TSTP Solution File: SWW209+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWW209+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 13:22:08 EDT 2022
% Result : Unknown 12.10s 11.97s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW209+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 02:51:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 11.99/11.88 ----- Otter 3.3f, August 2004 -----
% 11.99/11.88 The process was started by sandbox on n024.cluster.edu,
% 11.99/11.88 Wed Jul 27 02:51:55 2022
% 11.99/11.88 The command was "./otter". The process ID is 21470.
% 11.99/11.88
% 11.99/11.88 set(prolog_style_variables).
% 11.99/11.88 set(auto).
% 11.99/11.88 dependent: set(auto1).
% 11.99/11.88 dependent: set(process_input).
% 11.99/11.88 dependent: clear(print_kept).
% 11.99/11.88 dependent: clear(print_new_demod).
% 11.99/11.88 dependent: clear(print_back_demod).
% 11.99/11.88 dependent: clear(print_back_sub).
% 11.99/11.88 dependent: set(control_memory).
% 11.99/11.88 dependent: assign(max_mem, 12000).
% 11.99/11.88 dependent: assign(pick_given_ratio, 4).
% 11.99/11.88 dependent: assign(stats_level, 1).
% 11.99/11.88 dependent: assign(max_seconds, 10800).
% 11.99/11.88 clear(print_given).
% 11.99/11.88
% 11.99/11.88 formula_list(usable).
% 11.99/11.88 all A (A=A).
% 11.99/11.88 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).
% 11.99/11.88 all B_m B_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,B_m),hAPP(v_f____,B_n))).
% 11.99/11.88 all B_m B_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,B_m),hAPP(v_ga____,B_n))).
% 11.99/11.88 c_SEQ_Osubse_q(v_f____).
% 11.99/11.88 c_SEQ_Osubse_q(v_ga____).
% 11.99/11.88 all V_h_2 V_gb_2 T_d V_fa_2 T_a T_b T_c (hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_fa_2),hAPP(c_Fun_Ocomp(T_d,T_c,T_a,V_gb_2),V_h_2))=hAPP(c_Fun_Ocomp(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_fa_2),V_gb_2)),V_h_2)).
% 11.99/11.88 all V_xa_2 V_gb_2 V_fa_2 T_c T_a T_b (hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2),V_gb_2),V_xa_2)=hAPP(V_fa_2,hAPP(V_gb_2,V_xa_2))).
% 11.99/11.88 all T_e T_d T_c T_a T_b V_x_H_2 V_g_H_2 V_f_H_2 V_xa_2 V_gb_2 V_fa_2 (hAPP(V_fa_2,hAPP(V_gb_2,V_xa_2))=hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2))->hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2),V_gb_2),V_xa_2)=hAPP(hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2),V_g_H_2),V_x_H_2)).
% 11.99/11.88 all V_v_2 V_c_2 V_b_2 V_a_2 T_a T_b T_c (hAPP(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)).
% 11.99/11.88 all V_v_2 V_d_2 V_c_2 T_d V_b_2 V_a_2 T_a T_b T_c (hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2)=hAPP(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))).
% 11.99/11.88 all V_d_2 V_c_2 T_d V_b_2 V_a_2 T_a T_b T_c (hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2)=hAPP(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))))).
% 11.99/11.88 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 11.99/11.88 all V_n_2 V_m_2 (V_m_2!=V_n_2<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)).
% 11.99/11.88 all V_y V_x (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x))).
% 11.99/11.88 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 11.99/11.88 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)->V_m!=V_n).
% 11.99/11.88 all V_t V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)->V_s!=V_t).
% 11.99/11.88 all V_P_2 V_n_2 V_m_2 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))-> ((V_m_2=V_n_2->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))-> ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))))).
% 11.99/11.88 all V_fa_2 (c_SEQ_Osubse_q(V_fa_2)<-> (all B_m B_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m),hAPP(V_fa_2,B_n))))).
% 11.99/11.88 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (V_x!=V_y->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 11.99/11.88 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 11.99/11.88 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 11.99/11.88 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 11.99/11.88 all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))).
% 11.99/11.88 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))).
% 11.99/11.88 all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_b)->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))).
% 11.99/11.88 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))).
% 11.99/11.88 all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> -c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 11.99/11.88 all V_b V_a T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> -c_Orderings_Oord__class_Oless(T_a,V_b,V_a))).
