm__semiring__0(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Divides_Osemiring__div(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Orderings_Owellorder(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Orderings_Opreorder(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Orderings_Olinorder(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Groups_Omonoid__mult(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Groups_Omonoid__add(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Rings_Osemiring__0(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Rings_Omult__zero(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Orderings_Oorder(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Rings_Osemiring(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Orderings_Oord(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Groups_Ominus(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Power_Opower(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Groups_Ozero(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Groups_Oone(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Rings_Odvd(tc_Nat_Onat).
% 15.75/15.64 0 [] class_Lattices_Oboolean__algebra(tc_HOL_Obool).
% 15.75/15.64 0 [] class_Orderings_Opreorder(tc_HOL_Obool).
% 15.75/15.64 0 [] class_Orderings_Oorder(tc_HOL_Obool).
% 15.75/15.64 0 [] class_Orderings_Oord(tc_HOL_Obool).
% 15.75/15.64 0 [] class_Groups_Ouminus(tc_HOL_Obool).
% 15.75/15.64 0 [] class_Groups_Ominus(tc_HOL_Obool).
% 15.75/15.64 0 [] -class_Rings_Oidom(T_1)|class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Oidom(T_1)|class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Oidom(T_1)|class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Oidom(T_1)|class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Fields_Ofield(T_1)|class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Fields_Ofield(T_1)|class_Divides_Oring__div(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Oord(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ominus(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Power_Opower(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Groups_Ozero(T_1)|class_Groups_Ozero(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Oring(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Oidom(T_1)|class_Rings_Oidom(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Oone(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Odvd(tc_Polynomial_Opoly(T_1)).
% 15.75/15.64 0 [] hAPP(c_COMBI(T_a),V_P)=V_P.
% 15.75/15.64 0 [] hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q)=V_P.
% 15.75/15.64 0 [] hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_P_2),V_Q_2),V_R_2)=hAPP(V_P_2,hAPP(V_Q_2,V_R_2)).
% 15.75/15.64 0 [] hAPP(hAPP(c_COMBC(T_c,T_d,T_b,V_P_2),V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),V_Q_2).
% 15.75/15.64 0 [] hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)).
% 15.75/15.64 0 [] -hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2))|V_x_2=V_y_2.
% 15.75/15.64 0 [] V_x_2!=V_y_2|hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2)).
% 15.75/15.64 0 [] -hBOOL(c_fFalse).
% 15.75/15.64 0 [] hBOOL(c_fTrue).
% 15.75/15.64 0 [] -hBOOL(hAPP(c_fNot,V_P_2))| -hBOOL(V_P_2).
% 15.75/15.64 0 [] hBOOL(V_P_2)|hBOOL(hAPP(c_fNot,V_P_2)).
% 15.75/15.64 0 [] -hBOOL(V_P_2)| -hBOOL(V_Q_2)|hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)).
% 15.75/15.64 0 [] -hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))|hBOOL(V_P_2).
% 15.75/15.64 0 [] -hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))|hBOOL(V_Q_2).
% 15.75/15.64 0 [] B_a=c_Groups_Ozero__class_Ozero(t_a)|B_k=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,B_q)),B_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))!=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____))|hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),$f21(B_k,B_a,B_q))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____)),c_Groups_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),$f21(B_k,B_a,B_q)),B_k)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),B_a),B_q)),$f21(B_k,B_a,B_q)))).
% 15.75/15.64 0 [] class_Rings_Oidom(t_a).
% 15.75/15.64 end_of_list.
% 15.75/15.64
% 15.75/15.64 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 15.75/15.64
% 15.75/15.64 This ia a non-Horn set with equality. The strategy will be
% 15.75/15.64 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 15.75/15.64 deletion, with positive clauses in sos and nonpositive
% 15.75/15.64 clauses in usable.
% 15.75/15.64
% 15.75/15.64 dependent: set(knuth_bendix).
% 15.75/15.64 dependent: set(anl_eq).
% 15.75/15.64 dependent: set(para_from).
% 15.75/15.64 dependent: set(para_into).
% 15.75/15.64 dependent: clear(para_from_right).
% 15.75/15.64 dependent: clear(para_into_right).
% 15.75/15.64 dependent: set(para_from_vars).
% 15.75/15.64 dependent: set(eq_units_both_ways).
% 15.75/15.64 dependent: set(dynamic_demod_all).
% 15.75/15.64 dependent: set(dynamic_demod).
% 15.75/15.64 dependent: set(order_eq).
% 15.75/15.64 dependent: set(back_demod).
% 15.75/15.64 dependent: set(lrpo).
% 15.75/15.64 dependent: set(hyper_res).
% 15.75/15.64 dependent: set(unit_deletion).
% 15.75/15.64 dependent: set(factor).
% 15.75/15.64
% 15.75/15.64 ------------> process usable:
% 15.75/15.64 ** KEPT (pick-wt=14): 1 [] hAPP(A,$f1(B,A))!=hAPP(B,$f1(B,A))|A=B.
% 15.75/15.64 ** KEPT (pick-wt=8): 2 [] -class_Rings_Oidom(t_a)| -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_p)).
% 15.75/15.64 ** KEPT (pick-wt=6): 4 [copy,3,flip.2] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=$c1.
% 15.75/15.64 ** KEPT (pick-wt=10): 6 [copy,5,flip.2] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=hAPP(c_Polynomial_Opoly(t_a,v_cs____),$c1).
% 15.75/15.64 ** KEPT (pick-wt=6): 8 [copy,7,flip.2] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=$c2.
% 15.75/15.64 ** KEPT (pick-wt=10): 10 [copy,9,flip.2] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=hAPP(c_Polynomial_Opoly(t_a,v_cs____),$c2).
% 15.75/15.64 ** KEPT (pick-wt=28): 11 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,hAPP(hAPP(c_Polynomial_OpCons(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),hAPP(c_Polynomial_Opoly(A,C),D))).
% 15.75/15.64 ** KEPT (pick-wt=18): 12 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Oone__class_Oone(A).
% 15.75/15.64 ** KEPT (pick-wt=18): 13 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.64 ** KEPT (pick-wt=30): 15 [copy,14,flip.2] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)).
% 15.75/15.64 ** KEPT (pick-wt=30): 16 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)).
% 15.75/15.64 ** KEPT (pick-wt=12): 17 [] -class_Power_Opower(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(A).
% 15.75/15.64 ** KEPT (pick-wt=12): 18 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(A).
% 15.75/15.64 ** KEPT (pick-wt=21): 19 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.64 ** KEPT (pick-wt=21): 20 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=25): 21 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=22): 22 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),c_Groups_Oone__class_Oone(A))),B).
% 15.75/15.64 ** KEPT (pick-wt=26): 23 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),c_Groups_Oone__class_Oone(A))),B).
% 15.75/15.64 ** KEPT (pick-wt=26): 24 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),C)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Oone__class_Oone(A))),C).
% 15.75/15.64 ** KEPT (pick-wt=25): 25 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)).
% 15.75/15.64 ** KEPT (pick-wt=25): 27 [copy,26,flip.2] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)).
% 15.75/15.64 ** KEPT (pick-wt=18): 28 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)!=c_Polynomial_Opoly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.64 ** KEPT (pick-wt=18): 29 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)=c_Polynomial_Opoly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.64 ** KEPT (pick-wt=11): 30 [] -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(A,B,C)|hAPP(C,D)=hAPP(C,E).
% 15.75/15.64 ** KEPT (pick-wt=17): 31 [] c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(A,B,C)|hAPP(C,$f3(C,B,A))!=hAPP(C,$f2(C,B,A)).
% 15.75/15.64 ** KEPT (pick-wt=15): 33 [copy,32,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)).
% 15.75/15.64 ** KEPT (pick-wt=13): 34 [] -class_Groups_Ozero(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.64 ** KEPT (pick-wt=13): 35 [] -class_Groups_Ozero(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.64 ** KEPT (pick-wt=35): 36 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 15.75/15.64 ** KEPT (pick-wt=35): 37 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),E)).
% 15.75/15.64 ** KEPT (pick-wt=35): 38 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))).
% 15.75/15.64 ** KEPT (pick-wt=25): 39 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),C).
% 15.75/15.64 ** KEPT (pick-wt=25): 40 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.75/15.64 Following clause subsumed by 40 during input processing: 0 [flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.75/15.64 ** KEPT (pick-wt=25): 41 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 15.75/15.64 ** KEPT (pick-wt=15): 42 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B).
% 15.75/15.64 ** KEPT (pick-wt=35): 43 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E)).
