TSTP Solution File: SWW204+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWW204+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:22:07 EDT 2022
% Result : Unknown 13.13s 13.00s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWW204+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 03:00:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 13.02/12.93 ----- Otter 3.3f, August 2004 -----
% 13.02/12.93 The process was started by sandbox on n025.cluster.edu,
% 13.02/12.93 Wed Jul 27 03:00:00 2022
% 13.02/12.93 The command was "./otter". The process ID is 26137.
% 13.02/12.93
% 13.02/12.93 set(prolog_style_variables).
% 13.02/12.93 set(auto).
% 13.02/12.93 dependent: set(auto1).
% 13.02/12.93 dependent: set(process_input).
% 13.02/12.93 dependent: clear(print_kept).
% 13.02/12.93 dependent: clear(print_new_demod).
% 13.02/12.93 dependent: clear(print_back_demod).
% 13.02/12.93 dependent: clear(print_back_sub).
% 13.02/12.93 dependent: set(control_memory).
% 13.02/12.93 dependent: assign(max_mem, 12000).
% 13.02/12.93 dependent: assign(pick_given_ratio, 4).
% 13.02/12.93 dependent: assign(stats_level, 1).
% 13.02/12.93 dependent: assign(max_seconds, 10800).
% 13.02/12.93 clear(print_given).
% 13.02/12.93
% 13.02/12.93 formula_list(usable).
% 13.02/12.93 all A (A=A).
% 13.02/12.93 all V_gb_2 V_fa_2 ((all B_x (hAPP(V_fa_2,B_x)=hAPP(V_gb_2,B_x)))->V_fa_2=V_gb_2).
% 13.02/12.93 c_SEQ_Osubse_q(v_ga____).
% 13.02/12.93 all V_x T_a (class_Orderings_Opreorder(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_x))).
% 13.02/12.93 all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n))),v_r)).
% 13.02/12.93 hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)).
% 13.02/12.93 c_SEQ_Osubse_q(v_f____).
% 13.02/12.93 all V_w hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w),V_w)).
% 13.02/12.93 all V_w V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z),V_w))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w),V_z))).
% 13.02/12.93 all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_j),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i),V_k)))).
% 13.02/12.93 all V_w V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z),V_w))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w),V_z))->V_z=V_w)).
% 13.02/12.93 all V_gb_2 V_fa_2 T_a T_b (class_Orderings_Oord(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2),V_gb_2))<-> (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,B_x)),hAPP(V_gb_2,B_x)))))).
% 13.02/12.93 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))).
% 13.02/12.93 all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (V_x_2=V_y_2<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2),V_x_2)))).
% 13.02/12.93 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (V_x=V_y->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y)))).
% 13.02/12.93 hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))).
% 13.02/12.93 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x)))).
% 13.02/12.93 all V_x_2 V_gb_2 V_fa_2 T_a T_b (class_Orderings_Oord(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2),V_gb_2))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,V_x_2)),hAPP(V_gb_2,V_x_2))))).
% 13.02/12.93 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_z),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_z),V_x))))).
% 13.02/12.93 all V_x V_y T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))->V_x=V_y))).
% 13.02/12.93 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_z))))).
% 13.02/12.93 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))->V_x=V_y))).
% 13.02/12.93 all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))-> (V_b=V_c->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_a))))).
% 13.02/12.93 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (V_b=V_c->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_c))))).
% 13.02/12.93 all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_a))))).
% 13.02/12.93 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_c))))).
% 13.02/12.93 all V_x_2 V_y_2 T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2),V_x_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))<->V_x_2=V_y_2))).
% 13.02/12.93 all V_x_2 V_gb_2 V_fa_2 T_a T_b (class_Orderings_Oord(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2),V_gb_2))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,V_x_2)),hAPP(V_gb_2,V_x_2))))).
% 13.02/12.93 all V_x_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))<->V_x_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.93 all V_x T_a (class_RealVector_Oreal__normed__vector(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_a,V_x)))).
% 13.02/12.93 all V_x_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_RealVector_Onorm__class_Onorm(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.93 all T_a (class_RealVector_Oreal__normed__vector(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.02/12.93 all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)).
% 13.02/12.93 all V_n_2 V_fa_2 (c_SEQ_Osubse_q(V_fa_2)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),hAPP(V_fa_2,V_n_2)))).
% 13.02/12.93 all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)).
% 13.02/12.93 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.93 all V_x_2 T_a (class_Groups_Ozero(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=V_x_2<->V_x_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.93 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.93 all V_y V_x V_c T_a (class_RealVector_Oreal__normed__vector(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_c),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y))))->V_x=c_Groups_Ozero__class_Ozero(T_a)))).
% 13.02/12.93 all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 13.02/12.93 all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_n)).
% 13.02/12.93 all V_y V_x T_a (class_RealVector_Oreal__normed__div__algebra(T_a)->c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))).
% 13.02/12.93 all V_w V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z)).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))).
% 13.02/12.93 all V_m_2 V_n_2 (c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_RealDef_Oreal(tc_Nat_Onat,V_m_2)<->V_n_2=V_m_2).
% 13.02/12.93 all V_z3 V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3))).
% 13.02/12.93 all V_n V_m (V_m=V_n->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))).
% 13.02/12.93 all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_k)))).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->V_m=V_n)).
% 13.02/12.93 all V_c V_b V_a T_a (class_Groups_Oab__semigroup__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 13.02/12.93 all V_b T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)=c_Groups_Ozero__class_Ozero(T_a)).
% 13.02/12.93 all V_y T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)=c_Groups_Ozero__class_Ozero(T_a)).
% 13.02/12.93 all V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 13.02/12.93 all V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 13.02/12.93 all V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))))).
% 13.02/12.93 all V_m_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),V_m_2))).
% 13.02/12.93 all V_b_2 V_a_2 V_c_2 (V_c_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2)<->V_a_2=V_b_2)).
% 13.02/12.93 all V_b_2 V_a_2 V_c_2 (V_c_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2)<->V_a_2=V_b_2)).
% 13.02/12.93 all V_n_2 (c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.93 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.93 all V_a T_a (class_Rings_Olinordered__ring(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)))).
% 13.02/12.93 all V_b_2 V_a_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.02/12.93 all V_b_2 V_a_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2)))).
% 13.02/12.93 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))))).
% 13.02/12.93 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 13.02/12.93 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 13.02/12.93 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 13.02/12.93 all V_b V_a T_a (class_Rings_Oordered__ring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))))).
% 13.02/12.93 all V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))))).
% 13.02/12.93 all V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))))).
% 13.02/12.93 all V_c V_b V_a T_a (class_Rings_Oordered__comm__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))))).
% 13.02/12.93 all V_n (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.93 all V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.93 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)).
% 13.02/12.93 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)).
% 13.02/12.93 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)).
% 13.02/12.93 all V_l V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_l))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))))).
% 13.02/12.93 all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))).
% 13.02/12.93 all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))).
% 13.02/12.93 all V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))).
% 13.02/12.93 all V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))).
% 13.02/12.93 all V_n V_m (c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 13.02/12.93 all V_b V_a T_a (class_Rings_Ono__zero__divisors(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)=c_Groups_Ozero__class_Ozero(T_a)->V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.93 all V_b V_a T_a (class_Rings_Ono__zero__divisors(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a)))).
% 13.02/12.93 all V_b_2 V_a_2 T_a (class_Rings_Oring__no__zero__divisors(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.93 all V_a T_a (class_Rings_Omult__zero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 13.02/12.93 all V_a T_a (class_Rings_Omult__zero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 13.02/12.93 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.02/12.93 all V_b V_a T_a (class_Rings_Oordered__ring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))).
% 13.02/12.93 all V_d V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))))).
% 13.02/12.93 all V_d V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))))).
% 13.02/12.93 all V_c V_a V_b T_a (class_Rings_Oordered__ring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))))).
% 13.02/12.93 all V_c V_a V_b T_a (class_Rings_Oordered__ring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))))).
% 13.02/12.93 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Odecse_q(T_a,V_X_2)<-> (all B_m B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m),B_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m))))))).
% 13.02/12.93 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 13.02/12.93 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 13.02/12.93 all T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))& (all B_a B_b hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))))))).
% 13.02/12.93 all V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))& (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))))))).
% 13.02/12.93 all V_y T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))& (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))))))).
% 13.02/12.93 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Oincse_q(T_a,V_X_2)<-> (all B_m B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m),B_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))))))).
% 13.02/12.93 all T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K all B_a B_b hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))))).
% 13.02/12.93 all V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))))).
% 13.02/12.93 all V_y T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))))).
% 13.02/12.93 all V_k V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))).
% 13.02/12.93 all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)).
% 13.02/12.93 all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry))).
% 13.02/12.93 all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry))).
% 13.02/12.93 all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)))).
% 13.02/12.93 all V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly)).
% 13.02/12.93 all V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx))).
% 13.02/12.93 all V_ry V_rx V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry)).
% 13.02/12.93 all V_ry V_rx V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry))).
% 13.02/12.93 all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)).
% 13.02/12.93 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).
% 13.02/12.93 all V_p_2 T_a (class_Groups_Ozero(T_a)-> (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_p_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 13.02/12.93 all V_b V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b))),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b)))))).
% 13.02/12.93 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Omonose_q(T_a,V_X_2)<-> (all B_m B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m),B_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n)))))| (all B_m B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m),B_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m))))))).
% 13.02/12.93 all V_a_2 V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),V_a_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_RealDef_Oreal(tc_Nat_Onat,V_a_2))))).
% 13.02/12.93 all V_a_2 V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2),c_RComplete_Onatfloor(V_x_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)),V_x_2)))).
% 13.02/12.93 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Odecse_q(T_a,V_X_2)->c_SEQ_Omonose_q(T_a,V_X_2))).
% 13.02/12.93 all V_b V_a T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 13.02/12.93 all V_x T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)=V_x).
% 13.02/12.93 all V_n (c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n).
% 13.02/12.93 all V_n (c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n).
% 13.02/12.93 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.93 all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(V_x))).
% 13.02/12.93 all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_RComplete_Onatfloor(V_y)))).
% 13.02/12.93 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.93 all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatceiling(V_x))).
% 13.02/12.93 all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)),c_RComplete_Onatceiling(V_y)))).
% 13.02/12.93 all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)))).
% 13.02/12.93 all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))->c_RComplete_Onatfloor(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.93 all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),V_x))).
% 13.02/12.93 all V_a V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),c_RComplete_Onatfloor(V_a)))).
% 13.02/12.93 all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))->c_RComplete_Onatceiling(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.93 all V_a V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)),V_a))).
% 13.02/12.93 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Oincse_q(T_a,V_X_2)->c_SEQ_Omonose_q(T_a,V_X_2))).
% 13.02/12.93 all V_a T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)=V_a).
% 13.02/12.93 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> ((all B_m B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m),B_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n)))))->c_SEQ_Omonose_q(T_a,V_X_2))).
% 13.02/12.93 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> ((all B_m B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m),B_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m)))))->c_SEQ_Omonose_q(T_a,V_X_2))).
% 13.02/12.93 all V_q T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 13.02/12.93 all V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 13.02/12.93 c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))).
% 13.02/12.93 all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)))).
% 13.02/12.93 all V_n_2 V_k_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))<-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)))).
% 13.02/12.93 all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))<-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)))).
% 13.02/12.93 all V_s V_y V_r V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_r))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s)))))).
% 13.02/12.93 all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 13.02/12.93 c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))).
% 13.02/12.93 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (V_x!=V_y-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))))).
% 13.02/12.93 all V_x T_a (class_Orderings_Opreorder(T_a)-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_x))).
% 13.02/12.93 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (V_x_2!=V_y_2<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)))).
% 13.02/12.93 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))|V_x_2=V_y_2)).
% 13.02/12.93 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))).
% 13.02/12.93 all V_x_2 V_y_2 T_a (class_Orderings_Olinorder(T_a)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))<->V_x_2=V_y_2))).
% 13.02/12.93 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (V_x!=V_y-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))))).
% 13.02/12.93 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->V_x!=V_y)).
% 13.02/12.93 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))).
% 13.02/12.93 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))).
% 13.02/12.93 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->V_x!=V_y)).
% 13.02/12.93 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->V_y!=V_x)).
% 13.02/12.93 all V_b V_a T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)))).
% 13.02/12.93 all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))).
% 13.02/12.93 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c))))).
% 13.02/12.93 all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a))))).
% 13.02/12.93 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (V_b=V_c->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c))))).
% 13.02/12.93 all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))-> (V_b=V_c->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a))))).
% 13.02/12.93 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z))))).
% 13.02/12.93 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x))))).
% 13.02/12.93 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))).
% 13.02/12.93 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))-> (V_x!=V_y->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))))).
% 13.02/12.93 all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n))).
% 13.02/12.93 all V_n_2 V_m_2 (V_m_2!=V_n_2<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))).
% 13.02/12.93 all V_y V_x (V_x!=V_y-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y),V_x)))).
% 13.02/12.93 all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n))).
% 13.02/12.93 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))->V_m!=V_n).
% 13.02/12.93 all V_t V_s (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s),V_t))->V_s!=V_t).
% 13.02/12.93 all V_P_2 V_n_2 V_m_2 ((hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))-> ((V_m_2=V_n_2->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))-> ((hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))))).
% 13.02/12.93 all V_m_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))).
% 13.02/12.93 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2),V_x_2)))).
% 13.02/12.93 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)))).
% 13.02/12.93 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))).
% 13.02/12.93 all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))&V_x_2!=V_y_2)).
% 13.02/12.93 all V_y_2 V_x_2 T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))& -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2),V_x_2)))).
% 13.02/12.93 all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|V_x_2=V_y_2)).
% 13.02/12.93 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x)))).
% 13.02/12.93 all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)))).
% 13.02/12.93 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))<->V_x_2=V_y_2))).
% 13.02/12.93 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))).
% 13.02/12.93 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))))).
% 13.02/12.93 all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)))).
% 13.02/12.93 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y)))).
% 13.02/12.93 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))<->V_x_2=V_y_2))).
% 13.02/12.93 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x=V_y)).
% 13.02/12.93 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (V_a!=V_b->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))).
% 13.02/12.93 all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))-> (V_a!=V_b->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))))).
% 13.02/12.93 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z))))).
% 13.02/12.93 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_z),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x))))).
% 13.02/12.93 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z))))).
% 13.02/12.93 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x))))).
% 13.02/12.93 all V_n (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.93 all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 13.02/12.93 all V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))).
% 13.02/12.93 all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 13.02/12.93 all V_y_2 V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2))&V_x_2!=V_y_2).
% 13.02/12.93 all V_y_2 V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))|V_x_2=V_y_2).
% 13.02/12.93 all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))&V_m_2!=V_n_2).
% 13.02/12.93 all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=V_n_2).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))-> (V_m!=V_n->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)))).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|V_m=V_n->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))).
% 13.02/12.93 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))).
% 13.02/12.93 all V_fa_2 (c_SEQ_Osubse_q(V_fa_2)<-> (all B_m B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m),B_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m)),hAPP(V_fa_2,B_n)))))).
% 13.02/12.93 all V_a T_a (class_Rings_Olinordered__ring(T_a)-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a)))).
% 13.02/12.93 all V_b_2 V_c_2 V_a_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)))).
% 13.02/12.93 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)))).
% 13.02/12.93 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))))).
% 13.02/12.93 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))))).
% 13.02/12.93 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 13.02/12.93 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 13.02/12.93 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))))).
% 13.02/12.93 all V_a V_b T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))))).
% 13.02/12.93 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2))))).
% 13.02/12.93 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 13.02/12.93 all V_b V_a T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))))).
% 13.02/12.93 all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))))).
% 13.02/12.93 all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))))).
% 13.02/12.93 all V_c V_b V_a T_a (class_Rings_Olinordered__comm__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))))).
% 13.02/12.93 all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))))).
% 13.02/12.93 all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))))).
% 13.02/12.93 all V_n V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_n)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_n)))).
% 13.02/12.93 all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))).
% 13.02/12.93 all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 13.02/12.93 all V_n_2 V_k_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 13.02/12.93 all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))))).
% 13.02/12.93 all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))))).
% 13.02/12.93 all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)))).
% 13.02/12.93 all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)<->V_m_2=V_n_2)).
% 13.02/12.93 all V_y V_x V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y))))).
% 13.02/12.93 all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))))).
% 13.02/12.93 all V_y_2 V_x_2 V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)))).
% 13.02/12.93 all V_x T_a (class_RealVector_Oreal__normed__vector(T_a)-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))).
% 13.02/12.93 all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))).
% 13.02/12.93 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2))))).
% 13.02/12.93 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2),V_a_2))))).
% 13.02/12.93 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))))).
% 13.02/12.93 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))))).
% 13.02/12.93 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))))).
% 13.02/12.93 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))))))).
% 13.02/12.93 all V_b V_c V_a T_a (class_Rings_Olinordered__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))).
% 13.02/12.93 all V_b V_c V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))).
% 13.02/12.93 all V_b V_a V_c T_a (class_Rings_Olinordered__semiring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))).
% 13.02/12.93 all V_b V_a V_c T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))).
% 13.02/12.93 all V_b V_c V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))))).
% 13.02/12.93 all V_b V_a V_c T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))))).
% 13.02/12.93 all V_x_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)))<->V_x_2!=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.93 all V_y_2 V_x_2 V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2)))).
% 13.02/12.93 all V_y_2 V_x_2 V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2)))).
% 13.02/12.93 -(all B_g (c_SEQ_Osubse_q(B_g)-> -c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,B_g)))))).
% 13.02/12.93 all V_x_2 (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)))<->V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.02/12.93 all V_y T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))& (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))))))).
% 13.02/12.93 all V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))& (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))))))).
% 13.02/12.93 all T_a (class_RealVector_Oreal__normed__algebra(T_a)-> (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))& (all B_a B_b hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))))))).
% 13.02/12.93 hAPP(c_Complex_OIm,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.93 all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),V_y))).
% 13.02/12.93 all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)<-> (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))& (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),B_K))))))).
% 13.02/12.93 exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))& (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))))).
% 13.02/12.93 all V_y V_x (hAPP(c_Complex_ORe,V_x)=hAPP(c_Complex_ORe,V_y)-> (hAPP(c_Complex_OIm,V_x)=hAPP(c_Complex_OIm,V_y)->V_x=V_y)).
% 13.02/12.93 all V_y_2 V_x_2 (V_x_2=V_y_2<->hAPP(c_Complex_ORe,V_x_2)=hAPP(c_Complex_ORe,V_y_2)&hAPP(c_Complex_OIm,V_x_2)=hAPP(c_Complex_OIm,V_y_2)).
% 13.02/12.93 hAPP(c_Complex_ORe,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.93 all V_gb_2 V_fa_2 T_a T_b (class_Orderings_Oord(T_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2),V_gb_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2),V_gb_2))& -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_gb_2),V_fa_2)))).
% 13.02/12.93 all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))).
% 13.02/12.93 exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))& (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))))).
% 13.02/12.93 exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))& (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))))).
% 13.02/12.93 exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))& (all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))))).
% 13.02/12.93 exists B_K all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))).
% 13.02/12.93 exists B_K all B_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))).
% 13.02/12.93 all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)-> (exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))& (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),B_K))))))).
% 13.02/12.93 all V_X_2 V_K_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_K_2))-> ((all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),V_K_2)))->c_SEQ_OBse_q(T_a,V_X_2)))).
% 13.02/12.93 all V_K_2 V_X_2 V_N_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> ((all B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_N_2),B_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),V_K_2))))->c_SEQ_OBse_q(T_a,V_X_2))).
% 13.02/12.93 all V_X_2 T_b (class_RealVector_Oreal__normed__vector(T_b)-> ((exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))& (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K)))))<-> (exists B_N all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))))))).
% 13.02/12.93 all V_X_2 T_b (class_RealVector_Oreal__normed__vector(T_b)-> ((exists B_K (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))& (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K)))))<-> (exists B_N all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))))))).
% 13.02/12.93 all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))-> (all B_y exists B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_x))))).
% 13.02/12.93 exists B_f (c_SEQ_Osubse_q(B_f)&c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,v_s),B_f))).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),c_Nat_OSuc(V_n)))).
% 13.02/12.93 all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Nat_OSuc(V_n))).
% 13.02/12.93 all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_OSuc(V_n))).
% 13.02/12.93 all V_y V_x (c_Nat_OSuc(V_x)=c_Nat_OSuc(V_y)->V_x=V_y).
% 13.02/12.93 all V_nat_H_2 V_nat_2 (c_Nat_OSuc(V_nat_2)=c_Nat_OSuc(V_nat_H_2)<->V_nat_2=V_nat_H_2).
% 13.02/12.93 all V_n (c_Nat_OSuc(V_n)!=V_n).
% 13.02/12.93 all V_n (V_n!=c_Nat_OSuc(V_n)).
% 13.02/12.93 all T_e T_d T_c T_a T_b V_x_H_2 V_g_H_2 V_f_H_2 V_x_2 V_gb_2 V_fa_2 (hAPP(V_fa_2,hAPP(V_gb_2,V_x_2))=hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2))->hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_x_2)=hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2,V_g_H_2),V_x_H_2)).
% 13.02/12.93 all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m)).
% 13.02/12.93 all V_nat_H (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_nat_H)).
% 13.02/12.93 all V_m (c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.93 all V_nat_H_1 (c_Nat_OSuc(V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.93 all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m)).
% 13.02/12.93 all V_m (c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),c_Nat_OSuc(V_n)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n)))-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->V_m=V_n)).
% 13.02/12.93 all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i)),V_k)))).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))-> (c_Nat_OSuc(V_m)!=V_n->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)))).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n)))).
% 13.02/12.93 all V_m V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Nat_OSuc(V_m)))->V_m=V_n)).
% 13.02/12.93 all V_m_2 V_n_2 (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2)))<->V_n_2=V_m_2)).
% 13.02/12.93 all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),c_Nat_OSuc(V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 13.02/12.93 all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=V_n_2).
% 13.02/12.93 all V_n_2 V_m_2 (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2)))).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n)))-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->V_m=c_Nat_OSuc(V_n))).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n)))).
% 13.02/12.93 all V_m_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),c_Nat_OSuc(V_m_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),V_m_2))).
% 13.02/12.93 all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=c_Nat_OSuc(V_n_2)).
% 13.02/12.93 all V_n_2 V_m_2 (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2))).
% 13.02/12.93 all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n)),V_n))).
% 13.02/12.93 all V_n_2 V_m_2 V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)<->V_m_2=V_n_2).
% 13.02/12.93 all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| (exists B_j (V_m_2=c_Nat_OSuc(B_j)&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_n_2))))).
% 13.02/12.93 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.93 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))<-> (exists B_m (V_n_2=c_Nat_OSuc(B_m)))).
% 13.02/12.93 all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.02/12.93 all V_m_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2))).
% 13.02/12.93 all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))).
% 13.02/12.93 all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),V_n_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n)))).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))).
% 13.02/12.93 all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2)))<->V_n_2=V_m_2)).
% 13.02/12.93 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))).
% 13.02/12.93 all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 13.02/12.94 all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))).
% 13.02/12.94 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Omonose_q(T_a,V_X_2)<-> (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,c_Nat_OSuc(B_n)))))| (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,c_Nat_OSuc(B_n))),hAPP(V_X_2,B_n)))))).
% 13.02/12.94 all V_fa_2 (c_SEQ_Osubse_q(V_fa_2)<-> (all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n)),hAPP(V_fa_2,c_Nat_OSuc(B_n)))))).
% 13.02/12.94 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2)=c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2))).
% 13.02/12.94 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))))).
% 13.02/12.94 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))))).
% 13.02/12.94 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))))).
% 13.02/12.94 all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2))).
% 13.02/12.94 all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)))).
% 13.02/12.94 all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)<-> (exists B_N all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))))))).
% 13.02/12.94 all V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)<-> (exists B_N all B_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))))))).
% 13.02/12.94 all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))->V_x=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.02/12.94 exists B_f (c_SEQ_Osubse_q(B_f)&c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,v_s),v_f____),B_f))).
% 13.02/12.94 all V_r (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r))-> (exists B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_r))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))))))).
% 13.02/12.94 all V_x V_y (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))-> (exists B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_y)),V_x))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))),V_y))))))).
% 13.02/12.94 all V_x_2 V_fa_2 V_c_2 T_c T_a T_b (hAPP(c_Fun_Ocomp(T_b,T_a,T_c,c_COMBK(T_a,T_b,V_c_2),V_fa_2),V_x_2)=V_c_2).
% 13.02/12.94 all V_v_2 V_c_2 V_b_2 V_a_2 T_a T_b T_c (c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)=V_c_2->hAPP(V_a_2,hAPP(V_b_2,V_v_2))=hAPP(V_c_2,V_v_2)).
% 13.02/12.94 all V_x_2 V_gb_2 V_fa_2 T_c T_a T_b (hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_x_2)=hAPP(V_fa_2,hAPP(V_gb_2,V_x_2))).
% 13.02/12.94 all V_x V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_x)=c_NthRoot_Oroot(V_m,c_NthRoot_Oroot(V_n,V_x))))).
% 13.02/12.94 all V_y V_x V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))->c_NthRoot_Oroot(V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_n,V_y))))).
% 13.02/12.94 all V_y V_x V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_n,V_y)))))).
% 13.02/12.94 all V_x_1 V_n_1 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_1))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_1))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_1,V_x_1))))).
% 13.02/12.94 all V_n (c_NthRoot_Oroot(V_n,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.02/12.94 all V_x (c_NthRoot_Oroot(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x)=V_x).
% 13.02/12.94 all V_x V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->c_NthRoot_Oroot(V_m,c_NthRoot_Oroot(V_n,V_x))=c_NthRoot_Oroot(V_n,c_NthRoot_Oroot(V_m,V_x)))).
% 13.02/12.94 all V_y_2 V_x_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))-> (c_NthRoot_Oroot(V_n_2,V_x_2)=c_NthRoot_Oroot(V_n_2,V_y_2)<->V_x_2=V_y_2)).
% 13.02/12.94 all V_y_2 V_x_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_NthRoot_Oroot(V_n_2,V_y_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2)))).
% 13.02/12.94 all V_y V_x V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_n,V_y))))).
% 13.02/12.94 all V_x_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))-> (c_NthRoot_Oroot(V_n_2,V_x_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.94 all V_y V_x V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_n,V_y))))).
% 13.02/12.94 all V_y_2 V_x_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_NthRoot_Oroot(V_n_2,V_y_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)))).
% 13.02/12.94 all V_y V_x V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->c_NthRoot_Oroot(V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_n,V_y))).
% 13.02/12.94 all V_x V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_x)=c_NthRoot_Oroot(V_m,c_NthRoot_Oroot(V_n,V_x)))).
% 13.02/12.94 all V_h_2 V_gb_2 T_d V_fa_2 T_a T_b T_c (c_Fun_Ocomp(T_c,T_b,T_a,V_fa_2,c_Fun_Ocomp(T_d,T_c,T_a,V_gb_2,V_h_2))=c_Fun_Ocomp(T_d,T_b,T_a,c_Fun_Ocomp(T_c,T_b,T_d,V_fa_2,V_gb_2),V_h_2)).
% 13.02/12.94 all V_x_2 V_gb_2 V_fa_2 T_c T_a T_b (hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_x_2)=hAPP(V_fa_2,hAPP(V_gb_2,V_x_2))).