% 15.75/15.64 ** KEPT (pick-wt=25): 44 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),C).
% 15.75/15.64 ** KEPT (pick-wt=25): 45 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 15.75/15.64 Following clause subsumed by 45 during input processing: 0 [flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 15.75/15.64 ** KEPT (pick-wt=25): 46 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)).
% 15.75/15.64 ** KEPT (pick-wt=15): 47 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),B).
% 15.75/15.64 ** KEPT (pick-wt=18): 48 [] -class_Groups_Ozero(A)|hAPP(hAPP(c_Polynomial_OpCons(A),B),C)!=hAPP(hAPP(c_Polynomial_OpCons(A),D),E)|B=D.
% 15.75/15.64 ** KEPT (pick-wt=18): 49 [] -class_Groups_Ozero(A)|hAPP(hAPP(c_Polynomial_OpCons(A),B),C)!=hAPP(hAPP(c_Polynomial_OpCons(A),D),E)|C=E.
% 15.75/15.64 ** KEPT (pick-wt=21): 50 [] -class_Groups_Ozero(A)|hAPP(hAPP(c_Polynomial_OpCons(A),B),C)=hAPP(hAPP(c_Polynomial_OpCons(A),D),E)|B!=D|C!=E.
% 15.75/15.64 ** KEPT (pick-wt=14): 51 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)!=c_Polynomial_Opoly(A,C)|B=C.
% 15.75/15.64 ** KEPT (pick-wt=14): 52 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)=c_Polynomial_Opoly(A,C)|B!=C.
% 15.75/15.64 ** KEPT (pick-wt=12): 53 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.64 ** KEPT (pick-wt=12): 54 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.64 ** KEPT (pick-wt=14): 56 [copy,55,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=B|C=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.64 ** KEPT (pick-wt=14): 58 [copy,57,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=B|C!=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.64 ** KEPT (pick-wt=11): 59 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A))=B.
% 15.75/15.64 ** KEPT (pick-wt=11): 60 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B)=B.
% 15.75/15.64 ** KEPT (pick-wt=41): 61 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|B=D|C=E.
% 15.75/15.64 ** KEPT (pick-wt=38): 62 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|B!=D.
% 15.75/15.64 ** KEPT (pick-wt=38): 63 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|C!=E.
% 15.75/15.64 ** KEPT (pick-wt=30): 64 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),C).
% 15.75/15.64 ** KEPT (pick-wt=30): 65 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.75/15.64 Following clause subsumed by 61 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B=C|D=E|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.75/15.64 Following clause subsumed by 62 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B!=C|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.75/15.64 Following clause subsumed by 63 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B!=C|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)).
% 15.75/15.64 ** KEPT (pick-wt=30): 67 [copy,66,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 15.75/15.64 ** KEPT (pick-wt=11): 68 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 15.75/15.64 ** KEPT (pick-wt=11): 69 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 15.75/15.64 ** KEPT (pick-wt=15): 70 [] -class_Rings_Oring__1__no__zero__divisors(A)|B=c_Groups_Ozero__class_Ozero(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.64 ** KEPT (pick-wt=30): 71 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)).
% 15.75/15.64 ** KEPT (pick-wt=30): 72 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)).
% 15.75/15.64 ** KEPT (pick-wt=25): 73 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 15.75/15.64 ** KEPT (pick-wt=12): 74 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Oone__class_Oone(A)),B)=c_Groups_Oone__class_Oone(A).
% 15.75/15.64 ** KEPT (pick-wt=11): 75 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat))=B.
% 15.75/15.64 ** KEPT (pick-wt=11): 76 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat))=B.
% 15.75/15.64 ** KEPT (pick-wt=16): 77 [] -class_Groups_Ozero(A)|hAPP(hAPP(c_Polynomial_OpCons(A),B),C)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.64 ** KEPT (pick-wt=17): 78 [] -class_Groups_Ozero(A)|hAPP(hAPP(c_Polynomial_OpCons(A),B),C)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.64 ** KEPT (pick-wt=21): 79 [] -class_Groups_Ozero(A)|hAPP(hAPP(c_Polynomial_OpCons(A),B),C)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.64 ** KEPT (pick-wt=15): 80 [] -class_Groups_Ozero(A)|hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Ozero__class_Ozero(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.64 ** KEPT (pick-wt=37): 81 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),B),C)),hAPP(hAPP(c_Polynomial_OpCons(A),D),E))=hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),E)).
% 15.75/15.64 ** KEPT (pick-wt=12): 82 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.64 ** KEPT (pick-wt=28): 83 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Polynomial_Opoly(A,B),D)),hAPP(c_Polynomial_Opoly(A,C),D)).
% 15.75/15.64 ** KEPT (pick-wt=28): 84 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Polynomial_Opoly(A,B),D)),hAPP(c_Polynomial_Opoly(A,C),D)).
% 15.75/15.64 ** KEPT (pick-wt=12): 85 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Polynomial_Opoly(A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)=c_Groups_Oone__class_Oone(A).
% 15.75/15.64 ** KEPT (pick-wt=24): 86 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Polynomial_Opoly(A,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),B),C)),D)=hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Polynomial_Opoly(A,B),D)),C).
% 15.75/15.64 ** KEPT (pick-wt=35): 87 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B=c_Groups_Ozero__class_Ozero(A)|C!=D|E=F|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),F)).
% 15.75/15.64 ** KEPT (pick-wt=13): 88 [] -class_Rings_Oidom(t_a)| -c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),v_c____),v_cs____))).
% 15.75/15.64 ** KEPT (pick-wt=25): 89 [] -class_Rings_Olinordered__ring__strict(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.64 ** KEPT (pick-wt=25): 90 [] -class_Rings_Olinordered__ring__strict(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.64 ** KEPT (pick-wt=29): 91 [] -class_Rings_Olinordered__ring__strict(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.64 ** KEPT (pick-wt=11): 92 [] -class_Power_Opower(A)|c_Power_Opower__class_Opower(A)=c_Power_Opower_Opower(A,c_Groups_Oone__class_Oone(A),c_Groups_Otimes__class_Otimes(A)).
% 15.75/15.64 ** KEPT (pick-wt=6): 94 [copy,93,flip.2] -class_Rings_Oidom(t_a)|c_Groups_Ozero__class_Ozero(t_a)!=$c4.
% 15.75/15.64 ** KEPT (pick-wt=16): 95 [] -class_Rings_Oidom(t_a)|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,$c3)),$c5))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,v_cs____).
% 15.75/15.64 ** KEPT (pick-wt=28): 97 [copy,96,flip.2] -class_Rings_Oidom(t_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),A),$c5)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),$c4),$c3)),A))=hAPP(c_Polynomial_Opoly(t_a,v_cs____),A).
% 15.75/15.64 ** KEPT (pick-wt=16): 99 [copy,98,flip.1] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=A|B=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=12): 100 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=A|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=13): 101 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=13): 102 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=17): 103 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=11): 104 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 15.75/15.64 ** KEPT (pick-wt=11): 105 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 15.75/15.64 ** KEPT (pick-wt=11): 106 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 15.75/15.64 ** KEPT (pick-wt=15): 107 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.64 ** KEPT (pick-wt=13): 108 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)=B.
% 15.75/15.64 ** KEPT (pick-wt=15): 109 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.64 ** KEPT (pick-wt=13): 110 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=B.
% 15.75/15.64 ** KEPT (pick-wt=35): 111 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)).
% 15.75/15.64 ** KEPT (pick-wt=20): 112 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),C)|B=C.
% 15.75/15.64 ** KEPT (pick-wt=20): 113 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)),C)|B!=C.
% 15.75/15.64 ** KEPT (pick-wt=10): 114 [] hAPP(c_Nat_OSuc,A)!=hAPP(c_Nat_OSuc,B)|A=B.
% 15.75/15.64 Following clause subsumed by 114 during input processing: 0 [] hAPP(c_Nat_OSuc,A)!=hAPP(c_Nat_OSuc,B)|A=B.
% 15.75/15.64 ** KEPT (pick-wt=10): 115 [] hAPP(c_Nat_OSuc,A)=hAPP(c_Nat_OSuc,B)|A!=B.
% 15.75/15.64 ** KEPT (pick-wt=5): 116 [] hAPP(c_Nat_OSuc,A)!=A.
% 15.75/15.64 Following clause subsumed by 116 during input processing: 0 [flip.1] hAPP(c_Nat_OSuc,A)!=A.