% 13.02/12.94 all V_v_2 V_d_2 V_c_2 T_d V_b_2 V_a_2 T_a T_b T_c (c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)=c_Fun_Ocomp(T_d,T_b,T_a,V_c_2,V_d_2)->hAPP(V_a_2,hAPP(V_b_2,V_v_2))=hAPP(V_c_2,hAPP(V_d_2,V_v_2))).
% 13.02/12.94 all V_d_2 V_c_2 T_d V_b_2 V_a_2 T_a T_b T_c (c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)=c_Fun_Ocomp(T_d,T_b,T_a,V_c_2,V_d_2)-> (all B_v (hAPP(V_a_2,hAPP(V_b_2,B_v))=hAPP(V_c_2,hAPP(V_d_2,B_v))))).
% 13.02/12.94 all V_x V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n,V_x))))).
% 13.02/12.94 all V_x_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))).
% 13.02/12.94 all V_y_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_2,V_y_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)))).
% 13.02/12.94 all V_y_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_2,V_y_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)))).
% 13.02/12.94 all V_x_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))).
% 13.02/12.94 all V_x V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n,V_x))))).
% 13.02/12.94 all V_x V_N V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_N,V_x))))))).
% 13.02/12.94 all V_x V_N V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_N,V_x))))))).
% 13.02/12.94 all V_x V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),V_n)=V_x)).
% 13.02/12.94 all V_x V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->c_NthRoot_Oroot(V_n,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=V_x)).
% 13.02/12.94 all V_x V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),V_n)=V_x)).
% 13.02/12.94 all V_n V_x T_a (class_RealVector_Oreal__normed__div__algebra(T_a)->c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n)).
% 13.02/12.94 all T_a (class_RealVector_Oreal__normed__algebra__1(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.02/12.94 all V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a)).
% 13.02/12.94 all V_x_2 T_a (class_Groups_Oone(T_a)-> (c_Groups_Oone__class_Oone(T_a)=V_x_2<->V_x_2=c_Groups_Oone__class_Oone(T_a))).
% 13.02/12.94 all V_n V_x T_a (class_RealVector_Oreal__normed__algebra__1(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n)))).
% 13.02/12.94 all V_q V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q))).
% 13.02/12.94 all T_a (class_Rings_Ozero__ne_q__one(T_a)->c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a)).
% 13.02/12.94 all T_a (class_Rings_Ozero__ne_q__one(T_a)->c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a)).
% 13.02/12.94 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a).
% 13.02/12.94 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a).
% 13.02/12.94 all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a).
% 13.02/12.94 all V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a).
% 13.02/12.94 all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a).
% 13.02/12.94 all V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a).
% 13.02/12.94 all V_q V_p V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q))).
% 13.02/12.94 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))->c_SEQ_OBse_q(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)))).
% 13.02/12.94 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.94 all V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z)=V_z).
% 13.02/12.94 all V_n V_r T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_r))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_r),c_Groups_Oone__class_Oone(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),c_Nat_OSuc(V_n))),V_r))))).
% 13.02/12.94 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))->c_SEQ_Omonose_q(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)))).
% 13.02/12.94 all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))).
% 13.02/12.94 all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))).
% 13.02/12.94 all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))).
% 13.02/12.94 all T_a (class_Rings_Olinordered__semidom(T_a)-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a)))).
% 13.02/12.94 all T_a (class_Rings_Olinordered__semidom(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a)))).
% 13.02/12.94 all T_a (class_Rings_Olinordered__semidom(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a)))).
% 13.02/12.94 all T_a (class_Rings_Olinordered__semidom(T_a)-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a)))).
% 13.02/12.94 all V_n V_m T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_m))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)))))).
% 13.02/12.94 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)))))).
% 13.02/12.94 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)))))).
% 13.02/12.94 all V_k V_x V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->c_NthRoot_Oroot(V_n,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_k))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),V_k)).
% 13.02/12.94 c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.94 all V_x_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))-> (c_NthRoot_Oroot(V_n_2,V_x_2)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)<->V_x_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.94 all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->c_NthRoot_Oroot(V_n,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.02/12.94 all V_n V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->c_NthRoot_Oroot(c_Nat_OSuc(V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),c_Nat_OSuc(V_n)))=V_x).
% 13.02/12.94 all V_x V_N V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(V_N,V_x)),c_NthRoot_Oroot(V_n,V_x)))))).
% 13.02/12.94 all V_x_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))).
% 13.02/12.94 all V_y_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_2,V_y_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_y_2)))).
% 13.02/12.94 all V_y_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_2,V_y_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_y_2)))).
% 13.02/12.94 all V_x_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))).
% 13.02/12.94 all V_x V_N V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_N,V_x)),c_NthRoot_Oroot(V_n,V_x)))))).
% 13.02/12.94 all V_x V_y V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))-> (hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_y),V_n)=V_x->c_NthRoot_Oroot(V_n,V_x)=V_y))).
% 13.02/12.94 all V_n V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))))))).
% 13.02/12.94 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))).
% 13.02/12.94 all V_y_2 V_x_2 V_b_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_b_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x_2),V_y_2))))).
% 13.02/12.94 all V_n V_m V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))))).
% 13.02/12.94 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_N))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))).
% 13.02/12.94 all V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_a).
% 13.02/12.94 all V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_x).
% 13.02/12.94 all V_n (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)=V_n).
% 13.02/12.94 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)).
% 13.02/12.94 all V_n (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n).
% 13.02/12.94 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)).
% 13.02/12.94 all V_n (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.02/12.94 all V_m_2 V_x_2 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.02/12.94 all V_n V_m V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)))).
% 13.02/12.94 all V_n_2 V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.94 all V_n V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))).
% 13.02/12.94 all V_n_2 V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))).
% 13.02/12.94 all V_n V_m (c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n)).
% 13.02/12.94 all V_n V_m (hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n)=c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))).
% 13.02/12.94 c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.94 all V_n V_m (V_m=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)->V_n=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.94 hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.94 hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.94 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.94 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.02/12.94 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.02/12.94 all V_n V_x (V_x=c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))->c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n)).
% 13.02/12.94 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(V_x_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2))).
% 13.02/12.94 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))).
% 13.02/12.94 all V_n V_a T_a (class_Rings_Oring__1__no__zero__divisors(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)!=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.94 all V_n V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 13.02/12.94 all V_n V_b V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))).
% 13.02/12.94 all V_n T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a)).
% 13.02/12.94 all V_n V_m V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n)).
% 13.02/12.94 all V_n V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))))).
% 13.02/12.94 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 13.02/12.94 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 13.02/12.94 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 13.02/12.94 all V_n_2 V_a_2 T_a (class_Power_Opower(T_a)&class_Rings_Omult__zero(T_a)&class_Rings_Ono__zero__divisors(T_a)&class_Rings_Ozero__ne_q__one(T_a)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a)&V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.02/12.94 all V_n_2 V_m_2 V_a_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a_2))-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)<->V_m_2=V_n_2))).
% 13.02/12.94 all V_n T_a (class_Power_Opower(T_a)&class_Rings_Osemiring__0(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_OSuc(V_n))=c_Groups_Ozero__class_Ozero(T_a)).
% 13.02/12.94 all V_n V_a T_a (class_Power_Opower(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 13.02/12.94 all V_n V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)).
% 13.02/12.94 all V_a T_a (class_Power_Opower(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a)).
% 13.02/12.94 all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))))).
% 13.02/12.94 all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->V_a=V_b)))).
% 13.02/12.94 all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))))).
% 13.02/12.94 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))).
% 13.02/12.94 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))).
% 13.02/12.94 all V_n T_a (class_Power_Opower(T_a)&class_Rings_Osemiring__0(T_a)-> (V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a))& (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.94 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)))))).
% 13.02/12.94 all V_y_2 V_x_2 V_b_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_b_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2),V_y_2))))).
% 13.02/12.94 all V_n V_m V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))))).
% 13.02/12.94 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)))))).
% 13.02/12.94 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_N))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)))))).
% 13.02/12.94 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))).
% 13.02/12.94 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))),c_Groups_Oone__class_Oone(T_a)))))).
% 13.02/12.94 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))))).
% 13.02/12.94 all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->V_a=V_b))))).
% 13.02/12.94 all T_a (class_Power_Opower(T_a)->c_Power_Opower__class_Opower(T_a)=c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a))).
% 13.02/12.94 all V_a V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))-> (exists B_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_x))&hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n)=V_a& (all B_y (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_y))&hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n)=V_a->B_y=B_x)))))).
% 13.02/12.94 all V_a V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))-> (exists B_r (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_r))&hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n)=V_a)))).
% 13.02/12.94 all V_n V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n)))).
% 13.02/12.94 all V_n V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Transcendental_Oln(V_x))).
% 13.02/12.94 all V_z V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_x)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_y)))).
% 13.02/12.94 all V_w V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z1),V_z2)),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w))).
% 13.02/12.94 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))).
% 13.02/12.94 all V_c_2 V_b_2 V_a_2 T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)<->V_b_2=V_c_2)).
% 13.02/12.94 all V_c_2 V_a_2 V_b_2 T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)<->V_b_2=V_c_2)).
% 13.02/12.94 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)).
% 13.02/12.94 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)).
% 13.02/12.94 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)).
% 13.02/12.94 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)).
% 13.02/12.94 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))).
% 13.02/12.94 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)).
% 13.02/12.94 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))).
% 13.02/12.94 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)).
% 13.02/12.94 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))).
% 13.02/12.94 all V_s V_y V_r V_x T_a (class_RealVector_Oreal__normed__vector(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_r))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_r),V_s)))))).
% 13.02/12.94 all V_y V_x T_a (class_RealVector_Oreal__normed__vector(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))))).
% 13.02/12.94 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))).
% 13.02/12.94 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)).
% 13.02/12.94 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))).
% 13.02/12.94 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))).
% 13.02/12.94 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))).
% 13.02/12.94 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))).
% 13.02/12.94 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))).
% 13.02/12.94 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_a_2!=V_b_2&V_c_2!=V_d_2<->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))).
% 13.02/12.94 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))).
% 13.02/12.94 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)).
% 13.02/12.94 all V_z_2 V_x_2 V_y_2 V_w_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))<->V_w_2=V_x_2|V_y_2=V_z_2)).
% 13.02/12.94 all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))).
% 13.02/12.94 all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))).
% 13.02/12.94 all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))))).
% 13.02/12.94 all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))))).
% 13.02/12.94 all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))))).
% 13.02/12.94 all V_b_2 V_a_2 V_c_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)))).
% 13.02/12.94 all V_b_2 V_c_2 V_a_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)))).
% 13.02/12.94 all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)))).
% 13.02/12.94 all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)))).
% 13.02/12.94 all V_d V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))))).
% 13.02/12.94 all V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))))).
% 13.02/12.94 all V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))))).
% 13.02/12.94 all V_b_2 V_a_2 V_c_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2)))).
% 13.02/12.94 all V_b_2 V_c_2 V_a_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2)))).
% 13.02/12.94 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).
% 13.02/12.94 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).
% 13.02/12.94 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.94 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).
% 13.02/12.94 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).
% 13.02/12.94 all V_a_2 V_b_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_b_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.94 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).
% 13.02/12.94 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).
% 13.02/12.94 all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))->c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)),c_Transcendental_Oln(V_y)))).
% 13.02/12.94 all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))),V_x))).
% 13.02/12.94 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)))).
% 13.02/12.94 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))))).
% 13.02/12.94 all V_y_2 V_x_2 T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2))-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))))).
% 13.02/12.94 all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))))).
% 13.02/12.94 all V_a V_b V_c T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))))).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 13.02/12.94 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)))).
% 13.02/12.94 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))))).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 13.02/12.94 all V_c V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))))).
% 13.02/12.94 all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))))).
% 13.02/12.94 all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))))).
% 13.02/12.94 all V_y_2 V_x_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(T_a)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.94 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))))).
% 13.02/12.94 all V_a T_a (class_Rings_Olinordered__semidom(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))))).
% 13.02/12.94 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)).
% 13.02/12.94 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)).
% 13.02/12.94 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)).
% 13.02/12.94 all V_y_2 V_x_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)&V_y_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.02/12.94 all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x)),V_x))).
% 13.02/12.94 all V_y_2 V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))-> (c_Transcendental_Oln(V_x_2)=c_Transcendental_Oln(V_y_2)<->V_x_2=V_y_2))).
% 13.02/12.94 all V_y_2 V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))))).
% 13.02/12.94 c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))))).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))))).
% 13.02/12.94 all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))))).
% 13.02/12.94 all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))))).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 13.02/12.94 all V_y V_x T_a (class_Rings_Olinordered__ring(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))))).
% 13.02/12.94 all V_y_2 V_x_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a)))<->V_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.94 all V_y V_x T_a (class_Rings_Olinordered__ring(T_a)-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a)))).
% 13.02/12.94 all V_y_2 V_x_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))))<->V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.94 all T_a (class_Rings_Olinordered__semidom(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))))).
% 13.02/12.94 all V_a_2 V_times_2 V_one_2 T_a (hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_one_2).
% 13.02/12.94 all V_n_2 V_a_2 V_times_2 V_one_2 T_a (hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2))=hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2))).
% 13.02/12.94 all V_n (c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.94 all V_y V_x (hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y)))).
% 13.02/12.94 all V_y_2 V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2))))).
% 13.02/12.94 all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x)))).
% 13.02/12.94 all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)))).
% 13.02/12.94 all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))).
% 13.02/12.94 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))).
% 13.02/12.94 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))-> (c_Transcendental_Oln(V_x_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_x_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.94 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)))).
% 13.02/12.94 all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x)))).
% 13.02/12.94 all V_v V_u V_y V_a V_x T_a (class_Rings_Olinordered__semiring__1(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v)=c_Groups_Oone__class_Oone(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)))))))).
% 13.02/12.94 all V_m_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)))).
% 13.02/12.94 all V_m_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),V_m_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))).
% 13.02/12.94 all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))).
% 13.02/12.94 all V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)))).
% 13.02/12.94 all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)))).
% 13.02/12.94 all V_v V_u V_y V_a V_x T_a (class_Rings_Olinordered__semiring__1__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v)=c_Groups_Oone__class_Oone(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)))))))).
% 13.02/12.94 all V_x V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))->c_RComplete_Onatfloor(V_x)=V_n)).
% 13.02/12.94 all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.02/12.94 all V_x V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))->c_RComplete_Onatceiling(V_x)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 13.02/12.94 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.94 all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 13.02/12.94 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))).
% 13.02/12.94 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).
% 13.02/12.94 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).
% 13.02/12.94 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)).
% 13.02/12.94 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)).
% 13.02/12.94 all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n))).
% 13.02/12.94 all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n)=c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))).
% 13.02/12.94 all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n))=c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))).
% 13.02/12.94 all V_y V_z V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))).
% 13.02/12.94 all V_z V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))).
% 13.02/12.94 all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_k))).
% 13.02/12.94 all V_n V_m V_l V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)))).
% 13.02/12.94 all V_l V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))))).
% 13.02/12.94 all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)))).
% 13.02/12.94 all V_m V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)))).
% 13.02/12.94 all V_m V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)))).
% 13.02/12.94 all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 13.02/12.94 all V_i V_j (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i))).
% 13.02/12.94 all V_j V_i (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i))).
% 13.02/12.94 all V_z V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))).
% 13.02/12.94 all V_y V_z V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))).
% 13.02/12.94 all V_n V_k V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))-> -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n)))).
% 13.02/12.94 all V_n V_k V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))).
% 13.02/12.94 all V_n V_k V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n))).
% 13.02/12.94 all V_l V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_l))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))))).
% 13.02/12.94 all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)))).
% 13.02/12.94 all V_m V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)))).
% 13.02/12.94 all V_m V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)))).
% 13.02/12.94 all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))).
% 13.02/12.94 all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))<-> (exists B_k (V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)))).
% 13.02/12.94 all V_l_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_l_2))<-> (exists B_n (V_l_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),B_n)))).
% 13.02/12.94 all V_m V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))).
% 13.02/12.94 all V_m V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))).
% 13.02/12.94 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)).
% 13.02/12.94 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))).
% 13.02/12.94 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))).
% 13.02/12.94 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).
% 13.02/12.94 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).
% 13.02/12.94 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)).
% 13.02/12.94 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))).
% 13.02/12.94 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))).
% 13.02/12.94 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).
% 13.02/12.94 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).
% 13.02/12.94 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))).
% 13.02/12.94 all V_k_2 V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,V_X_2)->c_SEQ_OBse_q(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2))))).
% 13.02/12.94 all V_k_2 V_X_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_SEQ_OBse_q(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2)))->c_SEQ_OBse_q(T_a,V_X_2))).
% 13.02/12.94 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))).
% 13.02/12.94 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))).
% 13.02/12.94 all V_n_2 V_m_2 (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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.02/12.94 all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.02/12.94 all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))).
% 13.02/12.94 all V_m V_i hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))).
% 13.02/12.94 all V_m V_i hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))).
% 13.02/12.94 all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))<-> (exists B_k (V_n_2=c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k))))).
% 13.02/12.94 all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),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))).
% 13.02/12.94 all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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))).
% 13.02/12.94 all V_n (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)).
% 13.02/12.94 all V_n (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))).
% 13.02/12.94 all V_y V_x (hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y))).
% 13.02/12.94 all V_y V_x (hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))).
% 13.02/12.94 all V_n V_m (c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 13.02/12.94 all V_z V_w hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_w),V_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)))).
% 13.02/12.94 all V_z V_y V_x (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z))).
% 13.02/12.94 all V_a V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_a)).
% 13.02/12.94 all V_n V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_z)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z),c_RealDef_Oreal(tc_Nat_Onat,V_n)))).
% 13.02/12.94 all V_a V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),V_a)).
% 13.02/12.94 all V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))->c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 13.02/12.94 all V_n V_b (V_b!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)-> (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (exists B_z hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),V_n))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))).
% 13.02/12.94 all V_n_2 V_P_2 (-hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))-> (hBOOL(hAPP(V_P_2,V_n_2))-> (exists B_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k),V_n_2))& (all B_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i),B_k))-> -hBOOL(hAPP(V_P_2,B_i))))&hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))).
% 13.02/12.94 all V_a V_n (c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))),V_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)))).
% 13.02/12.94 all V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z).
% 13.02/12.94 all V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)=V_z).
% 13.02/12.94 all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint)<->V_m_2=c_Groups_Oone__class_Oone(tc_Int_Oint)&V_n_2=c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 13.02/12.94 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))).
% 13.02/12.94 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))).
% 13.02/12.94 all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))))).
% 13.02/12.94 all V_w V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)).
% 13.02/12.94 all V_z3 V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3))).
% 13.02/12.94 all V_n V_a (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n)=c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a))).
% 13.02/12.94 all V_b V_a (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(V_b))=c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b))).
% 13.02/12.94 c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex).
% 13.02/12.94 all V_n V_a V_r (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(V_r,V_a)),V_n)=c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_r),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a))).
% 13.02/12.94 c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex).
% 13.02/12.94 all V_a V_n (c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a))=hAPP(c_Complex_ORe,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n))).
% 13.02/12.94 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)).
% 13.02/12.94 all V_z_2 V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2))).
% 13.02/12.94 all V_z_2 V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))).
% 13.02/12.94 all V_z V_w (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z))).
% 13.02/12.94 all V_z_2 V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))|V_w_2=V_z_2).
% 13.02/12.94 all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)))).
% 13.02/12.94 all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))).
% 13.02/12.94 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).
% 13.02/12.94 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).
% 13.02/12.94 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))).
% 13.02/12.94 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))).
% 13.02/12.94 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)).
% 13.02/12.94 all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j)))).
% 13.02/12.94 all V_z V_z_H V_w V_w_H (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H),V_w))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_H),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))))).
% 13.02/12.94 all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k)))).
% 13.02/12.94 all V_a V_r (hAPP(c_Complex_ORe,c_Complex_Orcis(V_r,V_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a))).
% 13.02/12.94 all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.94 c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.94 all V_w_2 V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),V_w_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2),V_w_2))&V_z_2!=V_w_2).
% 13.02/12.94 all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x),V_y))|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y),V_x))).
% 13.02/12.94 hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 13.02/12.94 all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))).
% 13.02/12.94 c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.02/12.94 all V_a (hAPP(c_Complex_ORe,c_Complex_Ocis(V_a))=c_Transcendental_Ocos(V_a)).
% 13.02/12.94 all V_a (c_Complex_Ocis(V_a)=c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_a)).
% 13.02/12.94 all V_a (c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)).
% 13.02/12.94 all V_b V_r2 V_a V_r1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(V_r1,V_a)),c_Complex_Orcis(V_r2,V_b))=c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r1),V_r2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b))).
% 13.02/12.94 all V_b V_a (c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(V_a)),c_Complex_Oexpi(V_b))).
% 13.02/12.94 all V_q V_r V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))-> (V_a=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q),c_Groups_Oone__class_Oone(tc_Int_Oint)))))).
% 13.02/12.94 all V_q V_r V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))-> (V_a=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q))))).
% 13.02/12.94 all V_r_H V_q_H V_b_H (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H))))).
% 13.02/12.94 all V_w hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w),V_w)).
% 13.02/12.94 all V_w V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z),V_w))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w),V_z))).
% 13.02/12.94 all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_j),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i),V_k)))).
% 13.02/12.94 all V_w V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z),V_w))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w),V_z))->V_z=V_w)).
% 13.02/12.94 all V_r_H V_q_H V_b_H V_r V_q V_b (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H),V_q)))))))).
% 13.02/12.94 all V_r V_q V_r_H V_q_H V_b (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r_H))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q),V_q_H)))))).
% 13.02/12.94 all V_r_H V_q_H V_b_H V_r V_q V_b (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q),V_q_H)))))))).
% 13.02/12.94 all V_r V_q V_r_H V_q_H V_b (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H),V_q)))))).
% 13.02/12.94 all V_r_H V_q_H V_b_H (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))).
% 13.02/12.94 all V_n V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)))).
% 13.02/12.94 all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))))).
% 13.02/12.94 all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))))).
% 13.02/12.94 hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.94 hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 13.02/12.94 all V_a V_n (c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a))=hAPP(c_Complex_OIm,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n))).
% 13.02/12.94 all V_n V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))-> (exists B_r (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_r))&hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),c_Nat_OSuc(V_n))=V_a))).
% 13.02/12.94 c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.94 all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.94 all V_a (hAPP(c_Complex_OIm,c_Complex_Ocis(V_a))=c_Transcendental_Osin(V_a)).
% 13.02/12.94 all V_x (c_Transcendental_Ocos(V_x)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)->c_Transcendental_Osin(V_x)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.02/12.94 all V_y V_x (c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Ocos(V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Osin(V_y)))).
% 13.02/12.94 all V_a V_r (hAPP(c_Complex_OIm,c_Complex_Orcis(V_r,V_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a))).
% 13.02/12.94 all V_x (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_x)))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.02/12.94 all V_x V_n T_a (class_Groups_Omonoid__mult(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))).
% 13.02/12.94 all V_m V_n T_a (class_Power_Opower(T_a)-> (V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=c_Groups_Oone__class_Oone(T_a))& (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))).
% 13.02/12.94 all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.02/12.94 all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))))).
% 13.02/12.94 all V_n V_m V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_m))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))).
% 13.02/12.94 all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)<->V_m_2=V_n_2))).
% 13.02/12.94 all V_n V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_n))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i))=V_i).
% 13.02/12.94 all V_l V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)))).
% 13.02/12.94 all V_l V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)))).
% 13.02/12.94 all V_n V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_m)).
% 13.02/12.94 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2),V_d_2))))).
% 13.02/12.94 all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))))).
% 13.02/12.94 all V_n V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),c_Nat_OSuc(V_m))).
% 13.02/12.94 all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.94 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.94 all V_n_2 V_m_2 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))).
% 13.02/12.94 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))).
% 13.02/12.94 all V_k_2 V_j_2 V_i_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2))).
% 13.02/12.94 all V_n V_m (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m).
% 13.02/12.94 all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))))).
% 13.02/12.94 all V_c V_b V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_c),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c))))).
% 13.02/12.94 all V_i V_j V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),V_j)).
% 13.02/12.94 all V_i_2 V_k_2 V_j_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)),V_i_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)))).
% 13.02/12.94 all V_m V_n V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_k)))).
% 13.02/12.94 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m).
% 13.02/12.94 all V_i V_j V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k)).
% 13.02/12.94 all V_i_2 V_j_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_j_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)))).
% 13.02/12.94 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_n)=V_m).
% 13.02/12.94 all V_k_2 V_j_2 V_i_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_k_2<->V_j_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2))).
% 13.02/12.94 all V_i V_j V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))).
% 13.02/12.94 all V_i V_j V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k)).
% 13.02/12.94 all V_i V_j V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i)).
% 13.02/12.94 all V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n).
% 13.02/12.94 all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)).
% 13.02/12.94 all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya)=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya))).
% 13.02/12.94 all V_b V_a_H V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b)=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b))).
% 13.02/12.94 all V_y V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y))).
% 13.02/12.94 all V_b_H V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H))=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H))).
% 13.02/12.94 all V_k V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))).
% 13.02/12.94 all V_n V_m V_k (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))).
% 13.02/12.94 all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))).
% 13.02/12.94 all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 13.02/12.94 all V_k V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k)).
% 13.02/12.94 all V_x_2 V_B_2 V_A_2 T_b T_a (class_Groups_Ominus(T_a)->hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2)=c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2))).
% 13.02/12.94 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Groups_Oab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)-> (V_a_2=V_b_2<->V_c_2=V_d_2))).
% 13.02/12.94 all V_k V_j V_i (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j)).
% 13.02/12.94 all V_x_2 V_B_2 V_A_2 T_b T_a (class_Groups_Ominus(T_a)->hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2)=c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2))).
% 13.02/12.94 all V_m_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 13.02/12.94 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_m)))).
% 13.02/12.94 all V_l V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_l))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))))).
% 13.02/12.94 all V_n V_k V_j (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n)),V_k))).
% 13.02/12.94 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),V_d_2))))).
% 13.02/12.94 all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=V_b_2)).
% 13.02/12.94 all V_b_2 V_a_2 T_a (class_Groups_Oab__group__add(T_a)-> (V_a_2=V_b_2<->c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.94 all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 13.02/12.94 all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 13.02/12.94 all V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.94 all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 13.02/12.94 all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.94 all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->V_m=V_n)).
% 13.02/12.94 all V_b V_a V_y V_x T_a (class_Rings_Oring(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b))).
% 13.02/12.94 all V_b V_a V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)))).
% 13.02/12.94 all V_d_2 V_b_2 V_c_2 V_e_2 V_a_2 T_a (class_Rings_Oring(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)<->V_c_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2))).
% 13.02/12.94 all V_d_2 V_b_2 V_c_2 V_e_2 V_a_2 T_a (class_Rings_Oring(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)<->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)=V_d_2)).
% 13.02/12.94 all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.02/12.94 all V_n V_k V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 13.02/12.94 all V_n V_m V_k (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 13.02/12.94 all V_k V_j V_i (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))).
% 13.02/12.94 all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_n)=V_m).
% 13.02/12.94 all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n),V_n)=V_m).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b)=V_a).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),V_b)=V_a).