% 15.75/15.64 ** KEPT (pick-wt=6): 117 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,A).
% 15.75/15.64 Following clause subsumed by 117 during input processing: 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,A).
% 15.75/15.64 ** KEPT (pick-wt=6): 118 [] hAPP(c_Nat_OSuc,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 Following clause subsumed by 118 during input processing: 0 [] hAPP(c_Nat_OSuc,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 Following clause subsumed by 117 during input processing: 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,A).
% 15.75/15.64 Following clause subsumed by 118 during input processing: 0 [] hAPP(c_Nat_OSuc,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=17): 119 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.64 ** KEPT (pick-wt=17): 120 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.64 ** KEPT (pick-wt=23): 121 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.64 ** KEPT (pick-wt=21): 122 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.64 ** KEPT (pick-wt=15): 123 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=17): 124 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.64 ** KEPT (pick-wt=21): 125 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)|A=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=23): 126 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)|A=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.64 ** KEPT (pick-wt=19): 127 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=21): 128 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.64 ** KEPT (pick-wt=21): 129 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)|A!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=21): 130 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.64 ** KEPT (pick-wt=21): 131 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=23): 132 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.64 ** KEPT (pick-wt=19): 133 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=21): 134 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.64 ** KEPT (pick-wt=21): 135 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=21): 136 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.64 ** KEPT (pick-wt=16): 137 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),hAPP(c_Nat_OSuc,B))=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.64 ** KEPT (pick-wt=22): 138 [] -class_Power_Opower(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 15.75/15.64 ** KEPT (pick-wt=22): 139 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 15.75/15.64 ** KEPT (pick-wt=22): 141 [copy,140,flip.2] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)).
% 15.75/15.64 Following clause subsumed by 139 during input processing: 0 [flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 15.75/15.64 ** KEPT (pick-wt=22): 142 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,C)).
% 15.75/15.64 ** KEPT (pick-wt=10): 143 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.64 ** KEPT (pick-wt=10): 144 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.64 ** KEPT (pick-wt=25): 145 [] -class_Groups_Oab__semigroup__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.75/15.64 ** KEPT (pick-wt=25): 146 [] -class_Groups_Oab__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 15.75/15.64 ** KEPT (pick-wt=18): 147 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)|C=D.
% 15.75/15.64 ** KEPT (pick-wt=18): 148 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)|C!=D.
% 15.75/15.64 ** KEPT (pick-wt=18): 149 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)|B=D.
% 15.75/15.64 ** KEPT (pick-wt=18): 150 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)|B!=D.
% 15.75/15.64 Following clause subsumed by 147 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)|C=D.
% 15.75/15.64 ** KEPT (pick-wt=18): 151 [] -class_Groups_Ocancel__ab__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)|C=D.
% 15.75/15.64 Following clause subsumed by 149 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)|B=D.
% 15.75/15.64 ** KEPT (pick-wt=10): 152 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)!=B|B=c_Groups_Oone__class_Oone(A).
% 15.75/15.64 ** KEPT (pick-wt=10): 153 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)=B|B!=c_Groups_Oone__class_Oone(A).
% 15.75/15.64 ** KEPT (pick-wt=17): 154 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=13): 155 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=13): 156 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=20): 157 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B=C|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=16): 158 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B!=C.
% 15.75/15.64 ** KEPT (pick-wt=17): 159 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=20): 160 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)|A=C|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=16): 161 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)|A!=C.
% 15.75/15.64 ** KEPT (pick-wt=17): 162 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=16): 163 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)|B=C.
% 15.75/15.64 ** KEPT (pick-wt=16): 164 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)|B!=C.
% 15.75/15.64 ** KEPT (pick-wt=16): 165 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)|A=C.
% 15.75/15.64 ** KEPT (pick-wt=16): 166 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)|A!=C.
% 15.75/15.64 ** KEPT (pick-wt=13): 168 [copy,167,flip.1] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=13): 170 [copy,169,flip.1] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=17): 172 [copy,171,flip.1] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.64 Following clause subsumed by 168 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.64 Following clause subsumed by 170 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.64 Following clause subsumed by 172 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.64 ** KEPT (pick-wt=11): 173 [] -class_Groups_Omonoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B)=B.
% 15.75/15.64 ** KEPT (pick-wt=11): 174 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B)=B.
% 15.75/15.64 ** KEPT (pick-wt=15): 175 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)|B=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.64 ** KEPT (pick-wt=15): 176 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)|B!=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.64 ** KEPT (pick-wt=11): 177 [] -class_Groups_Omonoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A))=B.
% 15.75/15.64 ** KEPT (pick-wt=11): 178 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A))=B.
% 15.75/15.64 ** KEPT (pick-wt=11): 179 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 15.75/15.64 ** KEPT (pick-wt=12): 181 [copy,180,flip.3] -class_Rings_Oidom(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))|c_Groups_Ozero__class_Ozero(t_a)!=$c7.
% 15.75/15.64 ** KEPT (pick-wt=12): 183 [copy,182,flip.3] -class_Rings_Oidom(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=$c8.
% 15.75/15.65 ** KEPT (pick-wt=26): 184 [] -class_Rings_Oidom(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,$c6)),$c8)),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(t_a,v_cs____).
% 15.75/15.65 ** KEPT (pick-wt=44): 186 [copy,185,flip.3] -class_Rings_Oidom(t_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,v_cs____))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(t_a,v_cs____),c_Groups_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),A),$c8)),hAPP(c_Polynomial_Opoly(t_a,hAPP(hAPP(c_Polynomial_OpCons(t_a),$c7),$c6)),A)))=hAPP(c_Polynomial_Opoly(t_a,v_cs____),A).
% 15.75/15.65 ** KEPT (pick-wt=35): 188 [copy,187,flip.2] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),c_Polynomial_Opcompose(A,D,C)))=c_Polynomial_Opcompose(A,hAPP(hAPP(c_Polynomial_OpCons(A),B),D),C).
% 15.75/15.65 ** KEPT (pick-wt=22): 189 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Opoly(A,B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Oorder(A,C,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.65 ** KEPT (pick-wt=15): 190 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Opoly(A,B),C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.65 ** KEPT (pick-wt=17): 191 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Opoly(A,B),C)=c_Groups_Ozero__class_Ozero(A)|c_Polynomial_Oorder(A,C,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.65 Following clause subsumed by 157 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=C.
% 15.75/15.65 Following clause subsumed by 159 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.65 Following clause subsumed by 158 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B!=C.
% 15.75/15.65 ** KEPT (pick-wt=30): 193 [copy,192,flip.2] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 15.75/15.65 Following clause subsumed by 193 during input processing: 0 [flip.2] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 15.75/15.65 ** KEPT (pick-wt=30): 194 [] -class_Rings_Ocomm__semiring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.75/15.65 ** KEPT (pick-wt=30): 195 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.75/15.65 Following clause subsumed by 195 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.75/15.65 ** KEPT (pick-wt=12): 196 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Opcompose(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.65 ** KEPT (pick-wt=20): 197 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,c_Polynomial_Opcompose(A,B,C)),D)=hAPP(c_Polynomial_Opoly(A,B),hAPP(c_Polynomial_Opoly(A,C),D)).
% 15.75/15.65 ** KEPT (pick-wt=19): 198 [] -class_Rings_Ono__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 Following clause subsumed by 198 during input processing: 0 [] -class_Rings_Ono__zero__divisors(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)!=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 ** KEPT (pick-wt=19): 199 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 ** KEPT (pick-wt=15): 200 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 ** KEPT (pick-wt=15): 201 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 ** KEPT (pick-wt=12): 202 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 Following clause subsumed by 202 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 ** KEPT (pick-wt=12): 203 [] -class_Rings_Omult__zero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 ** KEPT (pick-wt=12): 204 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 Following clause subsumed by 204 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 ** KEPT (pick-wt=12): 205 [] -class_Rings_Omult__zero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 ** KEPT (pick-wt=7): 206 [] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 15.75/15.65 Following clause subsumed by 206 during input processing: 0 [flip.2] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 15.75/15.65 ** KEPT (pick-wt=40): 208 [copy,207,flip.2] -class_Rings_Osemiring(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)),E)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),E)).
% 15.75/15.65 ** KEPT (pick-wt=111): 209 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Opcompose(A,B,C)=c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(A),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_Polynomial_Opoly(A),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A))),A),c_COMBK(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A))),hAPP(c_COMBC(A,tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A))),A),c_COMBB(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(A),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A))),hAPP(c_COMBC(A,tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))))),hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C))),B).