% 13.02/12.94 all V_d_2 V_b_2 V_c_2 V_e_2 V_a_2 T_a (class_Rings_Oordered__ring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2))))).
% 13.02/12.94 all V_d_2 V_b_2 V_c_2 V_e_2 V_a_2 T_a (class_Rings_Oordered__ring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)),V_d_2)))).
% 13.02/12.94 all V_d_2 V_b_2 V_c_2 V_e_2 V_a_2 T_a (class_Rings_Oordered__ring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2))))).
% 13.02/12.94 all V_d_2 V_b_2 V_c_2 V_e_2 V_a_2 T_a (class_Rings_Oordered__ring(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)),V_d_2)))).
% 13.02/12.94 all V_x T_a (class_Rings_Oring__1(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)))).
% 13.02/12.94 all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_a)),c_RealVector_Onorm__class_Onorm(T_a,V_b))))).
% 13.02/12.94 all V_i V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i))),V_n))).
% 13.02/12.94 all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n).
% 13.02/12.94 all V_b_2 V_a_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))<-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))->hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))& (all B_d (V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)->hBOOL(hAPP(V_P_2,B_d))))).
% 13.02/12.94 all V_b_2 V_a_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))<-> -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))& -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| (exists B_d (V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)& -hBOOL(hAPP(V_P_2,B_d)))))).
% 13.02/12.94 all V_m V_j V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),c_Nat_OSuc(V_j))).
% 13.02/12.94 all V_m V_j V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m))).
% 13.02/12.94 all V_n_2 V_m_2 V_u_2 V_i_2 V_j_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)))).
% 13.02/12.94 all V_n V_m V_u V_i V_j (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j),V_i))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u)),V_m),V_n)).
% 13.02/12.94 all V_n_2 V_m_2 V_u_2 V_i_2 V_j_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)<->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)=V_n_2)).
% 13.02/12.94 all V_n_2 V_m_2 V_u_2 V_j_2 V_i_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))))).
% 13.02/12.94 all V_n V_m V_u V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u)),V_n))).
% 13.02/12.94 all V_n_2 V_m_2 V_u_2 V_j_2 V_i_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)<->V_m_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))).
% 13.02/12.94 all V_d V_c V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(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(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))))).
% 13.02/12.94 all V_y V_n V_p T_a (class_Groups_Omonoid__mult(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_p),V_n))->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y))).
% 13.02/12.94 all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=V_n).
% 13.02/12.94 all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->V_n=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 13.02/12.94 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)=c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)))).
% 13.02/12.94 all V_n_2 V_m_2 V_u_2 V_j_2 V_i_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))))).
% 13.02/12.94 all V_n_2 V_m_2 V_u_2 V_i_2 V_j_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)))).
% 13.02/12.94 all V_n V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)))).
% 13.02/12.94 all V_p V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=c_Groups_Oone__class_Oone(tc_Nat_Onat))& (V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))).
% 13.02/12.94 all V_y V_x T_a (class_Rings_Ocomm__ring__1(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))).
% 13.02/12.94 all V_r (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r))-> (exists B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_r))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r),c_RealDef_Oreal(tc_Nat_Onat,B_n)))))).
% 13.02/12.94 all V_X_2 V_M_2 T_a T_b (class_RealVector_Oreal__normed__vector(T_b)&class_Orderings_Oord(T_a)-> ((all B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2),B_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,B_n)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))-> (all B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2),B_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2))))))))).
% 13.02/12.94 all V_y_2 V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))).
% 13.02/12.94 all V_z2 V_z1 V_w (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))).
% 13.02/12.94 all V_w V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))).
% 13.02/12.94 all V_y V_x (hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y))).
% 13.02/12.94 all V_y V_x (hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y))).
% 13.02/12.94 all V_l_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_l_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))).
% 13.02/12.94 all V_p T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=V_p).
% 13.02/12.94 all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))))).
% 13.02/12.94 all V_z_2 V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))).
% 13.02/12.94 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 13.02/12.94 all V_y V_x (c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Osin(V_y)))).
% 13.02/12.94 all V_y V_x (c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_y)),c_Transcendental_Osin(V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_y)),c_Transcendental_Ocos(V_x)))).
% 13.02/12.94 all V_a V_b hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_b),V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a))).
% 13.02/12.94 all V_y V_x (c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y)))).
% 13.02/12.94 all V_y V_x (c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y)))).
% 13.02/12.94 all V_y V_x (c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_y)),c_Transcendental_Ocos(V_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_y)),c_Transcendental_Osin(V_x)))).
% 13.02/12.94 all V_x V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a)),V_x))->c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)).
% 13.02/12.94 all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)))).
% 13.02/12.94 all V_x V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a)),V_x))->c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)).
% 13.02/12.94 all V_y V_x (hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y)))).
% 13.02/12.94 all V_z (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))).
% 13.02/12.94 all V_k V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))->c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))).
% 13.02/12.94 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))).
% 13.02/12.94 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)).
% 13.02/12.94 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)).
% 13.02/12.94 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))).
% 13.02/12.94 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))).
% 13.02/12.94 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)).
% 13.02/12.94 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).
% 13.02/12.94 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))).
% 13.02/12.94 all V_a_2 V_b_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))).
% 13.02/12.94 all V_a_2 V_b_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)))).
% 13.02/12.94 all V_b V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))).
% 13.02/12.94 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)).
% 13.02/12.94 all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y))))).
% 13.02/12.94 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)).
% 13.02/12.94 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)).
% 13.02/12.94 c_Complex_Oii!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex).
% 13.02/12.94 c_Complex_Oii!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.02/12.94 hAPP(c_Complex_ORe,c_Complex_Oii)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.94 all V_b V_a_H V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),V_a_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))))).
% 13.02/12.94 all V_b V_a_H V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),V_a_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b))))).
% 13.02/12.94 all V_b V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_a))->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.94 all V_b V_b_H V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)))))).
% 13.02/12.94 all V_b V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))).
% 13.02/12.94 all V_a_2 V_b_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))).
% 13.02/12.94 all V_b V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),V_b))->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.94 all V_b V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))).
% 13.02/12.94 all V_b V_b_H V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)))))).
% 13.02/12.94 all V_b_2 V_a_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_2),V_a_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))).
% 13.02/12.94 all V_i_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2),V_i_2)))).
% 13.02/12.94 all V_a_2 V_b_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)))).
% 13.02/12.94 all V_k_2 V_i_2 (c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<->V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_i_2))).
% 13.02/12.94 all V_k V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k)),V_x)))).
% 13.02/12.94 all V_b V_a V_c (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c)).
% 13.02/12.94 hAPP(c_Complex_OIm,c_Complex_Oii)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.94 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)))).
% 13.02/12.94 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)))).
% 13.02/12.94 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)))).
% 13.02/12.94 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)))).
% 13.02/12.94 all V_r_1 V_y V_b_1 V_a_1 (V_a_1=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)-> ((hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1),V_b_1)))& (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1),V_r_1))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))-> (V_b_1!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1)=V_y))).
% 13.02/12.94 all V_k_2 V_n_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))<-> (V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)->hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))& (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))-> (all B_i ((exists B_j (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j),V_k_2))&V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)))->hBOOL(hAPP(V_P_2,B_i)))))& (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (all B_i ((exists B_j (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),B_j))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))&V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)))->hBOOL(hAPP(V_P_2,B_i)))))).
% 13.02/12.94 all V_y V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y)))))).
% 13.02/12.94 all V_x V_y ((hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y),V_x))->c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y))& (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y),V_x))->c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))))).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))))).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))))).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))))).
% 13.02/12.94 all V_d V_c V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(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),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))))).
% 13.02/12.94 all V_ra_2 V_a_2 V_x_2 T_a (class_Rings_Olinordered__idom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2))),V_ra_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2)),V_x_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ra_2))))).
% 13.02/12.94 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.94 all V_m (c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=V_m).
% 13.02/12.94 all V_k V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k)))).
% 13.02/12.94 all V_n V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_m)).
% 13.02/12.94 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)).
% 13.02/12.94 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)).
% 13.02/12.94 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))).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))).
% 13.02/12.94 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a)))).
% 13.02/12.94 all V_a_2 T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))<->V_a_2!=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.94 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))->c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a)).
% 13.02/12.94 all V_d V_b V_c V_a T_a (class_Rings_Olinordered__idom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),V_c))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b)),V_d))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)))))).
% 13.02/12.94 all T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a)).
% 13.02/12.94 all T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 13.02/12.94 all V_a_2 T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (c_Groups_Oabs__class_Oabs(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.94 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a))=c_Groups_Oabs__class_Oabs(T_a,V_a)).
% 13.02/12.94 all V_x (c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x))=c_RealDef_Oreal(tc_Nat_Onat,V_x)).
% 13.02/12.94 all V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a))=c_RealVector_Onorm__class_Onorm(T_a,V_a)).
% 13.02/12.94 all V_r (c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)).
% 13.02/12.94 all V_n V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n)).
% 13.02/12.94 all V_b V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))).
% 13.02/12.94 all V_a T_a (class_Rings_Olinordered__idom(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)).
% 13.02/12.94 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a)))).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)))).
% 13.02/12.94 all V_b V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(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_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))))).
% 13.02/12.94 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))->c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a)).
% 13.02/12.94 all V_a_2 T_a (class_Groups_Oordered__ab__group__add__abs(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.94 all V_a T_a (class_Groups_Oordered__ab__group__add__abs(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)))).
% 13.02/12.94 all V_n V_a T_a (class_Rings_Olinordered__idom(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n)))).
% 13.02/12.94 all V_b V_a T_a (class_Rings_Oordered__ring__abs(T_a)-> ((hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))))& (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))->c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))).
% 13.02/12.94 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x)=c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)))).
% 13.02/12.94 all V_a V_r (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(V_r,V_a))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r)).
% 13.02/12.94 all V_k V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m))))).
% 13.02/12.94 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n)=V_m).
% 13.02/12.94 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n)=V_m).
% 13.02/12.94 all V_n V_m V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)).
% 13.02/12.94 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_m)))).
% 13.02/12.94 all V_y V_x V_c (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_c),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y))))->V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.94 all V_x (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_x))).
% 13.02/12.94 all V_x V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->c_NthRoot_Oroot(V_n,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x))).
% 13.02/12.94 all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.94 all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Osin(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.94 all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))).
% 13.02/12.94 all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))).
% 13.02/12.94 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)))).
% 13.02/12.94 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)))).
% 13.02/12.94 all V_k_2 V_n_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))<-> (V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))& (V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (all B_i B_j (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_k_2))-> (V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)->hBOOL(hAPP(V_P_2,B_i))))))).
% 13.02/12.94 all V_b V_a T_a (class_RealVector_Oreal__normed__vector(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))))).
% 13.02/12.94 all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)))).
% 13.02/12.94 all V_x (c_Transcendental_Osin(V_x)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)->c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.02/12.94 all V_n_2 V_m_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| (exists B_q (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(B_q))))&hBOOL(hAPP(V_P_2,B_q))))).
% 13.02/12.94 all V_m_2 V_q_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(V_q_2))))<->V_q_2=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2))).
% 13.02/12.94 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)))).
% 13.02/12.94 all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y))))).
% 13.02/12.94 all V_x V_y (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y),V_x))->c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y)).
% 13.02/12.94 all V_d V_b V_c V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d))).
% 13.02/12.94 all V_y V_x (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)=c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y))))).
% 13.02/12.94 all V_n V_m (c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n))=c_Groups_Oone__class_Oone(tc_Int_Oint)->c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m)=c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 13.02/12.94 all V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))<->V_z_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 13.02/12.94 all V_b_2 V_a_2 (c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)<->V_a_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)&V_b_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.02/12.94 c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)=c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.02/12.94 all V_d V_c V_b V_a (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d))=c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_b),V_d))).
% 13.02/12.94 all V_real2_H_2 V_real1_H_2 V_real2_2 V_real1_2 (c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)=c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)<->V_real1_2=V_real1_H_2&V_real2_2=V_real2_H_2).
% 13.02/12.94 all V_y V_x (hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(V_x,V_y))=V_y).
% 13.02/12.94 all V_y V_x (hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(V_x,V_y))=V_x).
% 13.02/12.94 all V_z (c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,V_z),hAPP(c_Complex_OIm,V_z))=V_z).
% 13.02/12.94 all V_d V_c V_b V_a (c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d))=c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_d))).
% 13.02/12.94 all V_n V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n))).
% 13.02/12.94 all V_y_2 V_x_2 (c_Complex_Ocomplex_OComplex(V_x_2,V_y_2)=c_Complex_Oii<->V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)&V_y_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.02/12.94 c_Complex_Oii=c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.02/12.94 all V_b_2 V_a_2 (c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)<->V_a_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)&V_b_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.02/12.94 c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)=c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.02/12.94 all V_a (c_Complex_Ocis(V_a)=c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(V_a),c_Transcendental_Osin(V_a))).
% 13.02/12.94 all V_n_2 V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2)))<->V_x_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.94 all V_a (c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(V_a),c_Transcendental_Osin(V_a)))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.02/12.94 all V_d V_c V_b V_a (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d))=c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_d)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_d)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_c)))).
% 13.02/12.94 all V_y V_x (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y)=c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y)))).
% 13.02/12.94 all V_z V_x V_d (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z))).
% 13.02/12.94 all V_x V_z V_d (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))))).
% 13.02/12.94 all V_real2 V_real1 (c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(V_real1,V_real2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.94 all V_y (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))->c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.02/12.94 all V_y (V_y!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)->c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.02/12.94 all V_y (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))->c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.02/12.94 all V_real2 V_real1 (c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_real1,V_real2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.94 all V_real2_2 V_real1_2 V_f1_2 T_a (c_Complex_Ocomplex_Ocomplex__case(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2))=hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2)).
% 13.02/12.94 all V_real2_2 V_real1_2 V_f1_2 T_a (c_Complex_Ocomplex_Ocomplex__rec(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2))=hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2)).
% 13.02/12.94 all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y))->c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_y)))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_y))).
% 13.02/12.94 all V_y_2 V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2)))<-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)))& (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))).
% 13.02/12.94 all V_c V_b V_a T_a (class_Rings_Odivision__ring(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))=c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)).
% 13.02/12.94 all V_a V_r (c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_r))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,V_r)).
% 13.02/12.94 all V_n V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n)=c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))).
% 13.02/12.94 all V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)&class_RealVector_Oreal__normed__field(T_a)->c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))).
% 13.02/12.94 all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oidom(tc_Polynomial_Opoly(T_1))).
% 13.02/12.94 all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 13.02/12.94 all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1))).
% 13.02/12.94 class_Rings_Oidom(tc_Complex_Ocomplex).
% 13.02/12.94 class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex).
% 13.02/12.94 class_Rings_Ocomm__ring(tc_Complex_Ocomplex).
% 13.02/12.94 class_Rings_Oidom(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Ocomm__ring(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat).
% 13.02/12.94 class_Rings_Oidom(tc_Int_Oint).
% 13.02/12.94 class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint).
% 13.02/12.94 class_Rings_Ocomm__ring(tc_Int_Oint).
% 13.02/12.94 all T_2 T_1 (class_Orderings_Opreorder(T_1)->class_Orderings_Opreorder(tc_fun(T_2,T_1))).
% 13.02/12.94 all T_2 T_1 (class_Orderings_Oorder(T_1)->class_Orderings_Oorder(tc_fun(T_2,T_1))).
% 13.02/12.94 all T_2 T_1 (class_Orderings_Oord(T_1)->class_Orderings_Oord(tc_fun(T_2,T_1))).
% 13.02/12.94 all T_2 T_1 (class_Groups_Ominus(T_1)->class_Groups_Ominus(tc_fun(T_2,T_1))).
% 13.02/12.94 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 13.02/12.94 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 13.02/12.94 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 13.02/12.94 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 13.02/12.94 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint).
% 13.02/12.94 class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 13.02/12.94 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint).
% 13.02/12.94 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint).
% 13.02/12.94 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 13.02/12.94 class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 13.02/12.94 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 13.02/12.94 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 13.02/12.94 class_Rings_Oordered__cancel__semiring(tc_Int_Oint).
% 13.02/12.94 class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 13.02/12.94 class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 13.02/12.94 class_Rings_Oordered__comm__semiring(tc_Int_Oint).
% 13.02/12.94 class_Rings_Olinordered__semiring__1(tc_Int_Oint).
% 13.02/12.94 class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 13.02/12.94 class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 13.02/12.94 class_Rings_Olinordered__semiring(tc_Int_Oint).
% 13.02/12.94 class_Rings_Olinordered__semidom(tc_Int_Oint).
% 13.02/12.94 class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 13.02/12.94 class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 13.02/12.94 class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 13.02/12.94 class_Rings_Oordered__semiring(tc_Int_Oint).
% 13.02/12.94 class_Rings_Oordered__ring__abs(tc_Int_Oint).
% 13.02/12.94 class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 13.02/12.94 class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 13.02/12.94 class_Rings_Olinordered__ring(tc_Int_Oint).
% 13.02/12.94 class_Rings_Olinordered__idom(tc_Int_Oint).
% 13.02/12.94 class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 13.02/12.94 class_Rings_Ocomm__semiring__0(tc_Int_Oint).
% 13.02/12.94 class_Divides_Osemiring__div(tc_Int_Oint).
% 13.02/12.94 class_Rings_Ocomm__semiring(tc_Int_Oint).
% 13.02/12.94 class_Groups_Oab__group__add(tc_Int_Oint).
% 13.02/12.94 class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 13.02/12.94 class_Rings_Oordered__ring(tc_Int_Oint).
% 13.02/12.94 class_Orderings_Opreorder(tc_Int_Oint).
% 13.02/12.94 class_Orderings_Olinorder(tc_Int_Oint).
% 13.02/12.94 class_Groups_Omonoid__mult(tc_Int_Oint).
% 13.02/12.94 class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 13.02/12.94 class_Groups_Omonoid__add(tc_Int_Oint).
% 13.02/12.94 class_Rings_Osemiring__0(tc_Int_Oint).
% 13.02/12.94 class_Groups_Ogroup__add(tc_Int_Oint).
% 13.02/12.94 class_Rings_Omult__zero(tc_Int_Oint).
% 13.02/12.94 class_Orderings_Oorder(tc_Int_Oint).
% 13.02/12.94 class_Rings_Osemiring(tc_Int_Oint).
% 13.02/12.94 class_Orderings_Oord(tc_Int_Oint).
% 13.02/12.94 class_Rings_Oring__1(tc_Int_Oint).
% 13.02/12.94 class_Groups_Ominus(tc_Int_Oint).
% 13.02/12.94 class_Power_Opower(tc_Int_Oint).
% 13.02/12.94 class_Groups_Ozero(tc_Int_Oint).
% 13.02/12.94 class_Rings_Oring(tc_Int_Oint).
% 13.02/12.94 class_Groups_Oone(tc_Int_Oint).
% 13.02/12.94 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 13.02/12.94 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 13.02/12.94 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 13.02/12.94 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 13.02/12.94 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 13.02/12.94 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 13.02/12.94 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 13.02/12.94 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 13.02/12.94 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 13.02/12.94 class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 13.02/12.94 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 13.02/12.94 class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 13.02/12.94 class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 13.02/12.94 class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 13.02/12.94 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 13.02/12.94 class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 13.02/12.94 class_Rings_Oordered__semiring(tc_Nat_Onat).
% 13.02/12.94 class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 13.02/12.94 class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 13.02/12.94 class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 13.02/12.94 class_Rings_Ocomm__semiring__0(tc_Nat_Onat).
% 13.02/12.94 class_Divides_Osemiring__div(tc_Nat_Onat).
% 13.02/12.94 class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 13.02/12.94 class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 13.02/12.94 class_Orderings_Opreorder(tc_Nat_Onat).
% 13.02/12.94 class_Orderings_Olinorder(tc_Nat_Onat).
% 13.02/12.94 class_Groups_Omonoid__mult(tc_Nat_Onat).
% 13.02/12.94 class_Groups_Omonoid__add(tc_Nat_Onat).
% 13.02/12.94 class_Rings_Osemiring__0(tc_Nat_Onat).
% 13.02/12.94 class_Rings_Omult__zero(tc_Nat_Onat).
% 13.02/12.94 class_Orderings_Oorder(tc_Nat_Onat).
% 13.02/12.94 class_Rings_Osemiring(tc_Nat_Onat).
% 13.02/12.94 class_Orderings_Oord(tc_Nat_Onat).
% 13.02/12.94 class_Groups_Ominus(tc_Nat_Onat).
% 13.02/12.94 class_Power_Opower(tc_Nat_Onat).
% 13.02/12.94 class_Groups_Ozero(tc_Nat_Onat).
% 13.02/12.94 class_Groups_Oone(tc_Nat_Onat).
% 13.02/12.94 class_Orderings_Opreorder(tc_HOL_Obool).
% 13.02/12.94 class_Orderings_Oorder(tc_HOL_Obool).
% 13.02/12.94 class_Orderings_Oord(tc_HOL_Obool).
% 13.02/12.94 class_Groups_Ominus(tc_HOL_Obool).
% 13.02/12.94 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal).
% 13.02/12.94 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal).
% 13.02/12.94 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal).
% 13.02/12.94 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal).
% 13.02/12.94 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal).
% 13.02/12.94 class_RealVector_Oreal__normed__field(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Olinordered__semiring(tc_RealDef_Oreal).
% 13.02/12.94 class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Olinordered__semidom(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Oordered__semiring(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Olinordered__ring(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Olinordered__idom(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Odivision__ring(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Ocomm__semiring(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Oab__group__add(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Oordered__ring(tc_RealDef_Oreal).
% 13.02/12.94 class_Orderings_Opreorder(tc_RealDef_Oreal).
% 13.02/12.94 class_Orderings_Olinorder(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Omonoid__mult(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Omonoid__add(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Osemiring__0(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Ogroup__add(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Omult__zero(tc_RealDef_Oreal).
% 13.02/12.94 class_Orderings_Oorder(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Osemiring(tc_RealDef_Oreal).
% 13.02/12.94 class_Orderings_Oord(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Oring__1(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Ominus(tc_RealDef_Oreal).
% 13.02/12.94 class_Fields_Ofield(tc_RealDef_Oreal).
% 13.02/12.94 class_Power_Opower(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Ozero(tc_RealDef_Oreal).
% 13.02/12.94 class_Rings_Oring(tc_RealDef_Oreal).
% 13.02/12.94 class_Groups_Oone(tc_RealDef_Oreal).
% 13.02/12.94 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex).
% 13.02/12.94 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex).
% 13.02/12.94 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex).
% 13.02/12.94 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex).
% 13.02/12.94 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex).
% 13.02/12.94 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex).
% 13.02/12.94 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex).
% 13.02/12.94 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex).
% 13.02/12.94 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex).
% 13.02/12.94 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex).
% 13.02/12.94 class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex).
% 13.02/12.94 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex).
% 13.02/12.94 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex).
% 13.02/12.94 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex).
% 13.02/12.94 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex).
% 13.02/12.94 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex).
% 13.02/12.94 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex).
% 13.02/12.94 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex).
% 13.02/12.94 class_Rings_Odivision__ring(tc_Complex_Ocomplex).
% 13.02/12.94 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex).
% 13.02/12.94 class_Groups_Oab__group__add(tc_Complex_Ocomplex).
% 13.02/12.94 class_Rings_Ozero__ne_q__one(tc_Complex_Ocomplex).
% 13.02/12.94 class_Groups_Omonoid__mult(tc_Complex_Ocomplex).
% 13.02/12.94 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex).
% 13.02/12.94 class_Groups_Omonoid__add(tc_Complex_Ocomplex).
% 13.02/12.94 class_Rings_Osemiring__0(tc_Complex_Ocomplex).
% 13.02/12.94 class_Groups_Ogroup__add(tc_Complex_Ocomplex).
% 13.02/12.94 class_Rings_Omult__zero(tc_Complex_Ocomplex).
% 13.02/12.94 class_Rings_Osemiring(tc_Complex_Ocomplex).
% 13.02/12.94 class_Rings_Oring__1(tc_Complex_Ocomplex).
% 13.02/12.94 class_Groups_Ominus(tc_Complex_Ocomplex).
% 13.02/12.94 class_Fields_Ofield(tc_Complex_Ocomplex).
% 13.02/12.94 class_Power_Opower(tc_Complex_Ocomplex).
% 13.02/12.94 class_Groups_Ozero(tc_Complex_Ocomplex).
% 13.02/12.94 class_Rings_Oring(tc_Complex_Ocomplex).
% 13.02/12.94 class_Groups_Oone(tc_Complex_Ocomplex).
% 13.02/12.94 all T_1 (class_Rings_Oidom(T_1)->class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))).
% 13.02/12.94 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 13.02/12.94 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1))).
% 13.02/12.94 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1))).
% 13.02/12.94 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Oidom(T_1)->class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Fields_Ofield(T_1)->class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Oorder(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Osemiring(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Oord(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Oring__1(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ominus(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Power_Opower(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Groups_Ozero(T_1)->class_Groups_Ozero(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Oring(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Oone(tc_Polynomial_Opoly(T_1))).
% 13.02/12.95 all V_Q V_P T_b T_a (hAPP(c_COMBK(T_a,T_b,V_P),V_Q)=V_P).
% 13.02/12.95 all V_R_2 V_Q_2 V_P_2 T_c T_a T_b (hAPP(c_COMBB(T_b,T_a,T_c,V_P_2,V_Q_2),V_R_2)=hAPP(V_P_2,hAPP(V_Q_2,V_R_2))).
% 13.02/12.95 all V_R_2 V_Q_2 V_P_2 T_a T_c T_b (hAPP(c_COMBC(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),V_Q_2)).
% 13.02/12.95 -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)).
% 13.02/12.95 end_of_list.
% 13.02/12.95
% 13.02/12.95 -------> usable clausifies to:
% 13.02/12.95
% 13.02/12.95 list(usable).
% 13.02/12.95 0 [] A=A.
% 13.02/12.95 0 [] hAPP(V_fa_2,$f1(V_gb_2,V_fa_2))!=hAPP(V_gb_2,$f1(V_gb_2,V_fa_2))|V_fa_2=V_gb_2.
% 13.02/12.95 0 [] c_SEQ_Osubse_q(v_ga____).
% 13.02/12.95 0 [] -class_Orderings_Opreorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_x)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n))),v_r)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)).
% 13.02/12.95 0 [] c_SEQ_Osubse_q(v_f____).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w),V_w)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z),V_w))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w),V_z)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_j),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i),V_k)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z),V_w))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w),V_z))|V_z=V_w.
% 13.02/12.95 0 [] -class_Orderings_Oord(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2),V_gb_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,B_x)),hAPP(V_gb_2,B_x))).
% 13.02/12.95 0 [] -class_Orderings_Oord(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2),V_gb_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,$f2(V_gb_2,V_fa_2,T_a,T_b))),hAPP(V_gb_2,$f2(V_gb_2,V_fa_2,T_a,T_b)))).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|V_x_2!=V_y_2|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|V_x_2!=V_y_2|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2),V_x_2)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|V_x_2=V_y_2| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2),V_x_2)).
% 13.02/12.95 0 [] -class_Orderings_Opreorder(T_a)|V_x!=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x)).
% 13.02/12.95 0 [] -class_Orderings_Oord(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2),V_gb_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,V_x_2)),hAPP(V_gb_2,V_x_2))).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_z),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_z),V_x)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|V_x=V_y.
% 13.02/12.95 0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_z)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))|V_x=V_y.
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))|V_b!=V_c|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_a)).
% 13.02/12.95 0 [] -class_Orderings_Oord(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))|V_b!=V_c|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_c)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_a)).
% 13.02/12.95 0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_c)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))|V_x_2=V_y_2.
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2),V_x_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 13.02/12.95 0 [] -class_Orderings_Oord(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2),V_gb_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,V_x_2)),hAPP(V_gb_2,V_x_2))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|V_x_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_a,V_x))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,V_x_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)).
% 13.02/12.95 0 [] -c_SEQ_Osubse_q(V_fa_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),hAPP(V_fa_2,V_n_2))).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] -class_Groups_Ozero(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=V_x_2|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Groups_Ozero(T_a)|c_Groups_Ozero__class_Ozero(T_a)=V_x_2|V_x_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_c),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y))))|V_x=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_n)).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__div__algebra(T_a)|c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)).
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m)).
% 13.02/12.95 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)!=c_RealDef_Oreal(tc_Nat_Onat,V_m_2)|V_n_2=V_m_2.
% 13.02/12.95 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_RealDef_Oreal(tc_Nat_Onat,V_m_2)|V_n_2!=V_m_2.
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3)).
% 13.02/12.95 0 [] V_m!=V_n|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_k)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|V_m=V_n.
% 13.02/12.95 0 [] -class_Groups_Oab__semigroup__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),V_m_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),V_m_2)).
% 13.02/12.95 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2)|V_a_2=V_b_2.
% 13.02/12.95 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2)|V_a_2!=V_b_2.
% 13.02/12.95 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2)|V_a_2=V_b_2.
% 13.02/12.95 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2)|V_a_2!=V_b_2.
% 13.02/12.95 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2)).
% 13.02/12.95 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 13.02/12.95 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Oordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 13.02/12.95 0 [] -class_Rings_Oordered__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 13.02/12.95 0 [] -class_Rings_Oordered__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))).
% 13.02/12.95 0 [] -class_Rings_Oordered__comm__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))).
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 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).
% 13.02/12.95 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).
% 13.02/12.95 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).
% 13.02/12.95 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).
% 13.02/12.95 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.
% 13.02/12.95 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).
% 13.02/12.95 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).
% 13.02/12.95 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.
% 13.02/12.95 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).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_l))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))).
% 13.02/12.95 0 [] c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 13.02/12.95 0 [] -class_Rings_Ono__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Ono__zero__divisors(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_b_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Omult__zero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Omult__zero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Oordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 13.02/12.95 0 [] -class_Rings_Oordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 13.02/12.95 0 [] -class_Rings_Oordered__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))).
% 13.02/12.95 0 [] -class_Rings_Oordered__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))).
% 13.02/12.95 0 [] -class_Rings_Oordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))).
% 13.02/12.95 0 [] -class_Rings_Oordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Odecse_q(T_a,V_X_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m),B_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m))).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Odecse_q(T_a,V_X_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f4(V_X_2,T_a)),$f3(V_X_2,T_a))).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Odecse_q(T_a,V_X_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f3(V_X_2,T_a))),hAPP(V_X_2,$f4(V_X_2,T_a)))).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f5(T_a))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),$f5(T_a)))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f6(V_x,T_a))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),$f6(V_x,T_a)))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f7(V_y,T_a))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),$f7(V_y,T_a)))).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Oincse_q(T_a,V_X_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m),B_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Oincse_q(T_a,V_X_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f9(V_X_2,T_a)),$f8(V_X_2,T_a))).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Oincse_q(T_a,V_X_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f9(V_X_2,T_a))),hAPP(V_X_2,$f8(V_X_2,T_a)))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),$f10(T_a)))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),$f11(V_x,T_a)))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),$f12(V_y,T_a)))).
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)).
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a).
% 13.02/12.95 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.
% 13.02/12.95 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).
% 13.02/12.95 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.
% 13.02/12.95 0 [] -class_Groups_Ozero(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_p_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.02/12.95 0 [] -class_Groups_Ozero(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_p_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b))),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b)))).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Omonose_q(T_a,V_X_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m),B_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,X1),X2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,X2)),hAPP(V_X_2,X1))).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f14(V_X_2,T_a)),$f13(V_X_2,T_a))).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f14(V_X_2,T_a))),hAPP(V_X_2,$f13(V_X_2,T_a)))).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f16(V_X_2,T_a)),$f15(V_X_2,T_a))).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f15(V_X_2,T_a))),hAPP(V_X_2,$f16(V_X_2,T_a)))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),V_a_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_RealDef_Oreal(tc_Nat_Onat,V_a_2))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),V_a_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_RealDef_Oreal(tc_Nat_Onat,V_a_2))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2),c_RComplete_Onatfloor(V_x_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)),V_x_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2),c_RComplete_Onatfloor(V_x_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)),V_x_2)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Odecse_q(T_a,V_X_2)|c_SEQ_Omonose_q(T_a,V_X_2).
% 13.02/12.95 0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b).
% 13.02/12.95 0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)=V_x.
% 13.02/12.95 0 [] c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n.
% 13.02/12.95 0 [] c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n.
% 13.02/12.95 0 [] c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(V_x))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_RComplete_Onatfloor(V_y))).
% 13.02/12.95 0 [] c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatceiling(V_x))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)),c_RComplete_Onatceiling(V_y))).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|c_RComplete_Onatfloor(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),V_x)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),c_RComplete_Onatfloor(V_a))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|c_RComplete_Onatceiling(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)),V_a)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Oincse_q(T_a,V_X_2)|c_SEQ_Omonose_q(T_a,V_X_2).
% 13.02/12.95 0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)=V_a.
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f18(V_X_2,T_a)),$f17(V_X_2,T_a)))|c_SEQ_Omonose_q(T_a,V_X_2).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f18(V_X_2,T_a))),hAPP(V_X_2,$f17(V_X_2,T_a))))|c_SEQ_Omonose_q(T_a,V_X_2).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f20(V_X_2,T_a)),$f19(V_X_2,T_a)))|c_SEQ_Omonose_q(T_a,V_X_2).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f19(V_X_2,T_a))),hAPP(V_X_2,$f20(V_X_2,T_a))))|c_SEQ_Omonose_q(T_a,V_X_2).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 13.02/12.95 0 [] c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_r))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.02/12.95 0 [] c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__idom(T_a)|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 13.02/12.95 0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_x)).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|V_x_2=V_y_2|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|V_x_2!=V_y_2| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|V_x_2!=V_y_2| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))|V_x_2=V_y_2.
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|V_x_2=V_y_2.
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x!=V_y.
% 13.02/12.95 0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 13.02/12.95 0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x!=V_y.
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_y!=V_x.
% 13.02/12.95 0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 13.02/12.95 0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)).
% 13.02/12.95 0 [] -class_Orderings_Oord(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))|V_b!=V_c|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))|V_b!=V_c|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)).
% 13.02/12.95 0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)).
% 13.02/12.95 0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n)).
% 13.02/12.95 0 [] V_m_2=V_n_2|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)).
% 13.02/12.95 0 [] V_m_2!=V_n_2| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] V_m_2!=V_n_2| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)).
% 13.02/12.95 0 [] V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y),V_x)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))|V_m!=V_n.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s),V_t))|V_s!=V_t.
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=V_n_2|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))|hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2),V_x_2)).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2),V_x_2)).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))|V_x_2=V_y_2.
% 13.02/12.95 0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2),V_x_2)).
% 13.02/12.95 0 [] -class_Orderings_Opreorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2),V_x_2)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|V_x_2=V_y_2.
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x)).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))|V_x_2=V_y_2.
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)).
% 13.02/12.95 0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y)).
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|V_x_2=V_y_2.
% 13.02/12.95 0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x=V_y.
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))|V_a=V_b|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))|V_a=V_b|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)).
% 13.02/12.95 0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_z),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)).
% 13.02/12.95 0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)).
% 13.02/12.95 0 [] V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.02/12.95 0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 13.02/12.95 0 [] V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2))|V_x_2=V_y_2.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))|V_x_2=V_y_2.
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2!=V_n_2.
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=V_n_2.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=V_n_2.
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2!=V_n_2.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|V_m=V_n|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 13.02/12.95 0 [] V_m!=V_n|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 13.02/12.95 0 [] -c_SEQ_Osubse_q(V_fa_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m),B_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m)),hAPP(V_fa_2,B_n))).
% 13.02/12.95 0 [] c_SEQ_Osubse_q(V_fa_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f22(V_fa_2)),$f21(V_fa_2))).
% 13.02/12.95 0 [] c_SEQ_Osubse_q(V_fa_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,$f22(V_fa_2))),hAPP(V_fa_2,$f21(V_fa_2)))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__comm__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_n)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_n)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2=V_n_2.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2!=V_n_2.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2),V_a_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2),V_a_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)))|V_x_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)))|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.02/12.95 0 [] c_SEQ_Osubse_q($c1).
% 13.02/12.95 0 [] c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,$c1)))).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)))|V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)))|V_x_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f23(V_y,T_a))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),$f23(V_y,T_a)))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f24(V_x,T_a))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),$f24(V_x,T_a)))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f25(T_a))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),$f25(T_a)))).
% 13.02/12.95 0 [] hAPP(c_Complex_OIm,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),V_y)).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f26(V_X_2,T_a))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),$f26(V_X_2,T_a))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_OBse_q(T_a,V_X_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,$f27(V_X_2,T_a,B_K)))),B_K)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$c2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),$c2))).
% 13.02/12.95 0 [] hAPP(c_Complex_ORe,V_x)!=hAPP(c_Complex_ORe,V_y)|hAPP(c_Complex_OIm,V_x)!=hAPP(c_Complex_OIm,V_y)|V_x=V_y.
% 13.02/12.95 0 [] V_x_2!=V_y_2|hAPP(c_Complex_ORe,V_x_2)=hAPP(c_Complex_ORe,V_y_2).
% 13.02/12.95 0 [] V_x_2!=V_y_2|hAPP(c_Complex_OIm,V_x_2)=hAPP(c_Complex_OIm,V_y_2).
% 13.02/12.95 0 [] V_x_2=V_y_2|hAPP(c_Complex_ORe,V_x_2)!=hAPP(c_Complex_ORe,V_y_2)|hAPP(c_Complex_OIm,V_x_2)!=hAPP(c_Complex_OIm,V_y_2).
% 13.02/12.95 0 [] hAPP(c_Complex_ORe,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.95 0 [] -class_Orderings_Oord(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2),V_gb_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2),V_gb_2)).
% 13.02/12.95 0 [] -class_Orderings_Oord(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2),V_gb_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_gb_2),V_fa_2)).
% 13.02/12.95 0 [] -class_Orderings_Oord(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2),V_gb_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_fa_2),V_gb_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_gb_2),V_fa_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$c3)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),$c3))).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$c4)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),$c4))).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$c5)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),$c5))).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),$c6))).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),$c7))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f28(V_X_2,T_a))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),$f28(V_X_2,T_a))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_K_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,$f29(V_X_2,V_K_2,T_a)))),V_K_2))|c_SEQ_OBse_q(T_a,V_X_2).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_N_2),$f30(V_K_2,V_X_2,V_N_2,T_a)))|c_SEQ_OBse_q(T_a,V_X_2).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,$f30(V_K_2,V_X_2,V_N_2,T_a)))),V_K_2))|c_SEQ_OBse_q(T_a,V_X_2).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,$f31(V_X_2,T_b,B_K)))),B_K))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f32(V_X_2,T_b))))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f33(V_X_2,T_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,$f34(V_X_2,T_b,B_N)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,X3))),$f33(V_X_2,T_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,$f34(V_X_2,T_b,B_N)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,$f35(V_X_2,T_b,B_K)))),B_K))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f36(V_X_2,T_b))))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f37(V_X_2,T_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,$f38(V_X_2,T_b,B_N)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,X4))),$f37(V_X_2,T_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,$f38(V_X_2,T_b,B_N)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,$f39(V_x,B_y))),V_x))).
% 13.02/12.95 0 [] c_SEQ_Osubse_q($c8).
% 13.02/12.95 0 [] c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,v_s),$c8)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),c_Nat_OSuc(V_n))).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Nat_OSuc(V_n))).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_OSuc(V_n))).
% 13.02/12.95 0 [] c_Nat_OSuc(V_x)!=c_Nat_OSuc(V_y)|V_x=V_y.
% 13.02/12.95 0 [] c_Nat_OSuc(V_nat_2)!=c_Nat_OSuc(V_nat_H_2)|V_nat_2=V_nat_H_2.
% 13.02/12.95 0 [] c_Nat_OSuc(V_nat_2)=c_Nat_OSuc(V_nat_H_2)|V_nat_2!=V_nat_H_2.
% 13.02/12.95 0 [] c_Nat_OSuc(V_n)!=V_n.
% 13.02/12.95 0 [] V_n!=c_Nat_OSuc(V_n).
% 13.02/12.95 0 [] hAPP(V_fa_2,hAPP(V_gb_2,V_x_2))!=hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2))|hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_x_2)=hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2,V_g_H_2),V_x_H_2).
% 13.02/12.95 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m).
% 13.02/12.95 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_nat_H).
% 13.02/12.95 0 [] c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] c_Nat_OSuc(V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m).
% 13.02/12.95 0 [] c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),c_Nat_OSuc(V_n)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|V_m=V_n.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i)),V_k)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|c_Nat_OSuc(V_m)=V_n|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Nat_OSuc(V_m)))|V_m=V_n.
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2)))|V_n_2=V_m_2.
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2)))|V_n_2!=V_m_2.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),c_Nat_OSuc(V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),c_Nat_OSuc(V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=V_n_2.
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))|V_m_2!=V_n_2.
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|V_m=c_Nat_OSuc(V_n).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),c_Nat_OSuc(V_m_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),V_m_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),c_Nat_OSuc(V_m_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),V_m_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=c_Nat_OSuc(V_n_2).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))|V_m_2!=c_Nat_OSuc(V_n_2).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n)),V_n)).
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)|V_m_2=V_n_2.
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)|V_m_2!=V_n_2.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Nat_OSuc($f40(V_n_2,V_m_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f40(V_n_2,V_m_2)),V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))|V_m_2!=c_Nat_OSuc(B_j)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_n_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|V_n_2=c_Nat_OSuc($f41(V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|V_n_2!=c_Nat_OSuc(B_m).
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2)))|V_n_2=V_m_2.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2)))|V_n_2!=V_m_2.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Omonose_q(T_a,V_X_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,c_Nat_OSuc(B_n))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,c_Nat_OSuc(X5))),hAPP(V_X_2,X5))).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f42(V_X_2,T_a))),hAPP(V_X_2,c_Nat_OSuc($f42(V_X_2,T_a))))).
% 13.02/12.95 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,c_Nat_OSuc($f43(V_X_2,T_a)))),hAPP(V_X_2,$f43(V_X_2,T_a)))).
% 13.02/12.95 0 [] -c_SEQ_Osubse_q(V_fa_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n)),hAPP(V_fa_2,c_Nat_OSuc(B_n)))).
% 13.02/12.95 0 [] c_SEQ_Osubse_q(V_fa_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,$f44(V_fa_2))),hAPP(V_fa_2,c_Nat_OSuc($f44(V_fa_2))))).
% 13.02/12.95 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2)=c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f45(V_X_2,T_a))))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_OBse_q(T_a,V_X_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,$f46(V_X_2,T_a,B_N)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f47(V_X_2,T_a))))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_SEQ_OBse_q(T_a,V_X_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,$f48(V_X_2,T_a,B_N)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))|V_x=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.95 0 [] c_SEQ_Osubse_q($c9).
% 13.02/12.95 0 [] c_SEQ_Omonose_q(tc_RealDef_Oreal,c_COMBB(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Nat_Onat,tc_RealDef_Oreal,tc_Nat_Onat,c_Fun_Ocomp(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,v_s),v_f____),$c9)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,$f49(V_r))),V_r)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f49(V_r))))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,$f50(V_x,V_y))),V_y)),V_x)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f50(V_x,V_y)))),V_y))).
% 13.02/12.95 0 [] hAPP(c_Fun_Ocomp(T_b,T_a,T_c,c_COMBK(T_a,T_b,V_c_2),V_fa_2),V_x_2)=V_c_2.
% 13.02/12.95 0 [] c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)!=V_c_2|hAPP(V_a_2,hAPP(V_b_2,V_v_2))=hAPP(V_c_2,V_v_2).
% 13.02/12.95 0 [] hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_x_2)=hAPP(V_fa_2,hAPP(V_gb_2,V_x_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_x)=c_NthRoot_Oroot(V_m,c_NthRoot_Oroot(V_n,V_x)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))|c_NthRoot_Oroot(V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_n,V_y)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_n,V_y))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_1))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_1))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_1,V_x_1))).
% 13.02/12.95 0 [] c_NthRoot_Oroot(V_n,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.95 0 [] c_NthRoot_Oroot(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x)=V_x.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|c_NthRoot_Oroot(V_m,c_NthRoot_Oroot(V_n,V_x))=c_NthRoot_Oroot(V_n,c_NthRoot_Oroot(V_m,V_x)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|c_NthRoot_Oroot(V_n_2,V_x_2)!=c_NthRoot_Oroot(V_n_2,V_y_2)|V_x_2=V_y_2.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|c_NthRoot_Oroot(V_n_2,V_x_2)=c_NthRoot_Oroot(V_n_2,V_y_2)|V_x_2!=V_y_2.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_NthRoot_Oroot(V_n_2,V_y_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_NthRoot_Oroot(V_n_2,V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_n,V_y))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|c_NthRoot_Oroot(V_n_2,V_x_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|c_NthRoot_Oroot(V_n_2,V_x_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_n,V_y))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_NthRoot_Oroot(V_n_2,V_y_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_NthRoot_Oroot(V_n_2,V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|c_NthRoot_Oroot(V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_n,V_y)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_x)=c_NthRoot_Oroot(V_m,c_NthRoot_Oroot(V_n,V_x)).
% 13.02/12.95 0 [] c_Fun_Ocomp(T_c,T_b,T_a,V_fa_2,c_Fun_Ocomp(T_d,T_c,T_a,V_gb_2,V_h_2))=c_Fun_Ocomp(T_d,T_b,T_a,c_Fun_Ocomp(T_c,T_b,T_d,V_fa_2,V_gb_2),V_h_2).
% 13.02/12.95 0 [] hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_x_2)=hAPP(V_fa_2,hAPP(V_gb_2,V_x_2)).
% 13.02/12.95 0 [] c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)!=c_Fun_Ocomp(T_d,T_b,T_a,V_c_2,V_d_2)|hAPP(V_a_2,hAPP(V_b_2,V_v_2))=hAPP(V_c_2,hAPP(V_d_2,V_v_2)).
% 13.02/12.95 0 [] c_Fun_Ocomp(T_c,T_b,T_a,V_a_2,V_b_2)!=c_Fun_Ocomp(T_d,T_b,T_a,V_c_2,V_d_2)|hAPP(V_a_2,hAPP(V_b_2,B_v))=hAPP(V_c_2,hAPP(V_d_2,B_v)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n,V_x))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_2,V_y_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_2,V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_2,V_y_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_2,V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n,V_x))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_N,V_x))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)),c_NthRoot_Oroot(V_N,V_x))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),V_n)=V_x.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|c_NthRoot_Oroot(V_n,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=V_x.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),V_n)=V_x.
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__div__algebra(T_a)|c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra__1(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a).
% 13.02/12.95 0 [] -class_Groups_Oone(T_a)|c_Groups_Oone__class_Oone(T_a)!=V_x_2|V_x_2=c_Groups_Oone__class_Oone(T_a).
% 13.02/12.95 0 [] -class_Groups_Oone(T_a)|c_Groups_Oone__class_Oone(T_a)=V_x_2|V_x_2!=c_Groups_Oone__class_Oone(T_a).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__algebra__1(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n))).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)).
% 13.02/12.95 0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a.
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a.
% 13.02/12.95 0 [] -class_Groups_Ocomm__monoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a.
% 13.02/12.95 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a.
% 13.02/12.95 0 [] -class_Groups_Ocomm__monoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a.
% 13.02/12.95 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a.
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_SEQ_OBse_q(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)).
% 13.02/12.95 0 [] c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z)=V_z.
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_r))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_r),c_Groups_Oone__class_Oone(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),c_Nat_OSuc(V_n))),V_r)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_SEQ_Omonose_q(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)).
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_m))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__idom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__idom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|c_NthRoot_Oroot(V_n,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_k))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Oroot(V_n,V_x)),V_k).
% 13.02/12.95 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|c_NthRoot_Oroot(V_n_2,V_x_2)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|V_x_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|c_NthRoot_Oroot(V_n_2,V_x_2)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|V_x_2!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|c_NthRoot_Oroot(V_n,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|c_NthRoot_Oroot(c_Nat_OSuc(V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),c_Nat_OSuc(V_n)))=V_x.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(V_N,V_x)),c_NthRoot_Oroot(V_n,V_x))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_2,V_y_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_2,V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_2,V_y_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_NthRoot_Oroot(V_n_2,V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n_2,V_x_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(V_N,V_x)),c_NthRoot_Oroot(V_n,V_x))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_y),V_n)!=V_x|c_NthRoot_Oroot(V_n,V_x)=V_y.
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_b_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_N))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 13.02/12.95 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_a.
% 13.02/12.95 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_x.
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)=V_n.
% 13.02/12.95 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).
% 13.02/12.95 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).
% 13.02/12.95 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).
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 13.02/12.95 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).
% 13.02/12.95 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).
% 13.02/12.95 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).
% 13.02/12.95 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.95 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.95 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_x_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)).
% 13.02/12.95 0 [] c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n).
% 13.02/12.95 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n)=c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)).
% 13.02/12.95 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.95 0 [] V_m!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)|V_n=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.95 0 [] hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.95 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.95 0 [] c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.02/12.95 0 [] c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.02/12.95 0 [] V_x!=c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))|c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(V_x_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(V_x_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.95 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.95 0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.02/12.95 0 [] -class_Groups_Ocomm__monoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)).
% 13.02/12.95 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a).
% 13.02/12.95 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 13.02/12.95 0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a_2))|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2)!=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)|V_m_2=V_n_2.
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a_2))|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)|V_m_2!=V_n_2.
% 13.02/12.95 0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_OSuc(V_n))=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Power_Opower(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.02/12.95 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a).
% 13.02/12.95 0 [] -class_Power_Opower(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))!=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|V_a=V_b.
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))).
% 13.02/12.95 0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a).
% 13.02/12.95 0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_b_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_N))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))),c_Groups_Oone__class_Oone(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)!=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|V_a=V_b.
% 13.02/12.95 0 [] -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(T_a)=c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f51(V_a,V_n))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),$f51(V_a,V_n)),V_n)=V_a.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_y))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n)!=V_a|B_y=$f51(V_a,V_n).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f52(V_a,V_n))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),$f52(V_a,V_n)),V_n)=V_a.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Transcendental_Oln(V_x)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_x)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_y))).
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z1),V_z2)),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)).
% 13.02/12.95 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)).
% 13.02/12.95 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)|V_b_2=V_c_2.
% 13.02/12.95 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)|V_b_2!=V_c_2.
% 13.02/12.95 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)|V_b_2=V_c_2.
% 13.02/12.95 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)|V_b_2!=V_c_2.
% 13.02/12.95 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.
% 13.02/12.95 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.
% 13.02/12.95 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.
% 13.02/12.95 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).
% 13.02/12.95 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)).
% 13.02/12.95 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).
% 13.02/12.95 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)).
% 13.02/12.95 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).
% 13.02/12.95 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)).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_r))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_r),V_s))).
% 13.02/12.95 0 [] -class_RealVector_Oreal__normed__vector(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))).
% 13.02/12.95 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)).
% 13.02/12.95 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).
% 13.02/12.95 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)).
% 13.02/12.95 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)).
% 13.02/12.95 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)).
% 13.02/12.95 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)).
% 13.02/12.95 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)).
% 13.02/12.95 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_a_2=V_b_2|V_c_2=V_d_2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)).
% 13.02/12.95 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_a_2!=V_b_2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)).
% 13.02/12.95 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_c_2!=V_d_2|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)).
% 13.02/12.95 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)).
% 13.02/12.95 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).
% 13.02/12.95 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))|V_w_2=V_x_2|V_y_2=V_z_2.
% 13.02/12.95 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))|V_w_2!=V_x_2.
% 13.02/12.95 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))|V_y_2!=V_z_2.
% 13.02/12.95 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 13.02/12.95 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 13.02/12.95 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))).
% 13.02/12.95 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))).
% 13.02/12.95 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))).
% 13.02/12.95 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)).
% 13.02/12.95 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)).
% 13.02/12.95 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)).
% 13.02/12.95 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)).
% 13.02/12.95 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)).
% 13.02/12.95 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)).
% 13.02/12.95 0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))).
% 13.02/12.95 0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))).
% 13.02/12.95 0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))).
% 13.02/12.95 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2)).
% 13.02/12.95 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2)).
% 13.02/12.95 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2)).
% 13.02/12.95 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2)).
% 13.02/12.95 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.
% 13.02/12.95 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.
% 13.02/12.95 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 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.
% 13.02/12.95 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.
% 13.02/12.95 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_b_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_b_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 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.
% 13.02/12.95 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.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))|c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)),c_Transcendental_Oln(V_y)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))),V_x)).
% 13.02/12.95 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)).
% 13.02/12.95 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)).
% 13.02/12.95 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))).
% 13.02/12.95 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)=c_Groups_Ozero__class_Ozero(T_a)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))).
% 13.02/12.95 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))).
% 13.02/12.95 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)).
% 13.02/12.95 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)).
% 13.02/12.95 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))).
% 13.02/12.95 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))).
% 13.02/12.95 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))).
% 13.02/12.95 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(T_a)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 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)).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))).
% 13.02/12.95 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).
% 13.02/12.95 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).
% 13.02/12.95 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).
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.95 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x)),V_x)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))|c_Transcendental_Oln(V_x_2)!=c_Transcendental_Oln(V_y_2)|V_x_2=V_y_2.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))|c_Transcendental_Oln(V_x_2)=c_Transcendental_Oln(V_y_2)|V_x_2!=V_y_2.
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.02/12.95 0 [] c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.95 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))).
% 13.02/12.95 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))).
% 13.02/12.95 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))).
% 13.02/12.95 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))).
% 13.02/12.95 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a)))|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a)))|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_a)))|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))))|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))))|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))))|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.95 0 [] -class_Rings_Olinordered__semidom(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))).
% 13.02/12.95 0 [] hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_one_2.
% 13.02/12.95 0 [] hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2))=hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)).
% 13.02/12.95 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.02/12.95 0 [] hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y))).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.02/12.95 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))|c_Transcendental_Oln(V_x_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))|c_Transcendental_Oln(V_x_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_x_2!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x))).
% 13.02/12.96 0 [] -class_Rings_Olinordered__semiring__1(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v)!=c_Groups_Oone__class_Oone(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),V_m_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__semiring__1__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v)!=c_Groups_Oone__class_Oone(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))|c_RComplete_Onatfloor(V_x)=V_n.
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))|c_RComplete_Onatceiling(V_x)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.02/12.96 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.96 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.02/12.96 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)).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=V_n.