% 15.75/15.65 ** KEPT (pick-wt=33): 210 [] -class_Rings_Ocomm__ring__1(A)|hAPP(c_Polynomial_Opoly(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Polynomial_Omonom(A,c_Groups_Oone__class_Oone(A),B)),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)),hAPP(c_Polynomial_Opoly(A,C),D)).
% 15.75/15.65 ** KEPT (pick-wt=15): 211 [] -class_Groups_Olinordered__ab__group__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 ** KEPT (pick-wt=15): 212 [] -class_Groups_Olinordered__ab__group__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 ** KEPT (pick-wt=38): 213 [] -class_Groups_Ozero(A)|hAPP(hAPP(hAPP(B,c_Groups_Ozero__class_Ozero(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)!=C|c_Polynomial_Opoly__rec(D,A,C,B,hAPP(hAPP(c_Polynomial_OpCons(A),E),F))=hAPP(hAPP(hAPP(B,E),F),c_Polynomial_Opoly__rec(D,A,C,B,F)).
% 15.75/15.65 ** KEPT (pick-wt=29): 214 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Polynomial_Ocoeff(A,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),B),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),C)),C)=c_Groups_Oone__class_Oone(A).
% 15.75/15.65 ** KEPT (pick-wt=38): 215 [] -class_Groups_Ozero(A)|c_Polynomial_Opoly__rec(B,A,C,D,hAPP(hAPP(c_Polynomial_OpCons(A),E),F))=hAPP(hAPP(hAPP(D,E),F),hAPP(hAPP(hAPP(c_If(B),hAPP(c_fe_qual(F),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))),C),c_Polynomial_Opoly__rec(B,A,C,D,F))).
% 15.75/15.65 ** KEPT (pick-wt=39): 216 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),D)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D))).
% 15.75/15.65 ** KEPT (pick-wt=15): 217 [] -class_Groups_Ozero(A)|B!=C|hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_Omonom(A,D,B)),C)=D.
% 15.75/15.65 ** KEPT (pick-wt=16): 218 [] -class_Groups_Ozero(A)|B=C|hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_Omonom(A,D,B)),C)=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 ** KEPT (pick-wt=21): 219 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Polynomial_Osmult(A),B),c_Polynomial_Omonom(A,C,D))=c_Polynomial_Omonom(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D).
% 15.75/15.65 ** KEPT (pick-wt=16): 220 [] -class_Groups_Ozero(A)|B!=C|hAPP(c_Polynomial_Ocoeff(A,B),D)=hAPP(c_Polynomial_Ocoeff(A,C),D).
% 15.75/15.65 ** KEPT (pick-wt=22): 221 [] -class_Groups_Ozero(A)|B=C|hAPP(c_Polynomial_Ocoeff(A,B),$f4(C,B,A))!=hAPP(c_Polynomial_Ocoeff(A,C),$f4(C,B,A)).
% 15.75/15.65 ** KEPT (pick-wt=12): 222 [] -class_Groups_Ozero(A)|c_Polynomial_Ocoeff(A,B)!=c_Polynomial_Ocoeff(A,C)|B=C.
% 15.75/15.65 ** KEPT (pick-wt=12): 223 [] -class_Groups_Ozero(A)|c_Polynomial_Ocoeff(A,B)=c_Polynomial_Ocoeff(A,C)|B!=C.
% 15.75/15.65 ** KEPT (pick-wt=14): 224 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,B,C)!=c_Polynomial_Omonom(A,D,C)|B=D.
% 15.75/15.65 ** KEPT (pick-wt=14): 225 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,B,C)=c_Polynomial_Omonom(A,D,C)|B!=D.
% 15.75/15.65 ** KEPT (pick-wt=23): 226 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Ocoeff(A,hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Polynomial_Ocoeff(A,C),D)).
% 15.75/15.65 ** KEPT (pick-wt=25): 228 [copy,227,flip.2] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Polynomial_Osmult(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Polynomial_Osmult(A),B),hAPP(hAPP(c_Polynomial_Osmult(A),C),D)).
% 15.75/15.65 ** KEPT (pick-wt=11): 229 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Polynomial_Osmult(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 15.75/15.65 ** KEPT (pick-wt=14): 230 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Polynomial_Osmult(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.65 ** KEPT (pick-wt=32): 232 [copy,231,flip.2] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),hAPP(hAPP(c_Polynomial_Osmult(A),B),D))=hAPP(hAPP(c_Polynomial_Osmult(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),C),D)).
% 15.75/15.65 ** KEPT (pick-wt=27): 233 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Polynomial_Osmult(A),C),D))=hAPP(hAPP(c_Polynomial_Osmult(A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D)).
% 15.75/15.65 ** KEPT (pick-wt=27): 234 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),D)=hAPP(hAPP(c_Polynomial_Osmult(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),C),D)).
% 15.75/15.65 ** KEPT (pick-wt=12): 235 [] -class_Groups_Ozero(A)|hAPP(c_Polynomial_Ocoeff(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 ** KEPT (pick-wt=13): 236 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Polynomial_Osmult(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.65 ** KEPT (pick-wt=21): 237 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Polynomial_Osmult(A),B),C)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.65 ** KEPT (pick-wt=16): 238 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Polynomial_Osmult(A),B),C)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B!=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 ** KEPT (pick-wt=17): 239 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Polynomial_Osmult(A),B),C)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|C!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.65 ** KEPT (pick-wt=30): 240 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Polynomial_Osmult(A),B),hAPP(hAPP(c_Polynomial_OpCons(A),C),D))=hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Polynomial_Osmult(A),B),D)).
% 15.75/15.65 ** KEPT (pick-wt=15): 241 [] -class_Groups_Ozero(A)|hAPP(c_Polynomial_Ocoeff(A,hAPP(hAPP(c_Polynomial_OpCons(A),B),C)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=B.
% 15.75/15.65 ** KEPT (pick-wt=20): 242 [] -class_Groups_Ozero(A)|hAPP(c_Polynomial_Ocoeff(A,hAPP(hAPP(c_Polynomial_OpCons(A),B),C)),hAPP(c_Nat_OSuc,D))=hAPP(c_Polynomial_Ocoeff(A,C),D).
% 15.75/15.65 ** KEPT (pick-wt=23): 243 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Polynomial_Opoly(A,C),D)).
% 15.75/15.65 ** KEPT (pick-wt=20): 244 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Polynomial_Osmult(A),B),C)!=hAPP(hAPP(c_Polynomial_OpCons(A),D),C)|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.65 ** KEPT (pick-wt=28): 245 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(c_Polynomial_Ocoeff(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Polynomial_Ocoeff(A,B),D)),hAPP(c_Polynomial_Ocoeff(A,C),D)).
% 15.75/15.65 ** KEPT (pick-wt=31): 246 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Polynomial_Osmult(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),D)),hAPP(hAPP(c_Polynomial_Osmult(A),C),D)).
% 15.75/15.65 ** KEPT (pick-wt=11): 247 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.65 ** KEPT (pick-wt=14): 248 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,B,C)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 ** KEPT (pick-wt=14): 249 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,B,C)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B!=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 ** KEPT (pick-wt=25): 250 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),c_Polynomial_Omonom(A,B,C)),c_Polynomial_Omonom(A,D,C))=c_Polynomial_Omonom(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D),C).
% 15.75/15.65 ** KEPT (pick-wt=28): 251 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),hAPP(hAPP(c_Polynomial_OpCons(A),D),C))!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.65 ** KEPT (pick-wt=112): 252 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)=c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(A),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_Polynomial_Opoly(A),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A))),A),c_COMBK(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A))),hAPP(c_COMBC(A,tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A))),A),c_COMBB(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A))),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(A),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A))),hAPP(c_COMBC(A,tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A)),C)))),hAPP(c_Polynomial_OpCons(A),c_Groups_Ozero__class_Ozero(A)))),B).
% 15.75/15.65 ** KEPT (pick-wt=19): 254 [copy,253,flip.2] -class_Groups_Ozero(A)|hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Ozero__class_Ozero(A)),c_Polynomial_Omonom(A,B,C))=c_Polynomial_Omonom(A,B,hAPP(c_Nat_OSuc,C)).
% 15.75/15.65 ** KEPT (pick-wt=22): 255 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Polynomial_Opoly(A,c_Polynomial_Omonom(A,B,C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)).
% 15.75/15.65 ** KEPT (pick-wt=16): 257 [copy,256,flip.2] -class_Groups_Ozero(A)|hAPP(hAPP(c_Polynomial_OpCons(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Polynomial_Omonom(A,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.75/15.65 ** KEPT (pick-wt=30): 258 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Polynomial_Omonom(A,B,C)),c_Polynomial_Omonom(A,D,E))=c_Polynomial_Omonom(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),E)).
% 15.75/15.65 ** KEPT (pick-wt=24): 259 [] -class_Groups_Ozero(A)|hAPP(hAPP(hAPP(B,c_Groups_Ozero__class_Ozero(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)!=C|c_Polynomial_Opoly__rec(D,A,C,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=C.
% 15.75/15.65 ** KEPT (pick-wt=16): 260 [] -class_Rings_Ocomm__semiring__1(A)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Polynomial_Ocoeff(A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)=c_Groups_Oone__class_Oone(A).
% 15.75/15.65 ** KEPT (pick-wt=16): 261 [] -class_Rings_Ocomm__semiring__1(A)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Polynomial_Ocoeff(A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)=c_Groups_Ozero__class_Ozero(A).
% 15.75/15.65 ** KEPT (pick-wt=39): 262 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Polynomial_OpCons(A),C),D))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),C),B)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),D))).
% 15.75/15.65 ** KEPT (pick-wt=83): 263 [] -class_Rings_Ocomm__semiring__0(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,B,C)=c_Polynomial_Opoly__rec(tc_Polynomial_Opoly(A),A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_Polynomial_Opoly(A),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A))),A),c_COMBK(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A))),hAPP(hAPP(c_COMBB(tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),A),hAPP(c_COMBS(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),hAPP(hAPP(c_COMBB(tc_Polynomial_Opoly(A),tc_fun(tc_Polynomial_Opoly(A),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A))),hAPP(c_Polynomial_Osmult(A),C)))),c_Polynomial_OpCons(A))),B).
% 15.75/15.65 ** KEPT (pick-wt=31): 264 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Polynomial_Osmult(A),C),c_Polynomial_Osynthetic__div(A,B,C)))=hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(c_Polynomial_Opoly(A,B),C)),c_Polynomial_Osynthetic__div(A,B,C)).
% 15.75/15.65 ** KEPT (pick-wt=28): 265 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Polynomial_Osmult(A),C),D))!=hAPP(hAPP(c_Polynomial_OpCons(A),E),D)|E=hAPP(c_Polynomial_Opoly(A,B),C).
% 15.75/15.65 ** KEPT (pick-wt=27): 266 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Polynomial_Osmult(A),C),D))!=hAPP(hAPP(c_Polynomial_OpCons(A),E),D)|D=c_Polynomial_Osynthetic__div(A,B,C).
% 15.75/15.65 ** KEPT (pick-wt=35): 268 [copy,267,flip.2] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,C,B))),hAPP(hAPP(c_Polynomial_OpCons(A),D),c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,C,B)))=c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,hAPP(hAPP(c_Polynomial_OpCons(A),D),C),B).
% 15.75/15.65 ** KEPT (pick-wt=34): 269 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),B),C)=c_Polynomial_OAbs__poly(A,hAPP(hAPP(c_COMBS(tc_Nat_Onat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_Nat_Onat),c_Groups_Oplus__class_Oplus(A)),c_Polynomial_Ocoeff(A,B))),c_Polynomial_Ocoeff(A,C))).
% 15.75/15.65 ** KEPT (pick-wt=24): 270 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Polynomial_Osmult(A),B),C)=c_Polynomial_OAbs__poly(A,hAPP(hAPP(c_COMBB(A,A,tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(A),B)),c_Polynomial_Ocoeff(A,C))).
% 15.75/15.65 ** KEPT (pick-wt=9): 271 [] -class_Groups_Ozero(A)|c_Polynomial_OAbs__poly(A,c_Polynomial_Ocoeff(A,B))=B.
% 15.75/15.65 ** KEPT (pick-wt=12): 272 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osynthetic__div(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.65 ** KEPT (pick-wt=12): 273 [] -class_Rings_Ocomm__semiring__0(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.65 ** KEPT (pick-wt=15): 274 [] -class_Rings_Ocomm__semiring__0(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,B,C)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.65 ** KEPT (pick-wt=15): 275 [] -class_Rings_Ocomm__semiring__0(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,B,C)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.75/15.65 ** KEPT (pick-wt=14): 276 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))=c_Polynomial_OAbs__poly(A,hAPP(c_COMBK(A,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(A))).
% 15.75/15.65 ** KEPT (pick-wt=38): 278 [copy,277,flip.2] -class_Groups_Ozero(A)|c_Polynomial_OAbs__poly(A,hAPP(c_COMBC(tc_Nat_Onat,A,A,hAPP(c_COMBC(tc_Nat_Onat,A,tc_fun(A,A),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(A,tc_fun(A,A)),tc_Nat_Onat),c_If(A)),c_fe_qual(B))),C)),c_Groups_Ozero__class_Ozero(A)))=c_Polynomial_Omonom(A,C,B).
% 15.75/15.65 ** KEPT (pick-wt=21): 279 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,B,C)),D)=hAPP(c_Polynomial_Opoly(A,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 15.75/15.65 ** KEPT (pick-wt=25): 280 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osynthetic__div(A,hAPP(hAPP(c_Polynomial_OpCons(A),B),C),D)=hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(c_Polynomial_Opoly(A,C),D)),c_Polynomial_Osynthetic__div(A,C,D)).
% 15.75/15.65 ** KEPT (pick-wt=22): 281 [] -class_Rings_Ocomm__semiring__0(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,hAPP(hAPP(c_Polynomial_OpCons(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)=hAPP(hAPP(c_Polynomial_OpCons(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).
% 15.75/15.65 ** KEPT (pick-wt=47): 282 [] -class_Rings_Ocomm__ring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),c_Polynomial_Osynthetic__div(A,C,B))),hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(c_Polynomial_Opoly(A,C),B)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))=C.
% 15.75/15.65 ** KEPT (pick-wt=17): 283 [] -class_Groups_Ozero(A)|hAPP(hAPP(c_Polynomial_OpCons(A),B),C)=c_Polynomial_OAbs__poly(A,c_Nat_Onat_Onat__case(A,B,c_Polynomial_Ocoeff(A,C))).
% 15.75/15.65 ** KEPT (pick-wt=13): 284 [] A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),A)=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.75/15.65 ** KEPT (pick-wt=26): 285 [] -class_Rings_Ocomm__semiring__1(A)|c_Polynomial_Odegree(A,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),B),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),C))=C.
% 15.75/15.65 ** KEPT (pick-wt=17): 286 [] -class_Groups_Ozero(A)|c_Polynomial_Ocoeff(A,hAPP(hAPP(c_Polynomial_OpCons(A),B),C))=c_Nat_Onat_Onat__case(A,B,c_Polynomial_Ocoeff(A,C)).
% 15.75/15.65 Following clause subsumed by 155 during input processing: 0 [] A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.65 Following clause subsumed by 35 during input processing: 0 [] -class_Groups_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.75/15.65 ** KEPT (pick-wt=16): 288 [copy,287,flip.3] -class_Groups_Ozero(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|hAPP(c_Nat_OSuc,c_Polynomial_Odegree(A,B))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(A,B).
% 15.75/15.65 ** KEPT (pick-wt=37): 289 [] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),B),C)),hAPP(hAPP(c_Polynomial_OpCons(A),D),E))=hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),D)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),C),E)).
% 15.75/15.65 ** KEPT (pick-wt=26): 290 [] -class_Groups_Oab__group__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),B),C))=hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C)).
% 15.75/15.65 Following clause subsumed by 290 during input processing: 0 [] -class_Groups_Oab__group__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),B),C))=hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C)).
% 15.75/15.65 ** KEPT (pick-wt=28): 291 [] -class_Rings_Ocomm__ring(A)|hAPP(c_Polynomial_Opoly(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C)),D)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(c_Polynomial_Opoly(A,B),D)),hAPP(c_Polynomial_Opoly(A,C),D)).
% 15.75/15.65 ** KEPT (pick-wt=20): 292 [] -class_Rings_Ocomm__ring(A)|hAPP(c_Polynomial_Opoly(A,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B)),C)=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(c_Polynomial_Opoly(A,B),C)).
% 15.75/15.65 ** KEPT (pick-wt=13): 293 [] -class_Groups_Oab__group__add(A)|c_Polynomial_Odegree(A,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B))=c_Polynomial_Odegree(A,B).
% 15.75/15.65 ** KEPT (pick-wt=18): 295 [copy,294,flip.2] -class_Rings_Ocomm__ring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C).