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 13.02/12.96 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).
% 13.02/12.96 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).
% 13.02/12.96 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).
% 13.02/12.96 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).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n)=c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n))=c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_k)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_l))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),$f53(V_n_2,V_m_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|V_n_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_l_2))|V_l_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),$f54(V_l_2,V_k_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_l_2))|V_l_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),B_n).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))).
% 13.02/12.96 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).
% 13.02/12.96 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)).
% 13.02/12.96 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)).
% 13.02/12.96 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.
% 13.02/12.96 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.
% 13.02/12.96 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).
% 13.02/12.96 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)).
% 13.02/12.96 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)).
% 13.02/12.96 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.
% 13.02/12.96 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.
% 13.02/12.96 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.
% 13.02/12.96 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.
% 13.02/12.96 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)).
% 13.02/12.96 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,V_X_2)|c_SEQ_OBse_q(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2))).
% 13.02/12.96 0 [] -class_RealVector_Oreal__normed__vector(T_a)| -c_SEQ_OBse_q(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2)))|c_SEQ_OBse_q(T_a,V_X_2).
% 13.02/12.96 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)).
% 13.02/12.96 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)).
% 13.02/12.96 0 [] 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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] 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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.96 0 [] 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).
% 13.02/12.96 0 [] 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=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.96 0 [] 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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] 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!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_n_2=c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),$f55(V_n_2,V_m_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_n_2!=c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),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)).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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)).
% 13.02/12.96 0 [] 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).
% 13.02/12.96 0 [] 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)).
% 13.02/12.96 0 [] hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)).
% 13.02/12.96 0 [] hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y)).
% 13.02/12.96 0 [] c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_w),V_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)))).
% 13.02/12.96 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_a).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_z)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z),c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),V_a).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.02/12.96 0 [] V_b=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),$f56(V_n,V_b)),V_n))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f57(V_n_2,V_P_2)),V_n_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i),$f57(V_n_2,V_P_2)))| -hBOOL(hAPP(V_P_2,B_i)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))|hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),$f57(V_n_2,V_P_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 13.02/12.96 0 [] c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))),V_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a))).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z.
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)=V_z.
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_m_2=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_n_2=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_m_2!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_n_2!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.02/12.96 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)).
% 13.02/12.96 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)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)).
% 13.02/12.96 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n)=c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(V_b))=c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b)).
% 13.02/12.96 0 [] c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(V_r,V_a)),V_n)=c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_r),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)).
% 13.02/12.96 0 [] c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a))=hAPP(c_Complex_ORe,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n)).
% 13.02/12.96 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).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))|V_w_2=V_z_2.
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))|V_w_2!=V_z_2.
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z.
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)=V_z.
% 13.02/12.96 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)).
% 13.02/12.96 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)).
% 13.02/12.96 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).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H),V_w))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_H),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))).
% 13.02/12.96 0 [] hAPP(c_Complex_ORe,c_Complex_Orcis(V_r,V_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.96 0 [] c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),V_w_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2),V_w_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),V_w_2))|V_z_2!=V_w_2.
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),V_w_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2),V_w_2))|V_z_2=V_w_2.
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x),V_y))|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y),V_x)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)).
% 13.02/12.96 0 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.02/12.96 0 [] hAPP(c_Complex_ORe,c_Complex_Ocis(V_a))=c_Transcendental_Ocos(V_a).
% 13.02/12.96 0 [] c_Complex_Ocis(V_a)=c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_a).
% 13.02/12.96 0 [] c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(V_r1,V_a)),c_Complex_Orcis(V_r2,V_b))=c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r1),V_r2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b)).
% 13.02/12.96 0 [] c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(V_a)),c_Complex_Oexpi(V_b)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))|V_a!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))|V_a!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w),V_w)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z),V_w))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w),V_z)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_j),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i),V_k)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z),V_w))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w),V_z))|V_z=V_w.
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H),V_q)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r_H))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q),V_q_H)).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q),V_q_H)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H),V_q)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 13.02/12.96 0 [] c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a))=hAPP(c_Complex_OIm,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f58(V_n,V_a))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),$f58(V_n,V_a)),c_Nat_OSuc(V_n))=V_a.
% 13.02/12.96 0 [] c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.96 0 [] hAPP(c_Complex_OIm,c_Complex_Ocis(V_a))=c_Transcendental_Osin(V_a).
% 13.02/12.96 0 [] c_Transcendental_Ocos(V_x)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|c_Transcendental_Osin(V_x)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.96 0 [] c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Ocos(V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Osin(V_y))).
% 13.02/12.96 0 [] hAPP(c_Complex_OIm,c_Complex_Orcis(V_r,V_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_x)))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.96 0 [] -class_Groups_Omonoid__mult(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n).
% 13.02/12.96 0 [] -class_Power_Opower(T_a)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=c_Groups_Oone__class_Oone(T_a).
% 13.02/12.96 0 [] -class_Power_Opower(T_a)|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_m))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)|V_m_2=V_n_2.
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)|V_m_2!=V_n_2.
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_n))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i))=V_i.
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_m)).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2),V_d_2)).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2),V_d_2)).
% 13.02/12.96 0 [] -class_RealVector_Oreal__normed__vector(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),c_Nat_OSuc(V_m))).
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m.
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_c),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),V_j).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)),V_i_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)),V_i_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_k))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m.
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_j_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_j_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_n)=V_m.
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)!=V_k_2|V_j_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_k_2|V_j_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i).
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n).
% 13.02/12.96 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya)=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)).
% 13.02/12.96 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b)=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)).
% 13.02/12.96 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)).
% 13.02/12.96 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H))=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)).
% 13.02/12.96 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)).
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k).
% 13.02/12.96 0 [] -class_Groups_Ominus(T_a)|hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2)=c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)).
% 13.02/12.96 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|V_a_2!=V_b_2|V_c_2=V_d_2.
% 13.02/12.96 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|V_a_2=V_b_2|V_c_2!=V_d_2.
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j).
% 13.02/12.96 0 [] -class_Groups_Ominus(T_a)|hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2)=c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_m)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_l))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n)),V_k)).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),V_d_2)).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),V_d_2)).
% 13.02/12.96 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=V_b_2.
% 13.02/12.96 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=V_b_2.
% 13.02/12.96 0 [] -class_Groups_Oab__group__add(T_a)|V_a_2!=V_b_2|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.96 0 [] -class_Groups_Oab__group__add(T_a)|V_a_2=V_b_2|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.96 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.96 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m=V_n.
% 13.02/12.96 0 [] -class_Rings_Oring(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)).
% 13.02/12.96 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))).
% 13.02/12.96 0 [] -class_Rings_Oring(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)|V_c_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2).
% 13.02/12.96 0 [] -class_Rings_Oring(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)|V_c_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2).
% 13.02/12.96 0 [] -class_Rings_Oring(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)=V_d_2.
% 13.02/12.96 0 [] -class_Rings_Oring(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)!=V_d_2.
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)).
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_n)=V_m.
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n),V_n)=V_m.
% 13.02/12.96 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b)=V_a.
% 13.02/12.96 0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),V_b)=V_a.
% 13.02/12.96 0 [] -class_Rings_Oordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2))).
% 13.02/12.96 0 [] -class_Rings_Oordered__ring(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2))).
% 13.02/12.96 0 [] -class_Rings_Oordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)),V_d_2)).
% 13.02/12.96 0 [] -class_Rings_Oordered__ring(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)),V_d_2)).
% 13.02/12.96 0 [] -class_Rings_Oordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2))).
% 13.02/12.96 0 [] -class_Rings_Oordered__ring(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2)),V_d_2))).
% 13.02/12.96 0 [] -class_Rings_Oordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)),V_d_2)).
% 13.02/12.96 0 [] -class_Rings_Oordered__ring(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)),V_d_2)).
% 13.02/12.96 0 [] -class_Rings_Oring__1(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))).
% 13.02/12.96 0 [] -class_RealVector_Oreal__normed__vector(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_a)),c_RealVector_Onorm__class_Onorm(T_a,V_b)))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i))),V_n)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n.
% 13.02/12.96 0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.02/12.96 0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|V_a_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))|V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),$f59(V_b_2,V_a_2,V_P_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))| -hBOOL(hAPP(V_P_2,$f59(V_b_2,V_a_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),$f59(V_b_2,V_a_2,V_P_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f59(V_b_2,V_a_2,V_P_2))).
% 13.02/12.96 0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.02/12.96 0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|V_a_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))|V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),$f60(V_b_2,V_a_2,V_P_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))| -hBOOL(hAPP(V_P_2,$f60(V_b_2,V_a_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),$f60(V_b_2,V_a_2,V_P_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f60(V_b_2,V_a_2,V_P_2))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),c_Nat_OSuc(V_j)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j),V_i))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u)),V_m),V_n).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)=V_n_2.
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)!=V_n_2.
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i),V_j))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u)),V_n)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)|V_m_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)|V_m_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2).
% 13.02/12.96 0 [] -class_RealVector_Oreal__normed__vector(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(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(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))).
% 13.02/12.96 0 [] -class_Groups_Omonoid__mult(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_p),V_n))|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=V_n.
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|V_n=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 13.02/12.96 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.
% 13.02/12.96 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)=c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)).
% 13.02/12.96 0 [] V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)).
% 13.02/12.96 0 [] V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.02/12.96 0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 13.02/12.96 0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,$f61(V_r),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_r)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r),c_RealDef_Oreal(tc_Nat_Onat,$f61(V_r)))).
% 13.02/12.96 0 [] -class_RealVector_Oreal__normed__vector(T_b)| -class_Orderings_Oord(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2),$f62(V_X_2,V_M_2,T_a,T_b)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2),B_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2))))).
% 13.02/12.96 0 [] -class_RealVector_Oreal__normed__vector(T_b)| -class_Orderings_Oord(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,$f62(V_X_2,V_M_2,T_a,T_b))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_M_2),B_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2))))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)).
% 13.02/12.96 0 [] hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y)).
% 13.02/12.96 0 [] hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_l_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_l_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=V_p.
% 13.02/12.96 0 [] -class_RealVector_Oreal__normed__vector(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 13.02/12.96 0 [] c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Osin(V_y))).
% 13.02/12.96 0 [] c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_y)),c_Transcendental_Osin(V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_y)),c_Transcendental_Ocos(V_x))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_b),V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a))).
% 13.02/12.96 0 [] c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))).
% 13.02/12.96 0 [] c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))).
% 13.02/12.96 0 [] c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_y)),c_Transcendental_Ocos(V_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_y)),c_Transcendental_Osin(V_x))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a)),V_x))|c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a)),V_x))|c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a).
% 13.02/12.96 0 [] hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))).
% 13.02/12.96 0 [] c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))|c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 13.02/12.96 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).
% 13.02/12.96 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).
% 13.02/12.96 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.
% 13.02/12.96 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.
% 13.02/12.96 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).
% 13.02/12.96 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).
% 13.02/12.96 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).
% 13.02/12.96 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.
% 13.02/12.96 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).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 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).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y))).
% 13.02/12.96 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).
% 13.02/12.96 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).
% 13.02/12.96 0 [] c_Complex_Oii!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] c_Complex_Oii!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] hAPP(c_Complex_ORe,c_Complex_Oii)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),V_a_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),V_a_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_a))|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),V_b))|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_2),V_a_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_2),V_a_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2),V_i_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2),V_i_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)).
% 13.02/12.96 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_i_2)).
% 13.02/12.96 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_i_2)).
% 13.02/12.96 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 13.02/12.96 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2),V_k_2)).
% 13.02/12.96 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_i_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k)),V_x)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c).
% 13.02/12.96 0 [] hAPP(c_Complex_OIm,c_Complex_Oii)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.96 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)).
% 13.02/12.96 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)).
% 13.02/12.96 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)).
% 13.02/12.96 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)).
% 13.02/12.96 0 [] V_a_1!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1),V_r_1))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_b_1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1)=V_y.
% 13.02/12.96 0 [] V_a_1!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1),V_b_1))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))|V_b_1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1)=V_y.
% 13.02/12.96 0 [] V_a_1!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1),V_b_1))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1),V_r_1))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_b_1=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1)=V_y.
% 13.02/12.96 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j),V_k_2))|V_n_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)|hBOOL(hAPP(V_P_2,B_i)).
% 13.02/12.96 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),X7))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,X7),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),X6)),X7)|hBOOL(hAPP(V_P_2,X6)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f65(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f65(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f66(V_k_2,V_n_2,V_P_2))),$f65(V_k_2,V_n_2,V_P_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))| -hBOOL(hAPP(V_P_2,$f66(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f63(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f63(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f65(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f63(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f65(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f63(V_k_2,V_n_2,V_P_2)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f66(V_k_2,V_n_2,V_P_2))),$f65(V_k_2,V_n_2,V_P_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f63(V_k_2,V_n_2,V_P_2)))| -hBOOL(hAPP(V_P_2,$f66(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f63(V_k_2,V_n_2,V_P_2)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f63(V_k_2,V_n_2,V_P_2)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f65(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f63(V_k_2,V_n_2,V_P_2)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f65(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f63(V_k_2,V_n_2,V_P_2)),V_k_2))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f66(V_k_2,V_n_2,V_P_2))),$f65(V_k_2,V_n_2,V_P_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f63(V_k_2,V_n_2,V_P_2)),V_k_2))| -hBOOL(hAPP(V_P_2,$f66(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f64(V_k_2,V_n_2,V_P_2))),$f63(V_k_2,V_n_2,V_P_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f64(V_k_2,V_n_2,V_P_2))),$f63(V_k_2,V_n_2,V_P_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f65(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f64(V_k_2,V_n_2,V_P_2))),$f63(V_k_2,V_n_2,V_P_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f65(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f64(V_k_2,V_n_2,V_P_2))),$f63(V_k_2,V_n_2,V_P_2))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f66(V_k_2,V_n_2,V_P_2))),$f65(V_k_2,V_n_2,V_P_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f64(V_k_2,V_n_2,V_P_2))),$f63(V_k_2,V_n_2,V_P_2))| -hBOOL(hAPP(V_P_2,$f66(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(V_P_2,$f64(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(V_P_2,$f64(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f65(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(V_P_2,$f64(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f65(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(V_P_2,$f64(V_k_2,V_n_2,V_P_2)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f66(V_k_2,V_n_2,V_P_2))),$f65(V_k_2,V_n_2,V_P_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(V_P_2,$f64(V_k_2,V_n_2,V_P_2)))| -hBOOL(hAPP(V_P_2,$f66(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f65(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f65(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f66(V_k_2,V_n_2,V_P_2))),$f65(V_k_2,V_n_2,V_P_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))| -hBOOL(hAPP(V_P_2,$f66(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f63(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f63(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f65(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f63(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f65(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f63(V_k_2,V_n_2,V_P_2)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f66(V_k_2,V_n_2,V_P_2))),$f65(V_k_2,V_n_2,V_P_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f63(V_k_2,V_n_2,V_P_2)))| -hBOOL(hAPP(V_P_2,$f66(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f63(V_k_2,V_n_2,V_P_2)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f63(V_k_2,V_n_2,V_P_2)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f65(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f63(V_k_2,V_n_2,V_P_2)),V_k_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f65(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f63(V_k_2,V_n_2,V_P_2)),V_k_2))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f66(V_k_2,V_n_2,V_P_2))),$f65(V_k_2,V_n_2,V_P_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,$f63(V_k_2,V_n_2,V_P_2)),V_k_2))| -hBOOL(hAPP(V_P_2,$f66(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f64(V_k_2,V_n_2,V_P_2))),$f63(V_k_2,V_n_2,V_P_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f64(V_k_2,V_n_2,V_P_2))),$f63(V_k_2,V_n_2,V_P_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f65(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f64(V_k_2,V_n_2,V_P_2))),$f63(V_k_2,V_n_2,V_P_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f65(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f64(V_k_2,V_n_2,V_P_2))),$f63(V_k_2,V_n_2,V_P_2))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f66(V_k_2,V_n_2,V_P_2))),$f65(V_k_2,V_n_2,V_P_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f64(V_k_2,V_n_2,V_P_2))),$f63(V_k_2,V_n_2,V_P_2))| -hBOOL(hAPP(V_P_2,$f66(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(V_P_2,$f64(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(V_P_2,$f64(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),$f65(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(V_P_2,$f64(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f65(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(V_P_2,$f64(V_k_2,V_n_2,V_P_2)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f66(V_k_2,V_n_2,V_P_2))),$f65(V_k_2,V_n_2,V_P_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(V_P_2,$f64(V_k_2,V_n_2,V_P_2)))| -hBOOL(hAPP(V_P_2,$f66(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y)))))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y),V_x))|c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y),V_x))|c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)))).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(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),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2))),V_ra_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2)),V_x_2)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2))),V_ra_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ra_2))).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2))),V_ra_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2)),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ra_2))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=V_m.
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_m)).
% 13.02/12.96 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).
% 13.02/12.96 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).
% 13.02/12.96 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).
% 13.02/12.96 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).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a_2)))|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))|c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a.
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),V_c))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b)),V_d))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a))=c_Groups_Oabs__class_Oabs(T_a,V_a).
% 13.02/12.96 0 [] c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x))=c_RealDef_Oreal(tc_Nat_Onat,V_x).
% 13.02/12.96 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a))=c_RealVector_Onorm__class_Onorm(T_a,V_a).
% 13.02/12.96 0 [] c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r)=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a))).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(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_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)))).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))|c_Groups_Oabs__class_Oabs(T_a,V_a)=V_a.
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.02/12.96 0 [] -class_Groups_Oordered__ab__group__add__abs(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oabs__class_Oabs(T_a,V_a))).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n))).
% 13.02/12.96 0 [] -class_Rings_Oordered__ring__abs(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)).
% 13.02/12.96 0 [] -class_Rings_Oordered__ring__abs(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)).
% 13.02/12.96 0 [] -class_Rings_Oordered__ring__abs(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)).
% 13.02/12.96 0 [] -class_Rings_Oordered__ring__abs(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x)=c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)).
% 13.02/12.96 0 [] c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(V_r,V_a))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n)=V_m.
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n)=V_m.
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_m)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_c),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y))))|V_x=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_x)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|c_NthRoot_Oroot(V_n,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))=c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_NthRoot_Oroot(V_n,V_x)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Osin(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)).
% 13.02/12.96 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.02/12.96 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_k_2))|V_n_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)|hBOOL(hAPP(V_P_2,B_i)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f67(V_k_2,V_n_2,V_P_2)),V_k_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),$f68(V_k_2,V_n_2,V_P_2))),$f67(V_k_2,V_n_2,V_P_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(V_P_2,$f68(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f67(V_k_2,V_n_2,V_P_2)),V_k_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),$f68(V_k_2,V_n_2,V_P_2))),$f67(V_k_2,V_n_2,V_P_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f68(V_k_2,V_n_2,V_P_2))).
% 13.02/12.96 0 [] -class_RealVector_Oreal__normed__vector(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)))).
% 13.02/12.96 0 [] c_Transcendental_Osin(V_x)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.96 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),$f69(V_n_2,V_m_2,V_P_2))),V_m_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc($f69(V_n_2,V_m_2,V_P_2))))).
% 13.02/12.96 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(V_P_2,$f69(V_n_2,V_m_2,V_P_2))).
% 13.02/12.96 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),$f69(V_n_2,V_m_2,V_P_2))),V_m_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc($f69(V_n_2,V_m_2,V_P_2))))).
% 13.02/12.96 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hBOOL(hAPP(V_P_2,$f69(V_n_2,V_m_2,V_P_2))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.02/12.96 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(B_q))))| -hBOOL(hAPP(V_P_2,B_q)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(V_q_2))))|V_q_2=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2))|V_q_2!=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(V_q_2))))|V_q_2!=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y),V_x))|c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y).
% 13.02/12.96 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)=c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y)))).
% 13.02/12.96 0 [] c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n))!=c_Groups_Oone__class_Oone(tc_Int_Oint)|c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m)=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))|V_z_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))|V_z_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 13.02/12.96 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|V_a_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.96 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|V_b_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.96 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)|V_a_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_b_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.96 0 [] c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)=c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d))=c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_b),V_d)).
% 13.02/12.96 0 [] c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)!=c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)|V_real1_2=V_real1_H_2.
% 13.02/12.96 0 [] c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)!=c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)|V_real2_2=V_real2_H_2.
% 13.02/12.96 0 [] c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)=c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)|V_real1_2!=V_real1_H_2|V_real2_2!=V_real2_H_2.
% 13.02/12.96 0 [] hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(V_x,V_y))=V_y.
% 13.02/12.96 0 [] hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(V_x,V_y))=V_x.
% 13.02/12.96 0 [] c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,V_z),hAPP(c_Complex_OIm,V_z))=V_z.
% 13.02/12.96 0 [] c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d))=c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_d)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n))).
% 13.02/12.96 0 [] c_Complex_Ocomplex_OComplex(V_x_2,V_y_2)!=c_Complex_Oii|V_x_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.96 0 [] c_Complex_Ocomplex_OComplex(V_x_2,V_y_2)!=c_Complex_Oii|V_y_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.96 0 [] c_Complex_Ocomplex_OComplex(V_x_2,V_y_2)=c_Complex_Oii|V_x_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.96 0 [] c_Complex_Oii=c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.02/12.96 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)|V_a_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.96 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)!=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)|V_b_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.96 0 [] c_Complex_Ocomplex_OComplex(V_a_2,V_b_2)=c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)|V_a_2!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|V_b_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.96 0 [] c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)=c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.02/12.96 0 [] c_Complex_Ocis(V_a)=c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(V_a),c_Transcendental_Osin(V_a)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2)))|V_x_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2)))|V_x_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2)))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(V_a),c_Transcendental_Osin(V_a)))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d))=c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_d)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_d)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_c))).
% 13.02/12.96 0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y)=c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))).
% 13.02/12.96 0 [] c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(V_real1,V_real2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))|c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.96 0 [] V_y=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.96 0 [] c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_real1,V_real2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] c_Complex_Ocomplex_Ocomplex__case(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2))=hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2).
% 13.02/12.96 0 [] c_Complex_Ocomplex_Ocomplex__rec(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2))=hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y))|c_RComplete_Onatfloor(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_y)))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_y).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2)).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)).
% 13.02/12.96 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.96 0 [] -class_Rings_Odivision__ring(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))=c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c).
% 13.02/12.96 0 [] c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_r))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,V_r).
% 13.02/12.96 0 [] -class_Fields_Ofield__inverse__zero(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)),V_n)=c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)).
% 13.02/12.96 0 [] -class_Fields_Ofield__inverse__zero(T_a)| -class_RealVector_Oreal__normed__field(T_a)|c_RealVector_Onorm__class_Onorm(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)).
% 13.02/12.96 0 [] -class_Rings_Oidom(T_1)|class_Rings_Oidom(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] class_Rings_Oidom(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Rings_Ocomm__ring(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Rings_Oidom(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Ocomm__ring(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Rings_Oidom(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Ocomm__ring(tc_Int_Oint).
% 13.02/12.96 0 [] -class_Orderings_Opreorder(T_1)|class_Orderings_Opreorder(tc_fun(T_2,T_1)).
% 13.02/12.96 0 [] -class_Orderings_Oorder(T_1)|class_Orderings_Oorder(tc_fun(T_2,T_1)).
% 13.02/12.96 0 [] -class_Orderings_Oord(T_1)|class_Orderings_Oord(tc_fun(T_2,T_1)).
% 13.02/12.96 0 [] -class_Groups_Ominus(T_1)|class_Groups_Ominus(tc_fun(T_2,T_1)).
% 13.02/12.96 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Oordered__cancel__semiring(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Oordered__comm__semiring(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Olinordered__semiring__1(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Olinordered__semiring(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Olinordered__semidom(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Oordered__semiring(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Oordered__ring__abs(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Olinordered__ring(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Olinordered__idom(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Ocomm__semiring__0(tc_Int_Oint).
% 13.02/12.96 0 [] class_Divides_Osemiring__div(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Ocomm__semiring(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Oab__group__add(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Oordered__ring(tc_Int_Oint).
% 13.02/12.96 0 [] class_Orderings_Opreorder(tc_Int_Oint).
% 13.02/12.96 0 [] class_Orderings_Olinorder(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Omonoid__mult(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Omonoid__add(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Osemiring__0(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Ogroup__add(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Omult__zero(tc_Int_Oint).
% 13.02/12.96 0 [] class_Orderings_Oorder(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Osemiring(tc_Int_Oint).
% 13.02/12.96 0 [] class_Orderings_Oord(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Oring__1(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Ominus(tc_Int_Oint).
% 13.02/12.96 0 [] class_Power_Opower(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Ozero(tc_Int_Oint).
% 13.02/12.96 0 [] class_Rings_Oring(tc_Int_Oint).
% 13.02/12.96 0 [] class_Groups_Oone(tc_Int_Oint).
% 13.02/12.96 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Rings_Oordered__semiring(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Rings_Ocomm__semiring__0(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Divides_Osemiring__div(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Orderings_Opreorder(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Orderings_Olinorder(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Groups_Omonoid__mult(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Groups_Omonoid__add(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Rings_Osemiring__0(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Rings_Omult__zero(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Orderings_Oorder(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Rings_Osemiring(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Orderings_Oord(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Groups_Ominus(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Power_Opower(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Groups_Ozero(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Groups_Oone(tc_Nat_Onat).
% 13.02/12.96 0 [] class_Orderings_Opreorder(tc_HOL_Obool).
% 13.02/12.96 0 [] class_Orderings_Oorder(tc_HOL_Obool).
% 13.02/12.96 0 [] class_Orderings_Oord(tc_HOL_Obool).
% 13.02/12.96 0 [] class_Groups_Ominus(tc_HOL_Obool).
% 13.02/12.96 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_RealVector_Oreal__normed__field(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Olinordered__semiring(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Olinordered__semidom(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Oab__semigroup__add(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Oordered__semiring(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Oordered__ring__abs(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Ono__zero__divisors(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Olinordered__ring(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Olinordered__idom(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Odivision__ring(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Ocomm__semiring(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Oab__group__add(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Oordered__ring(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Orderings_Opreorder(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Orderings_Olinorder(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Omonoid__mult(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Ocomm__ring__1(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Omonoid__add(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Osemiring__0(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Ogroup__add(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Omult__zero(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Orderings_Oorder(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Osemiring(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Orderings_Oord(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Oring__1(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Ominus(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Fields_Ofield(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Power_Opower(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Ozero(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Rings_Oring(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Groups_Oone(tc_RealDef_Oreal).
% 13.02/12.96 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Rings_Odivision__ring(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Rings_Ocomm__semiring(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Groups_Oab__group__add(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Rings_Ozero__ne_q__one(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Groups_Omonoid__mult(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Groups_Omonoid__add(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Rings_Osemiring__0(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Groups_Ogroup__add(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Rings_Omult__zero(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Rings_Osemiring(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Rings_Oring__1(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Groups_Ominus(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Fields_Ofield(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Power_Opower(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Groups_Ozero(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Rings_Oring(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] class_Groups_Oone(tc_Complex_Ocomplex).
% 13.02/12.96 0 [] -class_Rings_Oidom(T_1)|class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Oidom(T_1)|class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Oidom(T_1)|class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Oidom(T_1)|class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Fields_Ofield(T_1)|class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Oord(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ominus(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Power_Opower(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Groups_Ozero(T_1)|class_Groups_Ozero(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Oring(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Oone(tc_Polynomial_Opoly(T_1)).