% 15.75/15.65 ** KEPT (pick-wt=11): 296 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))=B.
% 15.75/15.65 ** KEPT (pick-wt=18): 297 [] -class_Groups_Oab__group__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),B).
% 15.75/15.65 ** KEPT (pick-wt=14): 298 [] -class_Groups_Ogroup__add(A)|B!=hAPP(c_Groups_Ouminus__class_Ouminus(A),C)|C=hAPP(c_Groups_Ouminus__class_Ouminus(A),B).
% 15.75/15.65 Following clause subsumed by 298 during input processing: 0 [] -class_Groups_Ogroup__add(A)|B=hAPP(c_Groups_Ouminus__class_Ouminus(A),C)|C!=hAPP(c_Groups_Ouminus__class_Ouminus(A),B).
% 15.75/15.65 ** KEPT (pick-wt=14): 299 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)!=C|hAPP(c_Groups_Ouminus__class_Ouminus(A),C)=B.
% 15.75/15.65 Following clause subsumed by 299 during input processing: 0 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)=C|hAPP(c_Groups_Ouminus__class_Ouminus(A),C)!=B.
% 15.75/15.65 ** KEPT (pick-wt=14): 300 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)!=hAPP(c_Groups_Ouminus__class_Ouminus(A),C)|B=C.
% 15.75/15.65 ** KEPT (pick-wt=14): 301 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)=hAPP(c_Groups_Ouminus__class_Ouminus(A),C)|B!=C.
% 15.75/15.65 ** KEPT (pick-wt=21): 302 [] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E)|B!=C|D=E.
% 15.75/15.65 ** KEPT (pick-wt=21): 303 [] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E)|B=C|D!=E.
% 15.75/15.65 ** KEPT (pick-wt=18): 304 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C).
% 15.75/15.65 ** KEPT (pick-wt=18): 306 [copy,305,flip.2] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C).
% 15.75/15.65 ** KEPT (pick-wt=18): 308 [copy,307,flip.2] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C).
% 15.75/15.65 ** KEPT (pick-wt=14): 309 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),c_Groups_Ozero__class_Ozero(A)),B)=hAPP(c_Groups_Ouminus__class_Ouminus(A),B).
% 15.75/15.65 ** KEPT (pick-wt=5): 310 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 15.75/15.65 ** KEPT (pick-wt=15): 311 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)),A)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 15.75/15.65 ** KEPT (pick-wt=25): 312 [] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),c_Polynomial_Omonom(A,B,C)),c_Polynomial_Omonom(A,D,C))=c_Polynomial_Omonom(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),D),C).
% 15.75/15.65 ** KEPT (pick-wt=31): 313 [] -class_Rings_Ocomm__ring(A)|hAPP(hAPP(c_Polynomial_Osmult(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),D)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),D)),hAPP(hAPP(c_Polynomial_Osmult(A),C),D)).
% 15.75/15.65 ** KEPT (pick-wt=28): 314 [] -class_Groups_Oab__group__add(A)|hAPP(c_Polynomial_Ocoeff(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C)),D)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(c_Polynomial_Ocoeff(A,B),D)),hAPP(c_Polynomial_Ocoeff(A,C),D)).
% 15.80/15.65 ** KEPT (pick-wt=22): 315 [] -class_Rings_Ocomm__ring(A)|hAPP(hAPP(c_Polynomial_Osmult(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)).
% 15.80/15.65 ** KEPT (pick-wt=20): 316 [] -class_Groups_Oab__group__add(A)|hAPP(c_Polynomial_Ocoeff(A,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B)),C)=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(c_Polynomial_Ocoeff(A,B),C)).
% 15.80/15.65 ** KEPT (pick-wt=18): 317 [] -class_Groups_Oab__group__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),c_Polynomial_Omonom(A,B,C))=c_Polynomial_Omonom(A,hAPP(c_Groups_Ouminus__class_Ouminus(A),B),C).
% 15.80/15.65 ** KEPT (pick-wt=11): 318 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),c_Groups_Ozero__class_Ozero(A))=B.
% 15.80/15.65 ** KEPT (pick-wt=11): 319 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),B)=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.65 ** KEPT (pick-wt=14): 320 [] -class_Groups_Oab__group__add(A)|B!=C|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.65 ** KEPT (pick-wt=14): 321 [] -class_Groups_Oab__group__add(A)|B=C|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)!=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.65 ** KEPT (pick-wt=14): 322 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=C.
% 15.80/15.65 ** KEPT (pick-wt=14): 323 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)=c_Groups_Ozero__class_Ozero(A)|B!=C.
% 15.80/15.65 ** KEPT (pick-wt=10): 324 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.65 ** KEPT (pick-wt=13): 325 [] -class_Groups_Ogroup__add(A)|c_Groups_Ozero__class_Ozero(A)!=hAPP(c_Groups_Ouminus__class_Ouminus(A),B)|c_Groups_Ozero__class_Ozero(A)=B.
% 15.80/15.65 ** KEPT (pick-wt=13): 326 [] -class_Groups_Ogroup__add(A)|c_Groups_Ozero__class_Ozero(A)=hAPP(c_Groups_Ouminus__class_Ouminus(A),B)|c_Groups_Ozero__class_Ozero(A)!=B.
% 15.80/15.65 ** KEPT (pick-wt=12): 328 [copy,327,flip.2] -class_Groups_Olinordered__ab__group__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.65 ** KEPT (pick-wt=12): 330 [copy,329,flip.2] -class_Groups_Olinordered__ab__group__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.65 ** KEPT (pick-wt=13): 331 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.65 ** KEPT (pick-wt=13): 332 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.65 Following clause subsumed by 328 during input processing: 0 [] -class_Groups_Olinordered__ab__group__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.65 Following clause subsumed by 330 during input processing: 0 [] -class_Groups_Olinordered__ab__group__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.65 ** KEPT (pick-wt=30): 334 [copy,333,flip.2] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),D)).
% 15.80/15.65 Following clause subsumed by 334 during input processing: 0 [flip.2] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),D)).
% 15.80/15.65 ** KEPT (pick-wt=30): 335 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),D)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.80/15.65 Following clause subsumed by 335 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),D)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 15.80/15.65 ** KEPT (pick-wt=15): 336 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),C)=B.
% 15.80/15.65 ** KEPT (pick-wt=15): 337 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),C)=B.
% 15.80/15.65 ** KEPT (pick-wt=21): 338 [] -class_Rings_Oring(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)).
% 15.80/15.65 ** KEPT (pick-wt=21): 340 [copy,339,flip.2] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 15.80/15.65 ** KEPT (pick-wt=21): 341 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 15.80/15.65 Following clause subsumed by 341 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 15.80/15.65 ** KEPT (pick-wt=21): 342 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 15.80/15.65 Following clause subsumed by 342 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 15.80/15.65 ** KEPT (pick-wt=21): 343 [] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)).
% 15.80/15.65 ** KEPT (pick-wt=21): 344 [] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C).
% 15.80/15.65 ** KEPT (pick-wt=24): 345 [] -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=hAPP(c_Groups_Ouminus__class_Ouminus(A),C).
% 15.80/15.65 ** KEPT (pick-wt=18): 346 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)|B!=C.
% 15.80/15.65 ** KEPT (pick-wt=21): 347 [] -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!=hAPP(c_Groups_Ouminus__class_Ouminus(A),C).
% 15.80/15.65 ** KEPT (pick-wt=24): 349 [copy,348,flip.2] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(c_Groups_Ouminus__class_Ouminus(A),C))=hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)).
% 15.80/15.65 ** KEPT (pick-wt=24): 350 [] -class_Groups_Ogroup__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)).
% 15.80/15.65 ** KEPT (pick-wt=18): 351 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C))=C.
% 15.80/15.65 ** KEPT (pick-wt=18): 352 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))=C.
% 15.80/15.65 ** KEPT (pick-wt=18): 353 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Odegree(A,c_Polynomial_Osynthetic__div(A,B,C))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Polynomial_Odegree(A,B)),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 15.80/15.65 ** KEPT (pick-wt=21): 354 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),A),B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=B.
% 15.80/15.65 ** KEPT (pick-wt=13): 355 [] -class_Groups_Oab__group__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.80/15.65 ** KEPT (pick-wt=23): 356 [] -class_Rings_Ocomm__ring(A)|hAPP(hAPP(c_Polynomial_Osmult(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),C))=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)).