% 13.02/12.96 0 [] hAPP(c_COMBK(T_a,T_b,V_P),V_Q)=V_P.
% 13.02/12.96 0 [] hAPP(c_COMBB(T_b,T_a,T_c,V_P_2,V_Q_2),V_R_2)=hAPP(V_P_2,hAPP(V_Q_2,V_R_2)).
% 13.02/12.96 0 [] hAPP(c_COMBC(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),V_Q_2).
% 13.02/12.96 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)).
% 13.02/12.96 end_of_list.
% 13.02/12.96
% 13.02/12.96 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 13.02/12.96
% 13.02/12.96 This ia a non-Horn set with equality. The strategy will be
% 13.02/12.96 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 13.02/12.96 deletion, with positive clauses in sos and nonpositive
% 13.02/12.96 clauses in usable.
% 13.02/12.96
% 13.02/12.96 dependent: set(knuth_bendix).
% 13.02/12.96 dependent: set(anl_eq).
% 13.02/12.96 dependent: set(para_from).
% 13.02/12.96 dependent: set(para_into).
% 13.02/12.96 dependent: clear(para_from_right).
% 13.02/12.96 dependent: clear(para_into_right).
% 13.02/12.96 dependent: set(para_from_vars).
% 13.02/12.96 dependent: set(eq_units_both_ways).
% 13.02/12.96 dependent: set(dynamic_demod_all).
% 13.02/12.96 dependent: set(dynamic_demod).
% 13.02/12.96 dependent: set(order_eq).
% 13.02/12.96 dependent: set(back_demod).
% 13.02/12.96 dependent: set(lrpo).
% 13.02/12.96 dependent: set(hyper_res).
% 13.02/12.96 dependent: set(unit_deletion).
% 13.02/12.96 dependent: set(factor).
% 13.02/12.96
% 13.02/12.96 ------------> process usable:
% 13.02/12.96 ** KEPT (pick-wt=14): 1 [] hAPP(A,$f1(B,A))!=hAPP(B,$f1(B,A))|A=B.
% 13.02/12.96 ** KEPT (pick-wt=8): 2 [] -class_Orderings_Opreorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),B)).
% 13.02/12.96 ** KEPT (pick-wt=18): 3 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),C)).
% 13.02/12.96 ** KEPT (pick-wt=15): 4 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),A))|A=B.
% 13.02/12.96 ** KEPT (pick-wt=20): 5 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E)),hAPP(D,E))).
% 13.02/12.96 ** KEPT (pick-wt=28): 6 [] -class_Orderings_Oord(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,$f2(D,C,B,A))),hAPP(D,$f2(D,C,B,A)))).
% 13.02/12.96 ** KEPT (pick-wt=14): 7 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 13.02/12.96 ** KEPT (pick-wt=11): 8 [] -class_Orderings_Oorder(A)|B!=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C)).
% 13.02/12.96 ** KEPT (pick-wt=11): 9 [] -class_Orderings_Oorder(A)|B!=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 13.02/12.96 ** KEPT (pick-wt=17): 10 [] -class_Orderings_Oorder(A)|B=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 13.02/12.96 ** KEPT (pick-wt=11): 11 [] -class_Orderings_Opreorder(A)|B!=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C)).
% 13.02/12.96 Following clause subsumed by 7 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 13.02/12.96 Following clause subsumed by 5 during input processing: 0 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E)),hAPP(D,E))).
% 13.02/12.96 ** KEPT (pick-wt=20): 12 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),C)).
% 13.02/12.96 Following clause subsumed by 10 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B))|C=B.
% 13.02/12.96 ** KEPT (pick-wt=20): 13 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 13.02/12.96 Following clause subsumed by 10 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B))|B=C.
% 13.02/12.96 ** KEPT (pick-wt=17): 14 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|B!=D|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),C)).
% 13.02/12.96 ** KEPT (pick-wt=17): 15 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|C!=D|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 13.02/12.96 ** KEPT (pick-wt=17): 16 [] -class_Orderings_Oorder(A)|B!=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),B)).
% 13.02/12.96 ** KEPT (pick-wt=17): 17 [] -class_Orderings_Oord(A)|B!=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 13.02/12.96 Following clause subsumed by 10 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B))|C=B.
% 13.02/12.96 Following clause subsumed by 8 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B))|C!=B.
% 13.02/12.96 Following clause subsumed by 5 during input processing: 0 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E)),hAPP(D,E))).
% 13.02/12.96 ** KEPT (pick-wt=15): 18 [] -class_RealVector_Oreal__normed__vector(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|B=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.96 ** KEPT (pick-wt=15): 19 [] -class_RealVector_Oreal__normed__vector(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|B!=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.96 ** KEPT (pick-wt=11): 20 [] -class_RealVector_Oreal__normed__vector(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(A,B))).
% 13.02/12.96 ** KEPT (pick-wt=12): 21 [] -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Onorm__class_Onorm(A,B)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.96 ** KEPT (pick-wt=12): 22 [] -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Onorm__class_Onorm(A,B)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.96 ** KEPT (pick-wt=9): 23 [] -class_RealVector_Oreal__normed__vector(A)|c_RealVector_Onorm__class_Onorm(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.96 ** KEPT (pick-wt=10): 24 [] -c_SEQ_Osubse_q(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),hAPP(A,B))).
% 13.02/12.96 ** KEPT (pick-wt=11): 25 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 ** KEPT (pick-wt=11): 26 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 ** KEPT (pick-wt=10): 27 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.96 ** KEPT (pick-wt=10): 28 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.96 ** KEPT (pick-wt=13): 29 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 ** KEPT (pick-wt=13): 30 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 ** KEPT (pick-wt=28): 31 [] -class_RealVector_Oreal__normed__vector(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),c_RealVector_Onorm__class_Onorm(A,D))))|C=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.96 ** KEPT (pick-wt=21): 32 [] -class_RealVector_Oreal__normed__div__algebra(A)|c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C)).
% 13.02/12.96 ** KEPT (pick-wt=10): 33 [] c_RealDef_Oreal(tc_Nat_Onat,A)!=c_RealDef_Oreal(tc_Nat_Onat,B)|A=B.
% 13.02/12.96 ** KEPT (pick-wt=10): 34 [] c_RealDef_Oreal(tc_Nat_Onat,A)=c_RealDef_Oreal(tc_Nat_Onat,B)|A!=B.
% 13.02/12.96 ** KEPT (pick-wt=9): 35 [] A!=B|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 13.02/12.96 ** KEPT (pick-wt=18): 36 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),C)).
% 13.02/12.96 ** KEPT (pick-wt=15): 37 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),A))|A=B.
% 13.02/12.96 ** KEPT (pick-wt=25): 38 [] -class_Groups_Oab__semigroup__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 13.02/12.96 ** KEPT (pick-wt=12): 39 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.96 Following clause subsumed by 39 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.96 ** KEPT (pick-wt=12): 40 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.96 Following clause subsumed by 40 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.96 ** KEPT (pick-wt=24): 41 [] -class_RealVector_Oreal__normed__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C)))).
% 13.02/12.96 ** KEPT (pick-wt=16): 42 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A)),c_RealDef_Oreal(tc_Nat_Onat,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 13.02/12.96 ** KEPT (pick-wt=16): 43 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A)),c_RealDef_Oreal(tc_Nat_Onat,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 13.02/12.96 ** KEPT (pick-wt=20): 44 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)|B=C.
% 13.02/12.96 ** KEPT (pick-wt=20): 45 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)|B!=C.
% 13.02/12.96 ** KEPT (pick-wt=20): 46 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)|B=C.
% 13.02/12.96 ** KEPT (pick-wt=20): 47 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)|B!=C.
% 13.02/12.96 ** KEPT (pick-wt=10): 48 [] c_RealDef_Oreal(tc_Nat_Onat,A)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 ** KEPT (pick-wt=10): 49 [] c_RealDef_Oreal(tc_Nat_Onat,A)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 ** KEPT (pick-wt=14): 50 [] -class_Rings_Olinordered__ring(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B))).
% 13.02/12.96 ** KEPT (pick-wt=28): 51 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.96 ** KEPT (pick-wt=28): 52 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.96 ** KEPT (pick-wt=28): 53 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.96 ** KEPT (pick-wt=28): 54 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.96 ** KEPT (pick-wt=28): 55 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C)).
% 13.02/12.96 ** KEPT (pick-wt=28): 56 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.96 ** KEPT (pick-wt=28): 57 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.96 ** KEPT (pick-wt=28): 58 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C)).
% 13.02/12.96 ** KEPT (pick-wt=28): 59 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.96 ** KEPT (pick-wt=28): 60 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C)).
% 13.02/12.96 ** KEPT (pick-wt=28): 61 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.96 ** KEPT (pick-wt=28): 62 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C)).
% 13.02/12.96 ** KEPT (pick-wt=28): 63 [] -class_Rings_Oordered__cancel__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))).
% 13.02/12.96 ** KEPT (pick-wt=28): 64 [] -class_Rings_Oordered__cancel__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.96 ** KEPT (pick-wt=28): 65 [] -class_Rings_Oordered__cancel__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.96 Following clause subsumed by 65 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.96 ** KEPT (pick-wt=28): 66 [] -class_Rings_Oordered__ring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))).
% 13.02/12.96 ** KEPT (pick-wt=31): 67 [] -class_Rings_Oordered__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))).
% 13.02/12.96 ** KEPT (pick-wt=31): 68 [] -class_Rings_Oordered__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))).
% 13.02/12.96 ** KEPT (pick-wt=31): 69 [] -class_Rings_Oordered__comm__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))).
% 13.02/12.96 ** KEPT (pick-wt=17): 70 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 ** KEPT (pick-wt=13): 71 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 ** KEPT (pick-wt=13): 72 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 ** KEPT (pick-wt=20): 73 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B=C|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 ** KEPT (pick-wt=16): 74 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B!=C.
% 13.02/12.96 ** KEPT (pick-wt=17): 75 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 ** KEPT (pick-wt=20): 76 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)|A=C|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 ** KEPT (pick-wt=16): 77 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)|A!=C.
% 13.02/12.96 ** KEPT (pick-wt=17): 78 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.96 ** KEPT (pick-wt=28): 79 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D))).
% 13.02/12.96 ** KEPT (pick-wt=22): 80 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))).
% 13.02/12.96 ** KEPT (pick-wt=22): 81 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C))).
% 13.02/12.96 ** KEPT (pick-wt=19): 82 [] -class_Rings_Ono__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.96 Following clause subsumed by 82 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).
% 13.02/12.96 ** KEPT (pick-wt=19): 83 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.96 ** KEPT (pick-wt=15): 84 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.96 ** KEPT (pick-wt=15): 85 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.97 ** KEPT (pick-wt=12): 86 [] -class_Rings_Omult__zero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.97 ** KEPT (pick-wt=12): 87 [] -class_Rings_Omult__zero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.97 Following clause subsumed by 64 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.97 Following clause subsumed by 65 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.97 ** KEPT (pick-wt=28): 88 [] -class_Rings_Oordered__ring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))).
% 13.02/12.97 Following clause subsumed by 66 during input processing: 0 [] -class_Rings_Oordered__ring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))).
% 13.02/12.97 ** KEPT (pick-wt=44): 89 [] -class_Rings_Oordered__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))).
% 13.02/12.97 ** KEPT (pick-wt=44): 90 [] -class_Rings_Oordered__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))).
% 13.02/12.97 ** KEPT (pick-wt=31): 91 [] -class_Rings_Oordered__ring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B))).
% 13.02/12.97 ** KEPT (pick-wt=31): 92 [] -class_Rings_Oordered__ring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))).
% 13.02/12.97 ** KEPT (pick-wt=21): 93 [] -class_Orderings_Oorder(A)| -c_SEQ_Odecse_q(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,D)),hAPP(B,C))).
% 13.02/12.97 ** KEPT (pick-wt=15): 94 [] -class_Orderings_Oorder(A)|c_SEQ_Odecse_q(A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f4(B,A)),$f3(B,A))).
% 13.02/12.97 ** KEPT (pick-wt=19): 95 [] -class_Orderings_Oorder(A)|c_SEQ_Odecse_q(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f3(B,A))),hAPP(B,$f4(B,A)))).
% 13.02/12.97 ** KEPT (pick-wt=12): 96 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.97 ** KEPT (pick-wt=12): 97 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.97 ** KEPT (pick-wt=10): 98 [] -class_RealVector_Oreal__normed__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f5(A))).
% 13.02/12.97 ** KEPT (pick-wt=30): 99 [] -class_RealVector_Oreal__normed__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))),$f5(A)))).
% 13.02/12.97 ** KEPT (pick-wt=11): 100 [] -class_RealVector_Oreal__normed__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f6(B,A))).
% 13.02/12.97 ** KEPT (pick-wt=24): 101 [] -class_RealVector_Oreal__normed__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,C)),$f6(B,A)))).
% 13.02/12.97 ** KEPT (pick-wt=11): 102 [] -class_RealVector_Oreal__normed__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f7(B,A))).
% 13.02/12.97 ** KEPT (pick-wt=24): 103 [] -class_RealVector_Oreal__normed__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),$f7(C,A)))).
% 13.02/12.97 ** KEPT (pick-wt=21): 104 [] -class_Orderings_Oorder(A)| -c_SEQ_Oincse_q(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,C)),hAPP(B,D))).
% 13.02/12.97 ** KEPT (pick-wt=15): 105 [] -class_Orderings_Oorder(A)|c_SEQ_Oincse_q(A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f9(B,A)),$f8(B,A))).
% 13.02/12.97 ** KEPT (pick-wt=19): 106 [] -class_Orderings_Oorder(A)|c_SEQ_Oincse_q(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f9(B,A))),hAPP(B,$f8(B,A)))).
% 13.02/12.97 ** KEPT (pick-wt=30): 107 [] -class_RealVector_Oreal__normed__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))),$f10(A)))).
% 13.02/12.97 ** KEPT (pick-wt=24): 108 [] -class_RealVector_Oreal__normed__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,C)),$f11(B,A)))).
% 13.02/12.97 ** KEPT (pick-wt=24): 109 [] -class_RealVector_Oreal__normed__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),$f12(C,A)))).
% 13.02/12.97 ** KEPT (pick-wt=35): 110 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),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)).
% 13.02/12.97 ** KEPT (pick-wt=35): 111 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),E)).
% 13.02/12.97 ** KEPT (pick-wt=35): 112 [] -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))).
% 13.02/12.97 ** KEPT (pick-wt=25): 113 [] -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).
% 13.02/12.97 ** KEPT (pick-wt=25): 114 [] -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)).
% 13.02/12.97 Following clause subsumed by 114 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)).
% 13.02/12.97 ** KEPT (pick-wt=25): 115 [] -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)).
% 13.02/12.97 ** KEPT (pick-wt=15): 116 [] -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).
% 13.02/12.97 Following clause subsumed by 73 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=C.
% 13.02/12.97 Following clause subsumed by 75 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.97 Following clause subsumed by 74 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B!=C.
% 13.02/12.97 ** KEPT (pick-wt=13): 117 [] -class_Groups_Ozero(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 13.02/12.97 ** KEPT (pick-wt=13): 118 [] -class_Groups_Ozero(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 13.02/12.97 ** KEPT (pick-wt=33): 119 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(A)),c_RComplete_Onatfloor(B))),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)))).
% 13.02/12.97 ** KEPT (pick-wt=37): 120 [] -class_Orderings_Oorder(A)| -c_SEQ_Omonose_q(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,C)),hAPP(B,D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,E),F))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,F)),hAPP(B,E))).
% 13.02/12.97 ** KEPT (pick-wt=15): 121 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f14(B,A)),$f13(B,A))).
% 13.02/12.97 ** KEPT (pick-wt=19): 122 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f14(B,A))),hAPP(B,$f13(B,A)))).
% 13.02/12.97 ** KEPT (pick-wt=15): 123 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f16(B,A)),$f15(B,A))).
% 13.02/12.97 ** KEPT (pick-wt=19): 124 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f15(B,A))),hAPP(B,$f16(B,A)))).
% 13.02/12.97 ** KEPT (pick-wt=22): 125 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),c_RealDef_Oreal(tc_Nat_Onat,B))).
% 13.02/12.97 ** KEPT (pick-wt=22): 126 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),c_RealDef_Oreal(tc_Nat_Onat,B))).
% 13.02/12.97 ** KEPT (pick-wt=22): 127 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),c_RComplete_Onatfloor(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B)),A)).
% 13.02/12.97 ** KEPT (pick-wt=22): 128 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),c_RComplete_Onatfloor(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B)),A)).
% 13.02/12.97 ** KEPT (pick-wt=8): 129 [] -class_Orderings_Oorder(A)| -c_SEQ_Odecse_q(A,B)|c_SEQ_Omonose_q(A,B).
% 13.02/12.97 ** KEPT (pick-wt=20): 130 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C).
% 13.02/12.97 ** KEPT (pick-wt=10): 131 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=B.
% 13.02/12.97 ** KEPT (pick-wt=14): 132 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatfloor(A)),c_RComplete_Onatfloor(B))).
% 13.02/12.97 ** KEPT (pick-wt=14): 133 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A)),c_RComplete_Onatceiling(B))).
% 13.02/12.97 ** KEPT (pick-wt=12): 134 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|c_RComplete_Onatfloor(A)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.97 ** KEPT (pick-wt=16): 135 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(A))),A)).
% 13.02/12.97 ** KEPT (pick-wt=15): 136 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),c_RComplete_Onatfloor(B))).
% 13.02/12.97 ** KEPT (pick-wt=12): 137 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|c_RComplete_Onatceiling(A)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.97 ** KEPT (pick-wt=15): 138 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),c_RealDef_Oreal(tc_Nat_Onat,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A)),B)).
% 13.02/12.97 ** KEPT (pick-wt=8): 139 [] -class_Orderings_Oorder(A)| -c_SEQ_Oincse_q(A,B)|c_SEQ_Omonose_q(A,B).
% 13.02/12.97 Following clause subsumed by 131 during input processing: 0 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=B.
% 13.02/12.97 ** KEPT (pick-wt=15): 140 [] -class_Orderings_Oorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f18(B,A)),$f17(B,A)))|c_SEQ_Omonose_q(A,B).
% 13.02/12.97 ** KEPT (pick-wt=19): 141 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f18(B,A))),hAPP(B,$f17(B,A))))|c_SEQ_Omonose_q(A,B).
% 13.02/12.97 ** KEPT (pick-wt=15): 142 [] -class_Orderings_Oorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f20(B,A)),$f19(B,A)))|c_SEQ_Omonose_q(A,B).
% 13.02/12.97 ** KEPT (pick-wt=19): 143 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f19(B,A))),hAPP(B,$f20(B,A))))|c_SEQ_Omonose_q(A,B).
% 13.02/12.97 ** KEPT (pick-wt=15): 144 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 13.02/12.97 ** KEPT (pick-wt=15): 145 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A)),B),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 13.02/12.97 ** KEPT (pick-wt=29): 146 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 13.02/12.97 Following clause subsumed by 80 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 13.02/12.97 ** KEPT (pick-wt=29): 147 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),C)).
% 13.02/12.97 Following clause subsumed by 81 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),C)).
% 13.02/12.97 Following clause subsumed by 146 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 13.02/12.97 Following clause subsumed by 80 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 13.02/12.97 ** KEPT (pick-wt=36): 148 [] -class_RealVector_Oreal__normed__algebra(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,D)),E))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),E))).
% 13.02/12.97 ** KEPT (pick-wt=7): 149 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.02/12.97 ** KEPT (pick-wt=17): 150 [] -class_Rings_Olinordered__idom(A)|B=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 ** KEPT (pick-wt=8): 151 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),B)).
% 13.02/12.97 ** KEPT (pick-wt=17): 152 [] -class_Orderings_Olinorder(A)|B=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 ** KEPT (pick-wt=11): 153 [] -class_Orderings_Olinorder(A)|B!=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)).
% 13.02/12.97 ** KEPT (pick-wt=11): 154 [] -class_Orderings_Olinorder(A)|B!=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 Following clause subsumed by 152 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B))|B=C.
% 13.02/12.97 ** KEPT (pick-wt=14): 155 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 Following clause subsumed by 153 during input processing: 0 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B!=C.
% 13.02/12.97 Following clause subsumed by 152 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 Following clause subsumed by 152 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B))|C=B.
% 13.02/12.97 Following clause subsumed by 153 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B))|C!=B.
% 13.02/12.97 Following clause subsumed by 152 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 ** KEPT (pick-wt=11): 156 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B!=C.
% 13.02/12.97 ** KEPT (pick-wt=14): 157 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 Following clause subsumed by 157 during input processing: 0 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 Following clause subsumed by 156 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B!=C.
% 13.02/12.97 ** KEPT (pick-wt=11): 158 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|C!=B.
% 13.02/12.97 Following clause subsumed by 157 during input processing: 0 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 ** KEPT (pick-wt=14): 159 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 ** KEPT (pick-wt=17): 160 [] -class_Orderings_Oord(A)|B!=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 13.02/12.97 ** KEPT (pick-wt=17): 161 [] -class_Orderings_Oorder(A)|B!=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),B)).
% 13.02/12.97 ** KEPT (pick-wt=17): 162 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|C!=D|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 13.02/12.97 ** KEPT (pick-wt=17): 163 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B!=D|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 13.02/12.97 ** KEPT (pick-wt=20): 164 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 13.02/12.97 ** KEPT (pick-wt=20): 165 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 13.02/12.97 Following clause subsumed by 157 during input processing: 0 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 Following clause subsumed by 152 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 ** KEPT (pick-wt=6): 166 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),A)).
% 13.02/12.97 ** KEPT (pick-wt=9): 167 [] A!=B| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 13.02/12.97 ** KEPT (pick-wt=9): 168 [] A!=B| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),A)).
% 13.02/12.97 Following clause subsumed by 166 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),A)).
% 13.02/12.97 Following clause subsumed by 168 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|B!=A.
% 13.02/12.97 Following clause subsumed by 167 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|A!=B.
% 13.02/12.97 ** KEPT (pick-wt=16): 169 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A)),c_RealDef_Oreal(tc_Nat_Onat,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 13.02/12.97 ** KEPT (pick-wt=16): 170 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A)),c_RealDef_Oreal(tc_Nat_Onat,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 13.02/12.97 ** KEPT (pick-wt=14): 171 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 13.02/12.97 ** KEPT (pick-wt=14): 172 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 13.02/12.97 Following clause subsumed by 171 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 Following clause subsumed by 172 during input processing: 0 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 Following clause subsumed by 171 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 ** KEPT (pick-wt=14): 173 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C)).
% 13.02/12.97 Following clause subsumed by 156 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B!=C.
% 13.02/12.97 ** KEPT (pick-wt=17): 174 [] -class_Orderings_Oorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|B=C.
% 13.02/12.97 ** KEPT (pick-wt=14): 175 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C)).
% 13.02/12.97 ** KEPT (pick-wt=14): 176 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 13.02/12.97 ** KEPT (pick-wt=20): 177 [] -class_Orderings_Opreorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 13.02/12.97 Following clause subsumed by 174 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B=C.
% 13.02/12.97 Following clause subsumed by 173 during input processing: 0 [] -class_Orderings_Oorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)).
% 13.02/12.97 Following clause subsumed by 8 during input processing: 0 [] -class_Orderings_Oorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|B!=C.
% 13.02/12.97 Following clause subsumed by 171 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 13.02/12.97 Following clause subsumed by 171 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 ** KEPT (pick-wt=17): 178 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|B=C.
% 13.02/12.97 ** KEPT (pick-wt=17): 179 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|B!=C.
% 13.02/12.97 Following clause subsumed by 174 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)).
% 13.02/12.97 ** KEPT (pick-wt=17): 180 [] -class_Orderings_Oorder(A)|B=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 Following clause subsumed by 172 during input processing: 0 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 13.02/12.97 Following clause subsumed by 175 during input processing: 0 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C)).
% 13.02/12.97 Following clause subsumed by 178 during input processing: 0 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B=C.
% 13.02/12.97 Following clause subsumed by 153 during input processing: 0 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B!=C.
% 13.02/12.97 Following clause subsumed by 174 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B=C.
% 13.02/12.97 Following clause subsumed by 174 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|B=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)).
% 13.02/12.97 Following clause subsumed by 180 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|C=B|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)).
% 13.02/12.97 ** KEPT (pick-wt=20): 181 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 13.02/12.97 ** KEPT (pick-wt=20): 182 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 13.02/12.97 ** KEPT (pick-wt=20): 183 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 13.02/12.97 ** KEPT (pick-wt=20): 184 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 13.02/12.97 ** KEPT (pick-wt=10): 185 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.97 Following clause subsumed by 149 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.02/12.97 Following clause subsumed by 168 during input processing: 0 [] A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 13.02/12.97 Following clause subsumed by 149 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.02/12.97 ** KEPT (pick-wt=12): 186 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),B)).
% 13.02/12.97 ** KEPT (pick-wt=9): 187 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B))|A!=B.
% 13.02/12.97 ** KEPT (pick-wt=15): 188 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),B))|A=B.
% 13.02/12.97 Following clause subsumed by 188 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B))|A=B.
% 13.02/12.97 Following clause subsumed by 186 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),B)).
% 13.02/12.97 ** KEPT (pick-wt=9): 189 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),B))|A!=B.
% 13.02/12.97 ** KEPT (pick-wt=12): 190 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 13.02/12.97 Following clause subsumed by 167 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|A!=B.
% 13.02/12.97 ** KEPT (pick-wt=15): 191 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|A=B.
% 13.02/12.97 Following clause subsumed by 191 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|A=B.
% 13.02/12.97 Following clause subsumed by 190 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 13.02/12.97 Following clause subsumed by 35 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|A!=B.
% 13.02/12.97 Following clause subsumed by 190 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 13.02/12.97 Following clause subsumed by 191 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|A=B|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 13.02/12.97 Following clause subsumed by 190 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 13.02/12.97 Following clause subsumed by 35 during input processing: 0 [] A!=B|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 13.02/12.97 ** KEPT (pick-wt=16): 192 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 13.02/12.97 ** KEPT (pick-wt=16): 193 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 13.02/12.97 ** KEPT (pick-wt=18): 194 [] -c_SEQ_Osubse_q(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B)),hAPP(A,C))).
% 13.02/12.97 ** KEPT (pick-wt=14): 195 [] c_SEQ_Osubse_q(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,$f22(A))),hAPP(A,$f21(A)))).
% 13.02/12.97 ** KEPT (pick-wt=14): 196 [] -class_Rings_Olinordered__ring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.97 ** KEPT (pick-wt=32): 197 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.97 ** KEPT (pick-wt=31): 198 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),B)).
% 13.02/12.97 ** KEPT (pick-wt=31): 199 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.97 ** KEPT (pick-wt=30): 200 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),B)).
% 13.02/12.97 ** KEPT (pick-wt=31): 201 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 13.02/12.97 ** KEPT (pick-wt=31): 202 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),B)).
% 13.02/12.97 ** KEPT (pick-wt=32): 203 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.97 ** KEPT (pick-wt=31): 204 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 13.02/12.97 ** KEPT (pick-wt=31): 205 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.97 ** KEPT (pick-wt=30): 206 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 13.02/12.97 ** KEPT (pick-wt=31): 207 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 13.02/12.97 ** KEPT (pick-wt=31): 208 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 13.02/12.97 ** KEPT (pick-wt=31): 209 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 13.02/12.97 Following clause subsumed by 207 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 13.02/12.97 ** KEPT (pick-wt=28): 210 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))).
% 13.02/12.97 ** KEPT (pick-wt=28): 211 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.97 ** KEPT (pick-wt=28): 212 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.97 ** KEPT (pick-wt=28): 213 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C)).
% 13.02/12.97 ** KEPT (pick-wt=28): 214 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 13.02/12.97 ** KEPT (pick-wt=31): 215 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 13.02/12.97 Following clause subsumed by 208 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 13.02/12.97 Following clause subsumed by 212 during input processing: 0 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.97 ** KEPT (pick-wt=28): 216 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))).
% 13.02/12.97 ** KEPT (pick-wt=31): 217 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D))).
% 13.02/12.97 ** KEPT (pick-wt=31): 218 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))).
% 13.02/12.97 ** KEPT (pick-wt=31): 219 [] -class_Rings_Olinordered__comm__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))).
% 13.02/12.97 Following clause subsumed by 202 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))).
% 13.02/12.97 Following clause subsumed by 208 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B))).
% 13.02/12.97 ** KEPT (pick-wt=22): 220 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_RealDef_Oreal(tc_Nat_Onat,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(A)),B)).
% 13.02/12.97 ** KEPT (pick-wt=19): 221 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 13.02/12.97 ** KEPT (pick-wt=19): 222 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)).
% 13.02/12.97 ** KEPT (pick-wt=26): 223 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)).
% 13.02/12.97 ** KEPT (pick-wt=23): 224 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 13.02/12.97 ** KEPT (pick-wt=22): 225 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 13.02/12.97 ** KEPT (pick-wt=29): 226 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 13.02/12.97 ** KEPT (pick-wt=23): 227 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)).
% 13.02/12.97 ** KEPT (pick-wt=22): 228 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),C)).
% 13.02/12.97 ** KEPT (pick-wt=29): 229 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),C)).
% 13.02/12.97 Following clause subsumed by 229 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C))).
% 13.02/12.97 Following clause subsumed by 226 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))).
% 13.02/12.97 Following clause subsumed by 225 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 13.02/12.97 Following clause subsumed by 226 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 13.02/12.97 ** KEPT (pick-wt=23): 230 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B=C.
% 13.02/12.97 Following clause subsumed by 74 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B!=C.
% 13.02/12.97 ** KEPT (pick-wt=29): 231 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C))).
% 13.02/12.97 ** KEPT (pick-wt=26): 232 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))).
% 13.02/12.97 ** KEPT (pick-wt=29): 233 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),C)).
% 13.02/12.97 ** KEPT (pick-wt=29): 234 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),C)).
% 13.02/12.97 ** KEPT (pick-wt=11): 235 [] -class_RealVector_Oreal__normed__vector(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.97 ** KEPT (pick-wt=9): 236 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.97 ** KEPT (pick-wt=31): 237 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D)).
% 13.02/12.97 ** KEPT (pick-wt=31): 238 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D)).
% 13.02/12.97 ** KEPT (pick-wt=31): 239 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),C)).
% 13.02/12.97 ** KEPT (pick-wt=31): 240 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),C)).
% 13.02/12.97 ** KEPT (pick-wt=44): 241 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))).
% 13.02/12.97 ** KEPT (pick-wt=44): 242 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))).
% 13.02/12.97 ** KEPT (pick-wt=44): 243 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))).
% 13.02/12.97 ** KEPT (pick-wt=44): 244 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))).
% 13.02/12.97 ** KEPT (pick-wt=31): 245 [] -class_Rings_Olinordered__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 13.02/12.97 ** KEPT (pick-wt=31): 246 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 13.02/12.97 ** KEPT (pick-wt=31): 247 [] -class_Rings_Olinordered__semiring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 13.02/12.97 ** KEPT (pick-wt=31): 248 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 13.02/12.97 ** KEPT (pick-wt=31): 249 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 13.02/12.97 ** KEPT (pick-wt=31): 250 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D)).
% 13.02/12.97 ** KEPT (pick-wt=15): 251 [] -class_RealVector_Oreal__normed__vector(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(A,B)))|B!=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.97 ** KEPT (pick-wt=15): 252 [] -class_RealVector_Oreal__normed__vector(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(A,B)))|B=c_Groups_Ozero__class_Ozero(A).
% 13.02/12.97 ** KEPT (pick-wt=29): 253 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),C)).
% 13.02/12.97 ** KEPT (pick-wt=29): 254 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),C)).
% 13.02/12.97 ** KEPT (pick-wt=29): 255 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),C)).
% 13.02/12.97 ** KEPT (pick-wt=29): 256 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),C)).
% 13.02/12.97 ** KEPT (pick-wt=16): 257 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A)))|A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.97 ** KEPT (pick-wt=11): 258 [] -class_RealVector_Oreal__normed__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f23(B,A))).
% 13.02/12.97 ** KEPT (pick-wt=24): 259 [] -class_RealVector_Oreal__normed__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),$f23(C,A)))).
% 13.02/12.97 ** KEPT (pick-wt=11): 260 [] -class_RealVector_Oreal__normed__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f24(B,A))).
% 13.02/12.97 ** KEPT (pick-wt=24): 261 [] -class_RealVector_Oreal__normed__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,C)),$f24(B,A)))).
% 13.02/12.97 ** KEPT (pick-wt=10): 262 [] -class_RealVector_Oreal__normed__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f25(A))).
% 13.02/12.97 ** KEPT (pick-wt=30): 263 [] -class_RealVector_Oreal__normed__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C))),$f25(A)))).
% 13.02/12.97 Following clause subsumed by 190 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 13.02/12.97 ** KEPT (pick-wt=14): 264 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f26(B,A))).
% 13.02/12.97 ** KEPT (pick-wt=17): 265 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),$f26(B,A))).
% 13.02/12.97 ** KEPT (pick-wt=25): 266 [] -class_RealVector_Oreal__normed__vector(A)|c_SEQ_OBse_q(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,$f27(B,A,C)))),C)).
% 13.02/12.97 ** KEPT (pick-wt=17): 267 [] hAPP(c_Complex_ORe,A)!=hAPP(c_Complex_ORe,B)|hAPP(c_Complex_OIm,A)!=hAPP(c_Complex_OIm,B)|A=B.
% 13.02/12.97 ** KEPT (pick-wt=10): 268 [] A!=B|hAPP(c_Complex_ORe,A)=hAPP(c_Complex_ORe,B).
% 13.02/12.97 ** KEPT (pick-wt=10): 269 [] A!=B|hAPP(c_Complex_OIm,A)=hAPP(c_Complex_OIm,B).
% 13.02/12.97 Following clause subsumed by 267 during input processing: 0 [] A=B|hAPP(c_Complex_ORe,A)!=hAPP(c_Complex_ORe,B)|hAPP(c_Complex_OIm,A)!=hAPP(c_Complex_OIm,B).
% 13.02/12.97 ** KEPT (pick-wt=18): 270 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(B,A),C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C),D)).
% 13.02/12.97 ** KEPT (pick-wt=18): 271 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(B,A),C),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D),C)).
% 13.02/12.97 ** KEPT (pick-wt=26): 272 [] -class_Orderings_Oord(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(B,A),C),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D),C)).
% 13.02/12.97 ** KEPT (pick-wt=14): 273 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f28(B,A))).
% 13.02/12.97 ** KEPT (pick-wt=17): 274 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),$f28(B,A))).
% 13.02/12.97 ** KEPT (pick-wt=25): 275 [] -class_RealVector_Oreal__normed__vector(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,$f29(C,B,A)))),B))|c_SEQ_OBse_q(A,C).
% 13.02/12.97 ** KEPT (pick-wt=15): 276 [] -class_RealVector_Oreal__normed__vector(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),$f30(C,D,B,A)))|c_SEQ_OBse_q(A,D).
% 13.02/12.97 ** KEPT (pick-wt=19): 277 [] -class_RealVector_Oreal__normed__vector(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,$f30(C,B,D,A)))),C))|c_SEQ_OBse_q(A,B).
% 13.02/12.97 ** KEPT (pick-wt=37): 278 [] -class_RealVector_Oreal__normed__vector(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,$f31(C,A,B)))),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,D))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f32(C,A))))).
% 13.02/12.97 ** KEPT (pick-wt=27): 279 [] -class_RealVector_Oreal__normed__vector(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f33(B,A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,$f34(B,A,C)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(C)))).
% 13.02/12.97 ** KEPT (pick-wt=30): 280 [] -class_RealVector_Oreal__normed__vector(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),$f33(B,A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,$f34(B,A,D)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(D)))).
% 13.02/12.97 ** KEPT (pick-wt=37): 281 [] -class_RealVector_Oreal__normed__vector(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,$f35(C,A,B)))),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(C,D))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f36(C,A))))).
% 13.02/12.97 ** KEPT (pick-wt=27): 282 [] -class_RealVector_Oreal__normed__vector(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f37(B,A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,$f38(B,A,C)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(C)))).
% 13.02/12.97 ** KEPT (pick-wt=30): 283 [] -class_RealVector_Oreal__normed__vector(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),$f37(B,A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,$f38(B,A,D)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(D)))).
% 13.02/12.97 ** KEPT (pick-wt=22): 284 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,$f39(A,B))),A))).
% 13.02/12.97 ** KEPT (pick-wt=14): 285 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A)),c_Nat_OSuc(B))).
% 13.02/12.97 ** KEPT (pick-wt=8): 286 [] c_Nat_OSuc(A)!=c_Nat_OSuc(B)|A=B.
% 13.02/12.97 Following clause subsumed by 286 during input processing: 0 [] c_Nat_OSuc(A)!=c_Nat_OSuc(B)|A=B.
% 13.02/12.97 ** KEPT (pick-wt=8): 287 [] c_Nat_OSuc(A)=c_Nat_OSuc(B)|A!=B.
% 13.02/12.97 ** KEPT (pick-wt=4): 288 [] c_Nat_OSuc(A)!=A.
% 13.02/12.97 Following clause subsumed by 288 during input processing: 0 [flip.1] c_Nat_OSuc(A)!=A.
% 13.02/12.97 ** KEPT (pick-wt=28): 289 [] hAPP(A,hAPP(B,C))!=hAPP(D,hAPP(E,F))|hAPP(c_Fun_Ocomp(G,H,I,A,B),C)=hAPP(c_Fun_Ocomp(J,H,K,D,E),F).
% 13.02/12.97 ** KEPT (pick-wt=5): 291 [copy,290,flip.1] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.97 Following clause subsumed by 291 during input processing: 0 [flip.1] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.97 Following clause subsumed by 291 during input processing: 0 [] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.97 Following clause subsumed by 291 during input processing: 0 [] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.97 Following clause subsumed by 291 during input processing: 0 [flip.1] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.97 Following clause subsumed by 291 during input processing: 0 [] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.97 ** KEPT (pick-wt=14): 292 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A)),c_Nat_OSuc(B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 13.02/12.97 ** KEPT (pick-wt=13): 293 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 13.02/12.97 ** KEPT (pick-wt=16): 294 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|A=B.
% 13.02/12.97 ** KEPT (pick-wt=19): 295 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A)),C)).
% 13.02/12.97 ** KEPT (pick-wt=17): 296 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|c_Nat_OSuc(A)=B|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A)),B)).
% 13.02/12.97 ** KEPT (pick-wt=13): 297 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(B))).
% 13.02/12.97 ** KEPT (pick-wt=16): 298 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(B)))|B=A.
% 13.02/12.97 Following clause subsumed by 294 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(B)))|A=B.
% 13.02/12.97 ** KEPT (pick-wt=16): 299 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(B)))|A!=B.
% 13.02/12.97 Following clause subsumed by 292 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A)),c_Nat_OSuc(B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 13.02/12.97 Following clause subsumed by 285 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A)),c_Nat_OSuc(B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 13.02/12.97 Following clause subsumed by 294 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|A=B.
% 13.02/12.97 Following clause subsumed by 297 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 13.02/12.97 ** KEPT (pick-wt=10): 300 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(B)))|A!=B.
% 13.02/12.97 ** KEPT (pick-wt=13): 301 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),c_Nat_OSuc(A))).
% 13.02/12.97 ** KEPT (pick-wt=13): 302 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 13.02/12.97 ** KEPT (pick-wt=17): 303 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),c_Nat_OSuc(B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|A=c_Nat_OSuc(B).
% 13.02/12.97 ** KEPT (pick-wt=13): 304 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),c_Nat_OSuc(B))).
% 13.02/12.97 ** KEPT (pick-wt=14): 305 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A)),c_Nat_OSuc(B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 13.02/12.98 ** KEPT (pick-wt=14): 306 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A)),c_Nat_OSuc(B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 13.02/12.98 Following clause subsumed by 303 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),c_Nat_OSuc(B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|A=c_Nat_OSuc(B).
% 13.02/12.98 Following clause subsumed by 304 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),c_Nat_OSuc(B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 13.02/12.98 Following clause subsumed by 35 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),c_Nat_OSuc(B)))|A!=c_Nat_OSuc(B).
% 13.02/12.98 ** KEPT (pick-wt=13): 307 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(B)),A)).
% 13.02/12.98 ** KEPT (pick-wt=7): 308 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A)),A)).
% 13.02/12.98 ** KEPT (pick-wt=18): 309 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),C)|B=C.
% 13.02/12.98 Following clause subsumed by 74 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),C)|B!=C.
% 13.02/12.98 ** KEPT (pick-wt=17): 311 [copy,310,flip.3] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(B)))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nat_OSuc($f40(B,A))=A.
% 13.02/12.98 ** KEPT (pick-wt=19): 312 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(B)))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f40(B,A)),B)).
% 13.02/12.98 ** KEPT (pick-wt=11): 313 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(B)))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.98 ** KEPT (pick-wt=17): 314 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(B)))|A!=c_Nat_OSuc(C)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),B)).
% 13.02/12.98 ** KEPT (pick-wt=12): 315 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.98 Following clause subsumed by 313 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.02/12.98 ** KEPT (pick-wt=12): 317 [copy,316,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|c_Nat_OSuc($f41(A))=A.
% 13.02/12.98 ** KEPT (pick-wt=11): 318 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|A!=c_Nat_OSuc(B).
% 13.02/12.98 ** KEPT (pick-wt=15): 319 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.98 ** KEPT (pick-wt=15): 320 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.98 ** KEPT (pick-wt=20): 321 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.98 ** KEPT (pick-wt=13): 322 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A)),B)).
% 13.02/12.98 ** KEPT (pick-wt=13): 323 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A)),B)).
% 13.02/12.98 ** KEPT (pick-wt=13): 324 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 13.02/12.98 ** KEPT (pick-wt=13): 325 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 13.02/12.98 Following clause subsumed by 323 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 13.02/12.98 Following clause subsumed by 322 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 13.02/12.98 Following clause subsumed by 325 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(B))).
% 13.02/12.98 Following clause subsumed by 322 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A)),B)).
% 13.02/12.98 ** KEPT (pick-wt=16): 326 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),c_Nat_OSuc(A)))|B=A.
% 13.02/12.98 Following clause subsumed by 300 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),c_Nat_OSuc(A)))|B!=A.
% 13.02/12.98 Following clause subsumed by 323 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 13.02/12.98 Following clause subsumed by 225 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 13.02/12.98 ** KEPT (pick-wt=24): 327 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 13.02/12.98 ** KEPT (pick-wt=24): 328 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 13.02/12.98 Following clause subsumed by 80 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(A)),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 13.02/12.98 ** KEPT (pick-wt=27): 329 [] -class_Orderings_Oorder(A)| -c_SEQ_Omonose_q(A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,C)),hAPP(B,c_Nat_OSuc(C))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,c_Nat_OSuc(D))),hAPP(B,D))).
% 13.02/12.98 ** KEPT (pick-wt=20): 330 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f42(B,A))),hAPP(B,c_Nat_OSuc($f42(B,A))))).
% 13.02/12.98 ** KEPT (pick-wt=20): 331 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,c_Nat_OSuc($f43(B,A)))),hAPP(B,$f43(B,A)))).
% 13.02/12.98 ** KEPT (pick-wt=13): 332 [] -c_SEQ_Osubse_q(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B)),hAPP(A,c_Nat_OSuc(B)))).
% 13.02/12.98 ** KEPT (pick-wt=15): 333 [] c_SEQ_Osubse_q(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,$f44(A))),hAPP(A,c_Nat_OSuc($f44(A))))).
% 13.02/12.98 ** KEPT (pick-wt=27): 334 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A))).
% 13.02/12.98 ** KEPT (pick-wt=27): 335 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))).
% 13.02/12.98 ** KEPT (pick-wt=29): 336 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A))).
% 13.02/12.98 ** KEPT (pick-wt=21): 337 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),A)).
% 13.02/12.98 ** KEPT (pick-wt=21): 338 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B)).
% 13.02/12.98 ** KEPT (pick-wt=29): 339 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),B)).
% 13.02/12.98 ** KEPT (pick-wt=20): 340 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f45(B,A))))).
% 13.02/12.98 ** KEPT (pick-wt=21): 341 [] -class_RealVector_Oreal__normed__vector(A)|c_SEQ_OBse_q(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,$f46(B,A,C)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(C)))).
% 13.02/12.98 ** KEPT (pick-wt=20): 342 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,C))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f47(B,A))))).
% 13.02/12.98 ** KEPT (pick-wt=21): 343 [] -class_RealVector_Oreal__normed__vector(A)|c_SEQ_OBse_q(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(B,$f48(B,A,C)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(C)))).
% 13.02/12.98 ** KEPT (pick-wt=18): 344 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.02/12.98 ** KEPT (pick-wt=16): 345 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,$f49(A))),A)).
% 13.02/12.98 ** KEPT (pick-wt=17): 346 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f49(A))))).
% 13.02/12.98 ** KEPT (pick-wt=29): 347 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,$f50(B,A))),A)),B)).
% 13.02/12.98 ** KEPT (pick-wt=30): 348 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f50(B,A)))),A))).
% 13.02/12.98 ** KEPT (pick-wt=17): 349 [] c_Fun_Ocomp(A,B,C,D,E)!=F|hAPP(D,hAPP(E,G))=hAPP(F,G).
% 13.02/12.98 ** KEPT (pick-wt=35): 350 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C))|c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),C)=c_NthRoot_Oroot(A,c_NthRoot_Oroot(B,C)).
% 13.02/12.98 ** KEPT (pick-wt=40): 352 [copy,351,flip.4] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Oroot(A,B)),c_NthRoot_Oroot(A,C))=c_NthRoot_Oroot(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)).
% 13.02/12.98 ** KEPT (pick-wt=30): 353 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(A,B)),c_NthRoot_Oroot(A,C))).
% 13.02/12.98 ** KEPT (pick-wt=23): 354 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(A,B))).
% 13.02/12.98 ** KEPT (pick-wt=25): 355 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B))|c_NthRoot_Oroot(A,c_NthRoot_Oroot(B,C))=c_NthRoot_Oroot(B,c_NthRoot_Oroot(A,C)).
% 13.02/12.98 ** KEPT (pick-wt=17): 356 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|c_NthRoot_Oroot(A,B)!=c_NthRoot_Oroot(A,C)|B=C.
% 13.02/12.98 ** KEPT (pick-wt=17): 357 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|c_NthRoot_Oroot(A,B)=c_NthRoot_Oroot(A,C)|B!=C.
% 13.02/12.98 ** KEPT (pick-wt=23): 358 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(A,B)),c_NthRoot_Oroot(A,C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),C)).
% 13.02/12.98 ** KEPT (pick-wt=23): 359 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(A,B)),c_NthRoot_Oroot(A,C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),C)).
% 13.02/12.98 Following clause subsumed by 359 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(A,B)),c_NthRoot_Oroot(A,C))).
% 13.02/12.98 ** KEPT (pick-wt=17): 360 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|c_NthRoot_Oroot(A,B)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.98 ** KEPT (pick-wt=17): 361 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|c_NthRoot_Oroot(A,B)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.02/12.98 ** KEPT (pick-wt=23): 362 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(A,B)),c_NthRoot_Oroot(A,C))).
% 13.02/12.98 ** KEPT (pick-wt=23): 363 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(A,B)),c_NthRoot_Oroot(A,C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),C)).
% 13.02/12.98 Following clause subsumed by 362 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(A,B)),c_NthRoot_Oroot(A,C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),C)).
% 13.02/12.98 ** KEPT (pick-wt=26): 365 [copy,364,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Oroot(A,B)),c_NthRoot_Oroot(A,C))=c_NthRoot_Oroot(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),C)).
% 13.02/12.98 ** KEPT (pick-wt=28): 366 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B))|c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),C)=c_NthRoot_Oroot(A,c_NthRoot_Oroot(B,C)).
% 13.02/12.98 ** KEPT (pick-wt=24): 367 [] c_Fun_Ocomp(A,B,C,D,E)!=c_Fun_Ocomp(F,B,C,G,H)|hAPP(D,hAPP(E,I))=hAPP(G,hAPP(H,I)).
% 13.02/12.98 Following clause subsumed by 367 during input processing: 0 [] c_Fun_Ocomp(A,B,C,D,E)!=c_Fun_Ocomp(F,B,C,G,H)|hAPP(D,hAPP(E,I))=hAPP(G,hAPP(H,I)).
% 13.02/12.98 ** KEPT (pick-wt=23): 368 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(A,B))).
% 13.02/12.98 ** KEPT (pick-wt=23): 369 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(A,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.98 ** KEPT (pick-wt=23): 370 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(A,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.98 ** KEPT (pick-wt=23): 371 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(A,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)).
% 13.02/12.98 Following clause subsumed by 368 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(A,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)).
% 13.02/12.98 ** KEPT (pick-wt=23): 372 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(A,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)).
% 13.02/12.98 ** KEPT (pick-wt=23): 373 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(A,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B)).
% 13.02/12.98 ** KEPT (pick-wt=23): 374 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(A,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.98 ** KEPT (pick-wt=23): 375 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(A,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.02/12.98 Following clause subsumed by 373 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_NthRoot_Oroot(A,B))).
% 13.02/12.98 ** KEPT (pick-wt=37): 376 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,C),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(A,C)),c_NthRoot_Oroot(B,C))).
% 13.02/12.98 ** KEPT (pick-wt=37): 377 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,C),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(A,C)),c_NthRoot_Oroot(B,C))).
% 13.02/12.98 ** KEPT (pick-wt=24): 378 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Oroot(A,B)),A)=B.
% 13.02/12.98 ** KEPT (pick-wt=24): 379 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))|c_NthRoot_Oroot(A,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),A))=B.
% 13.02/12.98 ** KEPT (pick-wt=24): 380 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Oroot(A,B)),A)=B.
% 13.02/12.98 ** KEPT (pick-wt=19): 381 [] -class_RealVector_Oreal__normed__div__algebra(A)|c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),C).
% 13.02/12.98 ** KEPT (pick-wt=9): 382 [] -class_RealVector_Oreal__normed__algebra__1(A)|c_RealVector_Onorm__class_Onorm(A,c_Groups_Oone__class_Oone(A))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.98 ** KEPT (pick-wt=12): 383 [] -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).
% 13.02/12.98 ** KEPT (pick-wt=10): 384 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)!=B|B=c_Groups_Oone__class_Oone(A).
% 13.02/12.98 ** KEPT (pick-wt=10): 385 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)=B|B!=c_Groups_Oone__class_Oone(A).
% 13.02/12.98 ** KEPT (pick-wt=22): 386 [] -class_RealVector_Oreal__normed__algebra__1(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),C))).
% 13.02/12.98 ** KEPT (pick-wt=30): 387 [] -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)).
% 13.02/12.98 ** KEPT (pick-wt=7): 389 [copy,388,flip.2] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 13.02/12.98 Following clause subsumed by 389 during input processing: 0 [] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 13.02/12.98 ** KEPT (pick-wt=11): 390 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 13.02/12.98 ** KEPT (pick-wt=11): 391 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 13.02/12.98 ** KEPT (pick-wt=11): 392 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 13.02/12.98 ** KEPT (pick-wt=11): 393 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 13.02/12.98 ** KEPT (pick-wt=11): 394 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 13.02/12.98 ** KEPT (pick-wt=11): 395 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 13.02/12.98 ** KEPT (pick-wt=25): 396 [] -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)).
% 13.02/12.98 ** KEPT (pick-wt=20): 397 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_SEQ_OBse_q(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A)).
% 13.02/12.98 ** KEPT (pick-wt=5): 398 [] c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.98 ** KEPT (pick-wt=28): 399 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Oone__class_Oone(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))),B)).
% 13.02/12.98 ** KEPT (pick-wt=20): 400 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_SEQ_Omonose_q(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A)).
% 13.02/12.98 ** KEPT (pick-wt=21): 401 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C)).
% 13.02/12.98 ** KEPT (pick-wt=21): 403 [copy,402,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 13.02/12.98 Following clause subsumed by 403 during input processing: 0 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 13.02/12.98 ** KEPT (pick-wt=10): 404 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.98 ** KEPT (pick-wt=10): 405 [] -class_Rings_Olinordered__semidom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Oone__class_Oone(A))).
% 13.02/12.98 ** KEPT (pick-wt=10): 406 [] -class_Rings_Olinordered__semidom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Oone__class_Oone(A))).
% 13.02/12.98 ** KEPT (pick-wt=10): 407 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),c_Groups_Ozero__class_Ozero(A))).
% 13.02/12.98 ** KEPT (pick-wt=28): 408 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))).
% 13.02/12.98 ** KEPT (pick-wt=34): 409 [] -class_Rings_Olinordered__idom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Oone__class_Oone(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),B)).
% 13.02/12.98 ** KEPT (pick-wt=34): 410 [] -class_Rings_Olinordered__idom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Oone__class_Oone(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B)),B)).
% 13.02/12.98 ** KEPT (pick-wt=24): 412 [copy,411,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Oroot(A,B)),C)=c_NthRoot_Oroot(A,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),C)).
% 13.02/12.98 ** KEPT (pick-wt=17): 413 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|c_NthRoot_Oroot(A,B)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|B=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.98 ** KEPT (pick-wt=17): 414 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|c_NthRoot_Oroot(A,B)=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|B!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.98 ** KEPT (pick-wt=14): 415 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|c_NthRoot_Oroot(A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.02/12.98 ** KEPT (pick-wt=19): 416 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|c_NthRoot_Oroot(c_Nat_OSuc(B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),c_Nat_OSuc(B)))=A.
% 13.02/12.98 ** KEPT (pick-wt=30): 417 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(B,C)),c_NthRoot_Oroot(A,C))).
% 13.02/12.98 ** KEPT (pick-wt=23): 418 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(A,B)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.98 ** KEPT (pick-wt=23): 419 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_NthRoot_Oroot(A,B)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.98 ** KEPT (pick-wt=23): 420 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_NthRoot_Oroot(A,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),B)).
% 13.02/12.98 ** KEPT (pick-wt=23): 421 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_NthRoot_Oroot(A,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),B)).
% 13.02/12.98 ** KEPT (pick-wt=23): 422 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_NthRoot_Oroot(A,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),B)).