% 15.80/15.65 ** KEPT (pick-wt=34): 357 [] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),C)=c_Polynomial_OAbs__poly(A,hAPP(hAPP(c_COMBS(tc_Nat_Onat,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(A)),c_Polynomial_Ocoeff(A,B))),c_Polynomial_Ocoeff(A,C))).
% 15.80/15.65 ** KEPT (pick-wt=21): 358 [] -class_Groups_Oab__group__add(A)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B)=c_Polynomial_OAbs__poly(A,hAPP(hAPP(c_COMBB(A,A,tc_Nat_Onat),c_Groups_Ouminus__class_Ouminus(A)),c_Polynomial_Ocoeff(A,B))).
% 15.80/15.65 ** KEPT (pick-wt=12): 359 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Odegree(A,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,B,C))=c_Polynomial_Odegree(A,B).
% 15.80/15.65 ** KEPT (pick-wt=10): 360 [] -class_Groups_Ozero(A)|c_Polynomial_Odegree(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.80/15.65 ** KEPT (pick-wt=14): 361 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.65 ** KEPT (pick-wt=17): 362 [] -class_Groups_Ogroup__add(A)|B!=hAPP(c_Groups_Ouminus__class_Ouminus(A),C)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.65 ** KEPT (pick-wt=17): 363 [] -class_Groups_Ogroup__add(A)|B=hAPP(c_Groups_Ouminus__class_Ouminus(A),C)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.65 ** KEPT (pick-wt=14): 364 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),B)=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.65 ** KEPT (pick-wt=14): 365 [] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),B)=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.66 ** KEPT (pick-wt=17): 366 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|hAPP(c_Groups_Ouminus__class_Ouminus(A),B)=C.
% 15.80/15.66 ** KEPT (pick-wt=65): 368 [copy,367,flip.2] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),E))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E)))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 15.80/15.66 ** KEPT (pick-wt=43): 369 [] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F)|D=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F).
% 15.80/15.66 ** KEPT (pick-wt=43): 370 [] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F)|D!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),E),B)),C)),F).
% 15.80/15.66 ** KEPT (pick-wt=43): 371 [] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D)=F.
% 15.80/15.66 ** KEPT (pick-wt=43): 372 [] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C)),F)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),C)),D)!=F.
% 15.80/15.66 ** KEPT (pick-wt=17): 374 [copy,373,flip.2] -class_Rings_Ocomm__ring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A))),B)=hAPP(c_Groups_Ouminus__class_Ouminus(A),B).
% 15.80/15.66 ** KEPT (pick-wt=22): 375 [] -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=hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)).
% 15.80/15.66 ** KEPT (pick-wt=15): 376 [] -class_Rings_Oring__1__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=c_Groups_Oone__class_Oone(A)|B!=c_Groups_Oone__class_Oone(A).
% 15.80/15.66 ** KEPT (pick-wt=18): 377 [] -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!=hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A)).
% 15.80/15.66 ** KEPT (pick-wt=14): 378 [] -class_Groups_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Polynomial_Odegree(A,c_Polynomial_Omonom(A,B,C))=C.
% 15.80/15.66 ** KEPT (pick-wt=10): 379 [] -class_Rings_Ocomm__semiring__1(A)|c_Polynomial_Odegree(A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.80/15.66 ** KEPT (pick-wt=17): 380 [] -class_Rings_Oidom(A)|B!=c_Groups_Ozero__class_Ozero(A)|c_Polynomial_Odegree(A,hAPP(hAPP(c_Polynomial_Osmult(A),B),C))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.80/15.66 ** KEPT (pick-wt=18): 381 [] -class_Rings_Oidom(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Polynomial_Odegree(A,hAPP(hAPP(c_Polynomial_Osmult(A),B),C))=c_Polynomial_Odegree(A,C).
% 15.80/15.66 ** KEPT (pick-wt=17): 382 [] -class_Groups_Ozero(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.66 Following clause subsumed by 382 during input processing: 0 [] -class_Groups_Ozero(A)|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.80/15.66 ** KEPT (pick-wt=17): 383 [] -class_Groups_Ozero(A)|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.80/15.66 ** KEPT (pick-wt=32): 384 [] -class_Rings_Oring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),c_Groups_Oone__class_Oone(A))),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 15.80/15.66 ** KEPT (pick-wt=15): 385 [] -class_Groups_Ozero(A)|c_Polynomial_Odegree(A,hAPP(hAPP(c_Polynomial_OpCons(A),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.80/15.66 ** KEPT (pick-wt=21): 386 [] -class_Groups_Ozero(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Odegree(A,hAPP(hAPP(c_Polynomial_OpCons(A),C),B))=hAPP(c_Nat_OSuc,c_Polynomial_Odegree(A,B)).
% 15.80/15.66 ** KEPT (pick-wt=32): 387 [] -class_Rings_Oidom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Odegree(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Polynomial_Odegree(A,B)),c_Polynomial_Odegree(A,C)).
% 15.80/15.66 ** KEPT (pick-wt=16): 388 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osynthetic__div(A,B,C)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Odegree(A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.80/15.66 ** KEPT (pick-wt=16): 389 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osynthetic__div(A,B,C)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Odegree(A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.80/15.66 ** KEPT (pick-wt=18): 390 [] -class_Groups_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Odegree(A,hAPP(hAPP(c_Polynomial_OpCons(A),C),B))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.80/15.66 Following clause subsumed by 386 during input processing: 0 [] -class_Groups_Ozero(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Odegree(A,hAPP(hAPP(c_Polynomial_OpCons(A),C),B))=hAPP(c_Nat_OSuc,c_Polynomial_Odegree(A,B)).
% 15.80/15.66 ** KEPT (pick-wt=41): 391 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Ocoeff(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Polynomial_Odegree(A,B)),c_Polynomial_Odegree(A,C)))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))),hAPP(c_Polynomial_Ocoeff(A,C),c_Polynomial_Odegree(A,C))).
% 15.80/15.66 ** KEPT (pick-wt=12): 392 [] A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=B.
% 15.80/15.66 ** KEPT (pick-wt=15): 393 [] -class_Power_Opower(A)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B)=c_Groups_Oone__class_Oone(A).
% 15.80/15.66 ** KEPT (pick-wt=30): 395 [copy,394,flip.3] -class_Power_Opower(A)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B).
% 15.80/15.66 ** KEPT (pick-wt=45): 396 [] -class_Rings_Ocomm__ring__1(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)).
% 15.80/15.66 ** KEPT (pick-wt=34): 397 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))!=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|B=C|B=hAPP(c_Groups_Ouminus__class_Ouminus(A),C).
% 15.80/15.66 ** KEPT (pick-wt=28): 398 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|B!=C.
% 15.80/15.66 ** KEPT (pick-wt=31): 399 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|B!=hAPP(c_Groups_Ouminus__class_Ouminus(A),C).
% 15.80/15.66 ** KEPT (pick-wt=33): 400 [] -class_Rings_Oring__1(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),c_Groups_Oone__class_Oone(A))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Oone__class_Oone(A))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),c_Groups_Oone__class_Oone(A))).
% 15.80/15.66 ** KEPT (pick-wt=45): 402 [copy,401,flip.2] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),E)),D))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),D)).
% 15.80/15.66 ** KEPT (pick-wt=17): 403 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|C=hAPP(c_Groups_Ouminus__class_Ouminus(A),B).
% 15.80/15.66 ** KEPT (pick-wt=17): 404 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=c_Groups_Ozero__class_Ozero(A)|C!=hAPP(c_Groups_Ouminus__class_Ouminus(A),B).
% 15.80/15.66 ** KEPT (pick-wt=40): 405 [] -class_Rings_Oidom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),c_Polynomial_Oorder(A,C,B))),B)).
% 15.80/15.66 ** KEPT (pick-wt=42): 406 [] -class_Rings_Oidom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(A,C,B)))),B)).
% 15.80/15.66 ** KEPT (pick-wt=10): 407 [] -class_Rings_Ocomm__semiring__1(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),c_Groups_Ozero__class_Ozero(A))).
% 15.80/15.66 ** KEPT (pick-wt=23): 408 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),D))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)).
% 15.80/15.66 ** KEPT (pick-wt=9): 409 [] -class_Rings_Ocomm__semiring__1(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),B)).
% 15.80/15.66 ** KEPT (pick-wt=14): 410 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),c_Groups_Ozero__class_Ozero(A)),B))|B=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.66 ** KEPT (pick-wt=21): 411 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),D)).
% 15.80/15.66 ** KEPT (pick-wt=21): 412 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)).