% 13.02/12.98 ** KEPT (pick-wt=23): 423 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_NthRoot_Oroot(A,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),B)).
% 13.02/12.98 ** KEPT (pick-wt=23): 424 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(A,B)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.98 ** KEPT (pick-wt=23): 425 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(A,B)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.02/12.98 ** KEPT (pick-wt=30): 426 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Oroot(B,C)),c_NthRoot_Oroot(A,C))).
% 13.02/12.98 ** KEPT (pick-wt=27): 427 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B),A)!=C|c_NthRoot_Oroot(A,C)=B.
% 13.02/12.98 ** KEPT (pick-wt=38): 428 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D))).
% 13.13/12.98 ** KEPT (pick-wt=28): 429 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))).
% 13.13/12.98 ** KEPT (pick-wt=31): 430 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C),D)).
% 13.13/12.98 ** KEPT (pick-wt=31): 431 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C),D)).
% 13.13/12.98 Following clause subsumed by 430 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C),D)).
% 13.13/12.98 ** KEPT (pick-wt=38): 432 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),c_Groups_Oone__class_Oone(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B))).
% 13.13/12.98 ** KEPT (pick-wt=11): 433 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat))=B.
% 13.13/12.98 ** KEPT (pick-wt=11): 434 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat))=B.
% 13.13/12.98 ** KEPT (pick-wt=13): 436 [copy,435,flip.1] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.13/12.98 ** KEPT (pick-wt=13): 438 [copy,437,flip.1] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.13/12.98 ** KEPT (pick-wt=17): 440 [copy,439,flip.1] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.13/12.98 Following clause subsumed by 436 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).
% 13.13/12.98 Following clause subsumed by 438 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).
% 13.13/12.98 Following clause subsumed by 440 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).
% 13.13/12.98 ** KEPT (pick-wt=19): 441 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.13/12.98 ** KEPT (pick-wt=14): 442 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.13/12.98 ** KEPT (pick-wt=15): 443 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.13/12.98 ** KEPT (pick-wt=29): 444 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 13.13/12.98 ** KEPT (pick-wt=23): 445 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.13/12.98 ** KEPT (pick-wt=19): 446 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 13.13/12.98 ** KEPT (pick-wt=16): 447 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.13/12.98 ** KEPT (pick-wt=21): 448 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))).
% 13.13/12.98 Following clause subsumed by 445 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 13.13/12.98 Following clause subsumed by 447 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.13/12.98 Following clause subsumed by 446 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 13.13/12.98 ** KEPT (pick-wt=16): 450 [copy,449,flip.1] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=A|B=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.13/12.98 ** KEPT (pick-wt=21): 452 [copy,451,flip.1] c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(A))!=A|c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(A)),B).
% 13.13/12.98 ** KEPT (pick-wt=15): 453 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)).
% 13.13/12.98 ** KEPT (pick-wt=15): 454 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)).
% 13.13/12.98 ** KEPT (pick-wt=15): 455 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.13/12.98 ** KEPT (pick-wt=15): 456 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.13/12.98 ** KEPT (pick-wt=15): 457 [] -class_Rings_Oring__1__no__zero__divisors(A)|B=c_Groups_Ozero__class_Ozero(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=c_Groups_Ozero__class_Ozero(A).
% 13.13/12.98 ** KEPT (pick-wt=25): 458 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 13.13/12.98 ** KEPT (pick-wt=30): 459 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)).
% 13.13/12.98 ** KEPT (pick-wt=12): 460 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Oone__class_Oone(A)),B)=c_Groups_Oone__class_Oone(A).
% 13.13/12.98 ** KEPT (pick-wt=25): 462 [copy,461,flip.2] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)).
% 13.13/12.98 ** KEPT (pick-wt=31): 463 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D))).
% 13.13/12.98 ** KEPT (pick-wt=21): 464 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))).
% 13.13/12.98 ** KEPT (pick-wt=21): 465 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))).
% 13.13/12.98 ** KEPT (pick-wt=21): 466 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))).
% 13.13/12.98 ** KEPT (pick-wt=21): 467 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 13.13/12.98 ** KEPT (pick-wt=21): 468 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.13/12.98 ** KEPT (pick-wt=25): 469 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.13/12.98 ** KEPT (pick-wt=25): 470 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)|C=D.
% 13.13/12.98 ** KEPT (pick-wt=25): 471 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)|C!=D.
% 13.13/12.98 ** KEPT (pick-wt=15): 472 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),c_Nat_OSuc(B))=c_Groups_Ozero__class_Ozero(A).
% 13.13/12.98 ** KEPT (pick-wt=21): 473 [] -class_Power_Opower(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 13.13/12.98 ** KEPT (pick-wt=21): 474 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B).
% 13.13/12.98 ** KEPT (pick-wt=12): 475 [] -class_Power_Opower(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(A).
% 13.13/12.98 ** KEPT (pick-wt=31): 476 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 13.13/12.98 ** KEPT (pick-wt=34): 477 [] -class_Rings_Olinordered__semidom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))!=hAPP(hAPP(c_Power_Opower__class_Opower(A),D),c_Nat_OSuc(C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|B=D.
% 13.13/12.98 ** KEPT (pick-wt=33): 478 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),c_Nat_OSuc(C))))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 13.13/12.98 ** KEPT (pick-wt=30): 479 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)))).
% 13.13/12.98 ** KEPT (pick-wt=26): 480 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)))).
% 13.13/12.98 ** KEPT (pick-wt=18): 481 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Oone__class_Oone(A).
% 13.13/12.98 ** KEPT (pick-wt=18): 482 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 13.13/12.98 ** KEPT (pick-wt=22): 483 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C)))).
% 13.13/12.98 ** KEPT (pick-wt=31): 484 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)).
% 13.13/12.98 ** KEPT (pick-wt=31): 485 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)).
% 13.13/12.98 Following clause subsumed by 484 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)).
% 13.13/12.98 Following clause subsumed by 485 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))).
% 13.13/12.98 ** KEPT (pick-wt=31): 486 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))).
% 13.13/12.98 ** KEPT (pick-wt=37): 487 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Oone__class_Oone(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))).
% 13.13/12.98 ** KEPT (pick-wt=29): 488 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Oone__class_Oone(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))),c_Groups_Oone__class_Oone(A))).
% 13.13/12.98 ** KEPT (pick-wt=38): 489 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),c_Groups_Oone__class_Oone(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B))).
% 13.13/12.98 ** KEPT (pick-wt=39): 490 [] -class_Rings_Olinordered__semidom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C))|B=D.
% 13.13/12.98 ** KEPT (pick-wt=11): 491 [] -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)).
% 13.13/12.98 ** KEPT (pick-wt=23): 492 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f51(B,A))).
% 13.13/12.98 ** KEPT (pick-wt=24): 493 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),$f51(B,A)),A)=B.
% 13.13/12.98 ** KEPT (pick-wt=34): 494 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),C))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),A)!=B|C=$f51(B,A).
% 13.13/12.98 ** KEPT (pick-wt=23): 495 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f52(B,A))).
% 13.13/12.98 ** KEPT (pick-wt=24): 496 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),$f52(B,A)),A)=B.
% 13.13/12.98 ** KEPT (pick-wt=37): 497 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B)),A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),B))).
% 13.13/12.98 ** KEPT (pick-wt=24): 498 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),A),B))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B)),c_Transcendental_Oln(A)).
% 13.13/12.98 ** KEPT (pick-wt=22): 499 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),B))).
% 13.13/12.98 ** KEPT (pick-wt=25): 500 [] -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)).
% 13.13/12.98 ** KEPT (pick-wt=18): 501 [] -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.
% 13.13/12.98 ** KEPT (pick-wt=18): 502 [] -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.
% 13.13/12.98 ** KEPT (pick-wt=18): 503 [] -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.
% 13.13/12.98 ** KEPT (pick-wt=18): 504 [] -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.
% 13.13/12.98 Following clause subsumed by 501 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.
% 13.13/12.98 ** KEPT (pick-wt=18): 505 [] -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.
% 13.13/12.98 Following clause subsumed by 503 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.
% 13.13/12.98 ** KEPT (pick-wt=15): 506 [] -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).
% 13.13/12.98 ** KEPT (pick-wt=25): 507 [] -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)).
% 13.13/12.98 ** KEPT (pick-wt=25): 509 [copy,508,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)).
% 13.13/12.98 Following clause subsumed by 509 during input processing: 0 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 13.13/12.98 ** KEPT (pick-wt=25): 510 [] -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).
% 13.13/12.98 ** KEPT (pick-wt=35): 511 [] -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)).
% 13.13/12.98 ** KEPT (pick-wt=36): 512 [] -class_RealVector_Oreal__normed__vector(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,B)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,D)),E))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),C),E))).
% 13.13/12.98 ** KEPT (pick-wt=24): 513 [] -class_RealVector_Oreal__normed__vector(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(A,B)),c_RealVector_Onorm__class_Onorm(A,C)))).
% 13.13/12.98 ** KEPT (pick-wt=30): 514 [] -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)).
% 13.13/12.98 ** KEPT (pick-wt=40): 516 [copy,515,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)).
% 13.13/12.98 ** KEPT (pick-wt=30): 518 [copy,517,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)).
% 13.13/12.98 Following clause subsumed by 518 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)).
% 13.13/12.98 ** KEPT (pick-wt=30): 519 [] -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)).
% 13.13/12.98 Following clause subsumed by 519 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)).
% 13.13/12.98 ** KEPT (pick-wt=30): 521 [copy,520,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)).
% 13.13/12.98 ** KEPT (pick-wt=41): 522 [] -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)).
% 13.13/12.98 ** KEPT (pick-wt=38): 523 [] -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)).
% 13.13/12.98 ** KEPT (pick-wt=38): 524 [] -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)).
% 13.13/12.98 ** KEPT (pick-wt=30): 525 [] -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)).
% 13.13/12.98 ** KEPT (pick-wt=30): 526 [] -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).
% 13.13/12.98 Following clause subsumed by 522 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|B=D|C=E.
% 13.13/12.98 Following clause subsumed by 523 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|B!=D.
% 13.13/12.98 Following clause subsumed by 524 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|C!=E.
% 13.13/12.98 ** KEPT (pick-wt=24): 527 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 13.13/12.98 ** KEPT (pick-wt=24): 528 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 13.13/12.98 ** KEPT (pick-wt=30): 529 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E))).
% 13.13/12.99 ** KEPT (pick-wt=24): 530 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))).
% 13.13/12.99 ** KEPT (pick-wt=24): 531 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D))).
% 13.13/12.99 Following clause subsumed by 527 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 13.13/12.99 ** KEPT (pick-wt=24): 532 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 13.13/12.99 Following clause subsumed by 528 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 13.13/12.99 ** KEPT (pick-wt=24): 533 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 13.13/12.99 ** KEPT (pick-wt=24): 534 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D)).
% 13.13/12.99 ** KEPT (pick-wt=24): 535 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 13.13/12.99 ** KEPT (pick-wt=30): 536 [] -class_Groups_Oordered__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),E))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E))).
% 13.13/12.99 ** KEPT (pick-wt=24): 537 [] -class_Groups_Oordered__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))).
% 13.13/12.99 ** KEPT (pick-wt=24): 538 [] -class_Groups_Oordered__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D))).
% 13.13/12.99 Following clause subsumed by 534 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D)).
% 13.13/12.99 ** KEPT (pick-wt=24): 539 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D)).
% 13.13/12.99 Following clause subsumed by 535 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 13.13/12.99 ** KEPT (pick-wt=24): 540 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 13.13/12.99 ** KEPT (pick-wt=11): 541 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A))=B.
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% 13.13/12.99 ** KEPT (pick-wt=28): 595 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 13.13/12.99 ** KEPT (pick-wt=28): 596 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 13.13/12.99 ** KEPT (pick-wt=24): 597 [] -class_Rings_Olinordered__ring(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))).
% 13.13/12.99 ** KEPT (pick-wt=28): 598 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))),c_Groups_Ozero__class_Ozero(A)))|B=c_Groups_Ozero__class_Ozero(A).
% 13.13/12.99 ** KEPT (pick-wt=28): 599 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))),c_Groups_Ozero__class_Ozero(A)))|C=c_Groups_Ozero__class_Ozero(A).
% 13.13/12.99 ** KEPT (pick-wt=32): 600 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))),c_Groups_Ozero__class_Ozero(A)))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 13.13/12.99 ** KEPT (pick-wt=24): 601 [] -class_Rings_Olinordered__ring(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))),c_Groups_Ozero__class_Ozero(A))).
% 13.13/12.99 ** KEPT (pick-wt=32): 602 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 13.13/12.99 ** KEPT (pick-wt=28): 603 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))))|B=c_Groups_Ozero__class_Ozero(A).
% 13.13/12.99 ** KEPT (pick-wt=28): 604 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))))|C=c_Groups_Ozero__class_Ozero(A).
% 13.13/12.99 ** KEPT (pick-wt=16): 605 [] -class_Rings_Olinordered__semidom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Oone__class_Oone(A)),c_Groups_Oone__class_Oone(A)))).
% 13.13/12.99 ** KEPT (pick-wt=28): 606 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(A)),c_Transcendental_Oln(B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),B)).
% 13.13/12.99 ** KEPT (pick-wt=28): 607 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(A)),c_Transcendental_Oln(B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),B)).
% 13.13/12.99 ** KEPT (pick-wt=15): 608 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(A))).
% 13.13/12.99 ** KEPT (pick-wt=22): 609 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)).
% 13.13/12.99 ** KEPT (pick-wt=22): 610 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.13/12.99 ** KEPT (pick-wt=22): 611 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.13/12.99 Following clause subsumed by 610 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.13/12.99 ** KEPT (pick-wt=16): 612 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|c_Transcendental_Oln(A)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.13/12.99 ** KEPT (pick-wt=16): 613 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|c_Transcendental_Oln(A)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.13/12.99 Following clause subsumed by 609 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)).
% 13.13/12.99 ** KEPT (pick-wt=22): 614 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)).
% 13.13/12.99 ** KEPT (pick-wt=15): 615 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(A))).
% 13.13/12.99 ** KEPT (pick-wt=58): 616 [] -class_Rings_Olinordered__semiring__1(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),F))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),E),F)!=c_Groups_Oone__class_Oone(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D))),C)).
% 13.13/12.99 ** KEPT (pick-wt=22): 617 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,B))).
% 13.13/12.99 ** KEPT (pick-wt=22): 618 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,B))).
% 13.13/12.99 ** KEPT (pick-wt=22): 619 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))).
% 13.13/12.99 ** KEPT (pick-wt=22): 620 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))).
% 13.13/12.99 ** KEPT (pick-wt=22): 621 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)).
% 13.13/12.99 Following clause subsumed by 608 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)).
% 13.13/12.99 Following clause subsumed by 621 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),A)).
% 13.13/12.99 ** KEPT (pick-wt=58): 622 [] -class_Rings_Olinordered__semiring__1__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),F))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),E),F)!=c_Groups_Oone__class_Oone(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D))),C)).
% 13.13/12.99 ** KEPT (pick-wt=26): 623 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))|c_RComplete_Onatfloor(B)=A.
% 13.13/12.99 ** KEPT (pick-wt=21): 624 [] -class_Rings_Olinordered__idom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 13.13/12.99 ** KEPT (pick-wt=21): 625 [] -class_Rings_Olinordered__idom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 13.13/12.99 ** KEPT (pick-wt=32): 626 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,A)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))|c_RComplete_Onatceiling(B)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.13/12.99 ** KEPT (pick-wt=15): 627 [] -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).
% 13.13/12.99 ** KEPT (pick-wt=15): 628 [] -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).
% 13.13/12.99 ** KEPT (pick-wt=24): 629 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(A)),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.13/12.99 ** KEPT (pick-wt=13): 630 [] 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).
% 13.13/12.99 ** KEPT (pick-wt=13): 631 [] 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).
% 13.13/12.99 ** KEPT (pick-wt=17): 632 [] 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).
% 13.13/12.99 ** KEPT (pick-wt=12): 633 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=A|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.13/12.99 ** KEPT (pick-wt=17): 634 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))).
% 13.13/12.99 ** KEPT (pick-wt=17): 635 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C))).
% 13.13/12.99 ** KEPT (pick-wt=17): 636 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),C)).
% 13.13/12.99 ** KEPT (pick-wt=25): 637 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),D)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)).
% 13.13/12.99 ** KEPT (pick-wt=28): 638 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D))).
% 13.13/12.99 ** KEPT (pick-wt=22): 639 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C))).
% 13.13/12.99 Following clause subsumed by 634 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))).
% 13.13/12.99 Following clause subsumed by 635 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C))).
% 13.13/12.99 ** KEPT (pick-wt=22): 640 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 13.13/12.99 ** KEPT (pick-wt=22): 641 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 13.13/12.99 ** KEPT (pick-wt=11): 642 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),B)).
% 13.13/12.99 ** KEPT (pick-wt=11): 643 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),A)).
% 13.13/12.99 ** KEPT (pick-wt=17): 644 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C))).
% 13.13/12.99 ** KEPT (pick-wt=17): 645 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))).
% 13.13/12.99 ** KEPT (pick-wt=17): 646 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),C)).
% 13.13/12.99 ** KEPT (pick-wt=17): 647 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 13.13/12.99 Following clause subsumed by 646 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),C)).
% 13.13/12.99 Following clause subsumed by 647 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 13.13/12.99 ** KEPT (pick-wt=28): 648 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D))).
% 13.13/12.99 ** KEPT (pick-wt=22): 649 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C))).
% 13.13/12.99 Following clause subsumed by 645 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))).
% 13.13/12.99 Following clause subsumed by 644 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C))).
% 13.13/12.99 ** KEPT (pick-wt=22): 650 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 13.13/12.99 ** KEPT (pick-wt=22): 651 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 13.13/12.99 ** KEPT (pick-wt=16): 653 [copy,652,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),$f53(B,A))=B.
% 13.13/12.99 ** KEPT (pick-wt=14): 654 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|B!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C).
% 13.13/12.99 ** KEPT (pick-wt=16): 656 [copy,655,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),$f54(B,A))=B.
% 13.13/12.99 Following clause subsumed by 654 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|B!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C).
% 13.13/12.99 ** KEPT (pick-wt=13): 657 [] -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.
% 13.13/12.99 ** KEPT (pick-wt=13): 658 [] -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.
% 13.13/12.99 ** KEPT (pick-wt=16): 659 [] 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.
% 13.13/12.99 ** KEPT (pick-wt=16): 660 [] 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.
% 13.13/12.99 ** KEPT (pick-wt=16): 661 [] 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.
% 13.13/12.99 ** KEPT (pick-wt=16): 662 [] 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.
% 13.13/12.99 ** KEPT (pick-wt=35): 663 [] -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)).
% 13.13/12.99 ** KEPT (pick-wt=19): 664 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,B)|c_SEQ_OBse_q(A,c_COMBB(tc_Nat_Onat,A,tc_Nat_Onat,B,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C))).
% 13.13/12.99 ** KEPT (pick-wt=19): 665 [] -class_RealVector_Oreal__normed__vector(A)| -c_SEQ_OBse_q(A,c_COMBB(tc_Nat_Onat,A,tc_Nat_Onat,B,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C)))|c_SEQ_OBse_q(A,B).
% 13.13/12.99 ** KEPT (pick-wt=30): 667 [copy,666,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)).
% 13.13/12.99 ** KEPT (pick-wt=30): 668 [] -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)).
% 13.13/12.99 ** KEPT (pick-wt=19): 669 [] 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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.13/12.99 ** KEPT (pick-wt=20): 670 [] 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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.13/12.99 ** KEPT (pick-wt=18): 671 [] 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).
% 13.13/12.99 ** KEPT (pick-wt=19): 672 [] 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=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.13/12.99 ** KEPT (pick-wt=19): 673 [] 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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.13/12.99 ** KEPT (pick-wt=19): 674 [] 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!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.13/12.99 ** KEPT (pick-wt=19): 675 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.13/12.99 ** KEPT (pick-wt=20): 676 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.13/12.99 ** KEPT (pick-wt=18): 677 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.13/12.99 ** KEPT (pick-wt=19): 678 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.13/12.99 ** KEPT (pick-wt=19): 679 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.13/12.99 ** KEPT (pick-wt=19): 680 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.13/12.99 ** KEPT (pick-wt=26): 681 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)).
% 13.13/12.99 Following clause subsumed by 635 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 13.13/12.99 Following clause subsumed by 634 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)).
% 13.13/12.99 ** KEPT (pick-wt=17): 683 [copy,682,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),$f55(B,A)))=B.
% 13.13/12.99 ** KEPT (pick-wt=15): 684 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|B!=c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)).
% 13.13/12.99 ** KEPT (pick-wt=24): 685 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_RealDef_Oreal(tc_Nat_Onat,B)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(A)),B).
% 13.13/12.99 ** KEPT (pick-wt=21): 686 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(A)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A),c_RealDef_Oreal(tc_Nat_Onat,B))).
% 13.13/12.99 ** KEPT (pick-wt=24): 687 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_RealDef_Oreal(tc_Nat_Onat,B)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(A)),B).
% 13.13/12.99 ** KEPT (pick-wt=24): 688 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(A)),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.13/12.99 ** KEPT (pick-wt=17): 689 [] hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f57(B,A)),B)).
% 13.13/12.99 ** KEPT (pick-wt=21): 690 [] hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C),$f57(B,A)))| -hBOOL(hAPP(A,C)).
% 13.13/12.99 ** KEPT (pick-wt=21): 691 [] hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),$f57(B,A)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 13.13/12.99 ** KEPT (pick-wt=20): 692 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|A=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.13/12.99 ** KEPT (pick-wt=20): 693 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|B=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.13/12.99 ** KEPT (pick-wt=24): 694 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)=c_Groups_Oone__class_Oone(tc_Int_Oint)|A!=c_Groups_Oone__class_Oone(tc_Int_Oint)|B!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.13/12.99 ** KEPT (pick-wt=29): 695 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B))).
% 13.13/12.99 ** KEPT (pick-wt=15): 696 [] 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).
% 13.13/12.99 ** KEPT (pick-wt=18): 697 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B)).
% 13.13/12.99 ** KEPT (pick-wt=18): 698 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint))))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B)).
% 13.13/12.99 ** KEPT (pick-wt=18): 699 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)).
% 13.13/12.99 ** KEPT (pick-wt=18): 700 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)).
% 13.13/12.99 Following clause subsumed by 700 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Groups_Oone__class_Oone(tc_Int_Oint))),B)).
% 13.13/12.99 ** KEPT (pick-wt=21): 701 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))|A=B.
% 13.13/12.99 ** KEPT (pick-wt=18): 702 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint))))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B)).
% 13.13/12.99 ** KEPT (pick-wt=15): 703 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),c_Groups_Oone__class_Oone(tc_Int_Oint))))|A!=B.
% 13.13/12.99 ** KEPT (pick-wt=20): 704 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A))).
% 13.13/12.99 ** KEPT (pick-wt=25): 705 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.13/12.99 ** KEPT (pick-wt=25): 706 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),A)),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.13/12.99 ** KEPT (pick-wt=22): 707 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),C),B))).
% 13.13/12.99 ** KEPT (pick-wt=28): 708 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),D))).
% 13.13/12.99 ** KEPT (pick-wt=22): 709 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C))).
% 13.13/12.99 ** KEPT (pick-wt=12): 710 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B)).
% 13.13/12.99 ** KEPT (pick-wt=9): 711 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))|A!=B.
% 13.13/12.99 ** KEPT (pick-wt=15): 712 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B))|A=B.
% 13.13/12.99 ** KEPT (pick-wt=14): 713 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)).
% 13.13/12.99 ** KEPT (pick-wt=14): 714 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)).
% 13.13/12.99 ** KEPT (pick-wt=5): 715 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.13/12.99 ** KEPT (pick-wt=34): 717 [copy,716,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))!=A| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,C),c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 13.13/12.99 ** KEPT (pick-wt=33): 719 [copy,718,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))!=A| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),C)).
% 13.13/12.99 ** KEPT (pick-wt=37): 720 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)).
% 13.13/12.99 ** KEPT (pick-wt=18): 721 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),C)).
% 13.13/12.99 ** KEPT (pick-wt=15): 722 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B),A))|A=B.
% 13.13/12.99 ** KEPT (pick-wt=72): 723 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),E)),F)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),E)),F)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),F))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,D),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,E),B)).
% 13.13/12.99 ** KEPT (pick-wt=51): 724 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)),E)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,E),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),E))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,D),B)).
% 13.13/12.99 ** KEPT (pick-wt=72): 725 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),E)),F)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),E)),F)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,F),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,D),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B),E)).
% 13.13/12.99 ** KEPT (pick-wt=51): 726 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),D)),E)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,C),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,E),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B),D)).
% 13.13/12.99 ** KEPT (pick-wt=38): 727 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)),C)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.13/12.99 ** KEPT (pick-wt=19): 728 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))).
% 13.13/12.99 ** KEPT (pick-wt=26): 729 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B))).
% 13.13/12.99 ** KEPT (pick-wt=26): 730 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),B))).
% 13.13/12.99 ** KEPT (pick-wt=16): 731 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),$f58(B,A))).
% 13.13/12.99 ** KEPT (pick-w
% 13.13/13.00 Search stopped in tp_alloc by max_mem option.
% 13.13/13.00 t=18): 732 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),$f58(B,A)),c_Nat_OSuc(B))=A.
% 13.13/13.00 ** KEPT (pick-wt=10): 733 [] c_Transcendental_Ocos(A)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal)|c_Transcendental_Osin(A)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.13/13.00 ** KEPT (pick-wt=31): 734 [] -class_Groups_Omonoid__mult(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),C)=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B).
% 13.13/13.00 ** KEPT (pick-wt=15): 735 [] -class_Power_Opower(A)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B)=c_Groups_Oone__class_Oone(A).
% 13.13/13.00 ** KEPT (pick-wt=28): 737 [copy,736,flip.3] -class_Power_Opower(A)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,c_Groups_Oone__class_Oone(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B).
% 13.13/13.00 ** KEPT (pick-wt=18): 738 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,B,C)),c_Groups_Ozero__class_Ozero(A))).
% 13.13/13.00 ** KEPT (pick-wt=18): 739 [] -class_Groups_Oordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,B,C)),c_Groups_Ozero__class_Ozero(A))).
% 13.13/13.00
% 13.13/13.00 Search stopped in tp_alloc by max_mem option.
% 13.13/13.00
% 13.13/13.00 ============ end of search ============
% 13.13/13.00
% 13.13/13.00 -------------- statistics -------------
% 13.13/13.00 clauses given 0
% 13.13/13.00 clauses generated 0
% 13.13/13.00 clauses kept 712
% 13.13/13.00 clauses forward subsumed 146
% 13.13/13.00 clauses back subsumed 0
% 13.13/13.00 Kbytes malloced 11718
% 13.13/13.00
% 13.13/13.00 ----------- times (seconds) -----------
% 13.13/13.00 user CPU time 0.11 (0 hr, 0 min, 0 sec)
% 13.13/13.00 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 13.13/13.00 wall-clock time 13 (0 hr, 0 min, 13 sec)
% 13.13/13.00
% 13.13/13.00 Process 26137 finished Wed Jul 27 03:00:13 2022
% 13.13/13.00 Otter interrupted
% 13.13/13.00 PROOF NOT FOUND
%------------------------------------------------------------------------------