% 15.80/15.66 ** KEPT (pick-wt=17): 413 [] -class_Rings_Odvd(A)|B!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),B)).
% 15.80/15.66 ** KEPT (pick-wt=33): 414 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),D),E))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))).
% 15.80/15.66 ** KEPT (pick-wt=21): 415 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))).
% 15.80/15.66 ** KEPT (pick-wt=21): 416 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))).
% 15.80/15.66 ** KEPT (pick-wt=14): 417 [] -class_Rings_Ocomm__semiring__1(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B))).
% 15.80/15.66 ** KEPT (pick-wt=14): 418 [] -class_Rings_Ocomm__semiring__1(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))).
% 15.80/15.66 ** KEPT (pick-wt=28): 419 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D))).
% 15.80/15.66 ** KEPT (pick-wt=28): 420 [] -class_Rings_Ocomm__ring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),D))).
% 15.80/15.66 ** KEPT (pick-wt=10): 421 [] -class_Rings_Ocomm__semiring__1(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),c_Groups_Oone__class_Oone(A)),B)).
% 15.80/15.66 ** KEPT (pick-wt=19): 422 [] -class_Rings_Ocomm__ring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)).
% 15.80/15.66 ** KEPT (pick-wt=19): 423 [] -class_Rings_Ocomm__ring__1(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),C))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)).
% 15.80/15.66 ** KEPT (pick-wt=19): 424 [] -class_Rings_Ocomm__ring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)).
% 15.80/15.66 ** KEPT (pick-wt=19): 425 [] -class_Rings_Ocomm__ring__1(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C)).
% 15.80/15.66 ** KEPT (pick-wt=26): 426 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D))).
% 15.80/15.66 ** KEPT (pick-wt=23): 427 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),D))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),D)).
% 15.80/15.66 ** KEPT (pick-wt=23): 428 [] -class_Rings_Ocomm__semiring__1(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),C))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Polynomial_Osmult(A),D),C))).
% 15.80/15.66 ** KEPT (pick-wt=13): 429 [] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=B.
% 15.80/15.66 ** KEPT (pick-wt=17): 430 [] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)=hAPP(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(A)),B).
% 15.80/15.66 ** KEPT (pick-wt=32): 432 [copy,431,flip.2] -class_Rings_Ocomm__ring(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),hAPP(hAPP(c_Polynomial_Osmult(A),B),D))=hAPP(hAPP(c_Polynomial_Osmult(A),B),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A)),C),D)).
% 15.80/15.66 ** KEPT (pick-wt=30): 433 [] -class_Rings_Oidom(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|B=c_Groups_Ozero__class_Ozero(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),D)).
% 15.80/15.66 ** KEPT (pick-wt=23): 434 [] -class_Rings_Oidom(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|B!=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.66 ** KEPT (pick-wt=26): 435 [] -class_Rings_Oidom(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),C),D)).
% 15.80/15.66 ** KEPT (pick-wt=30): 436 [] -class_Rings_Oidom(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))|C=c_Groups_Ozero__class_Ozero(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)).
% 15.80/15.66 ** KEPT (pick-wt=23): 437 [] -class_Rings_Oidom(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))|C!=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.66 ** KEPT (pick-wt=26): 438 [] -class_Rings_Oidom(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),D)).
% 15.80/15.66 ** KEPT (pick-wt=27): 439 [] -class_Fields_Ofield(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),hAPP(hAPP(c_Polynomial_Osmult(A),C),D)))|C=c_Groups_Ozero__class_Ozero(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),D)).
% 15.80/15.66 ** KEPT (pick-wt=27): 440 [] -class_Fields_Ofield(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),C))|D=c_Groups_Ozero__class_Ozero(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),D),B)),C)).
% 15.80/15.66 Following clause subsumed by 439 during input processing: 0 [] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),hAPP(hAPP(c_Polynomial_Osmult(A),B),D)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),D)).
% 15.80/15.66 ** KEPT (pick-wt=27): 441 [] -class_Fields_Ofield(A)|B=c_Groups_Ozero__class_Ozero(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),hAPP(hAPP(c_Polynomial_Osmult(A),B),D)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),D)).
% 15.80/15.66 ** KEPT (pick-wt=36): 442 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=hAPP(c_Polynomial_Ocoeff(A,C),c_Polynomial_Odegree(A,C))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),B),C))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),B))|B=C.
% 15.80/15.66 ** KEPT (pick-wt=24): 443 [] -class_Fields_Ofield(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),D))|B!=c_Groups_Ozero__class_Ozero(A)|D=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.80/15.66 ** KEPT (pick-wt=27): 444 [] -class_Fields_Ofield(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),D))|B=c_Groups_Ozero__class_Ozero(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),D)).
% 15.80/15.66 Following clause subsumed by 440 during input processing: 0 [] -class_Fields_Ofield(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),D))|B=c_Groups_Ozero__class_Ozero(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),D)).
% 15.80/15.66 ** KEPT (pick-wt=24): 445 [] -class_Fields_Ofield(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),D))|D!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B!=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.66 ** KEPT (pick-wt=28): 446 [] -class_Fields_Ofield(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_Osmult(A),B),C)),D))|D!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),C),D)).
% 15.80/15.66 ** KEPT (pick-wt=34): 447 [] -class_Rings_Oidom(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),B),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),C))|hAPP(c_Polynomial_Opoly(A,C),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.66 ** KEPT (pick-wt=34): 448 [] -class_Rings_Oidom(A)|hBOOL(hAPP(hAPP(c_R
% 15.80/15.66 Search stopped in tp_alloc by max_mem option.
% 15.80/15.66 ings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),B),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),C))|hAPP(c_Polynomial_Opoly(A,C),hAPP(c_Groups_Ouminus__class_Ouminus(A),B))!=c_Groups_Ozero__class_Ozero(A).
% 15.80/15.66 ** KEPT (pick-wt=34): 449 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Opoly(A,B),C)!=c_Groups_Ozero__class_Ozero(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),B)).
% 15.80/15.66 ** KEPT (pick-wt=34): 450 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Opoly(A,B),C)=c_Groups_Ozero__class_Ozero(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),B)).
% 15.80/15.66 ** KEPT (pick-wt=35): 451 [] -class_Rings_Oidom(A)|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),B)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),c_Polynomial_Oorder(A,B,C))),C)).
% 15.80/15.66 Following clause subsumed by 406 during input processing: 0 [] -class_Rings_Oidom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(A)),hAPP(hAPP(c_Polynomial_OpCons(A),hAPP(c_Groups_Ouminus__class_Ouminus(A),C)),hAPP(hAPP(c_Polynomial_OpCons(A),c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))),hAPP(c_Nat_OSuc,c_Polynomial_Oorder(A,C,B)))),B)).
% 15.80/15.66 ** KEPT (pick-wt=45): 452 [] -class_Rings_Ocomm__ring(A)| -class_Rings_Odvd(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),C))),E))).
% 15.80/15.66 ** KEPT (pick-wt=45): 453 [] -class_Rings_Ocomm__ring(A)| -class_Rings_Odvd(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),C))),E))).
% 15.80/15.66 Following clause subsumed by 452 during input processing: 0 [] -class_Rings_Ocomm__ring(A)| -class_Rings_Odvd(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E)))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),C))),E))).
% 15.80/15.66 Following clause subsumed by 453 during input processing: 0 [] -class_Rings_Ocomm__ring(A)| -class_Rings_Odvd(A)| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),C))|hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E)))| -hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),C))),E))).
% 15.80/15.66
% 15.80/15.66 Search stopped in tp_alloc by max_mem option.
% 15.80/15.66
% 15.80/15.66 ============ end of search ============
% 15.80/15.66
% 15.80/15.66 -------------- statistics -------------
% 15.80/15.66 clauses given 0
% 15.80/15.66 clauses generated 0
% 15.80/15.66 clauses kept 410
% 15.80/15.66 clauses forward subsumed 44
% 15.80/15.66 clauses back subsumed 0
% 15.80/15.66 Kbytes malloced 11718
% 15.80/15.66
% 15.80/15.66 ----------- times (seconds) -----------
% 15.80/15.66 user CPU time 0.19 (0 hr, 0 min, 0 sec)
% 15.80/15.66 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 15.80/15.66 wall-clock time 15 (0 hr, 0 min, 15 sec)
% 15.80/15.66
% 15.80/15.66 Process 30266 finished Wed Jul 27 03:05:06 2022
% 15.80/15.66 Otter interrupted
% 15.80/15.66 PROOF NOT FOUND
%------------------------------------------------------------------------------