% 11.99/11.88 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_y!=V_x)).
% 11.99/11.88 all V_x T_a (class_Orderings_Opreorder(T_a)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_x)).
% 11.99/11.88 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (V_xa_2!=V_ya_2<->c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2))).
% 11.99/11.88 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)|V_xa_2=V_ya_2)).
% 11.99/11.88 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x)).
% 11.99/11.88 all V_xa_2 V_ya_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->V_xa_2=V_ya_2))).
% 11.99/11.88 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 11.99/11.88 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)).
% 11.99/11.88 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 11.99/11.88 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 11.99/11.88 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)).
% 11.99/11.88 all V_fa_2 V_X_2 T_a (class_RealVector_Ometric__space(T_a)-> (c_SEQ_OCauchy(T_a,V_X_2)-> (c_SEQ_Osubse_q(V_fa_2)->c_SEQ_OCauchy(T_a,hAPP(c_Fun_Ocomp(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2),V_fa_2))))).
% 11.99/11.88 all V_fa_2 V_X_2 T_a (class_SEQ_Ocomplete__space(T_a)-> (c_SEQ_Oconvergent(T_a,V_X_2)-> (c_SEQ_Osubse_q(V_fa_2)->c_SEQ_Oconvergent(T_a,hAPP(c_Fun_Ocomp(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2),V_fa_2))))).
% 11.99/11.88 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 11.99/11.88 all V_fa_2 (c_SEQ_Osubse_q(V_fa_2)<-> (all B_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n),hAPP(V_fa_2,c_Nat_OSuc(B_n))))).
% 11.99/11.88 all V_ya_2 V_xa_2 V_fa_2 T_a T_b (class_Orderings_Oorder(T_b)&class_Orderings_Olinorder(T_a)-> (c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_fa_2)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(V_fa_2,V_xa_2),hAPP(V_fa_2,V_ya_2))<->c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)))).
% 11.99/11.88 all V_ya_2 V_xa_2 V_fa_2 T_a T_b (class_Orderings_Oorder(T_b)&class_Orderings_Oorder(T_a)-> (c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_fa_2)-> (c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)->c_Orderings_Oord__class_Oless(T_b,hAPP(V_fa_2,V_xa_2),hAPP(V_fa_2,V_ya_2))))).
% 11.99/11.88 all V_n_2 V_m_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))).
% 11.99/11.88 all V_n V_m T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))).
% 11.99/11.88 all V_n V_m T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 11.99/11.88 all V_gb_2 V_xa_2 V_fa_2 V_ac_2 V_upd_2 T_b T_a (c_Record_Oiso__tuple__update__accessor__cong__assist(T_a,T_b,V_upd_2,V_ac_2)-> (hAPP(V_fa_2,hAPP(V_ac_2,V_xa_2))=hAPP(V_ac_2,V_xa_2)->hAPP(hAPP(V_upd_2,hAPP(c_Fun_Ocomp(T_a,T_a,T_a,V_gb_2),V_fa_2)),V_xa_2)=hAPP(hAPP(V_upd_2,V_gb_2),V_xa_2))).
% 11.99/11.88 all V_gb_2 V_b_2 V_a_2 V_fa_2 T_a T_b T_c (hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_fa_2),c_Fun_Oswap(T_a,T_c,V_a_2,V_b_2,V_gb_2))=c_Fun_Oswap(T_a,T_b,V_a_2,V_b_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_fa_2),V_gb_2))).
% 11.99/11.88 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))).
% 11.99/11.88 all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)).
% 11.99/11.88 all V_X_2 T_a (class_RealVector_Ometric__space(T_a)-> (c_SEQ_Oconvergent(T_a,V_X_2)->c_SEQ_OCauchy(T_a,V_X_2))).
% 11.99/11.88 all V_X_2 T_a (class_SEQ_Ocomplete__space(T_a)-> (c_SEQ_OCauchy(T_a,V_X_2)->c_SEQ_Oconvergent(T_a,V_X_2))).
% 11.99/11.88 all V_X_2 T_a (class_SEQ_Ocomplete__space(T_a)-> (c_SEQ_OCauchy(T_a,V_X_2)<->c_SEQ_Oconvergent(T_a,V_X_2))).
% 11.99/11.88 all V_y V_x (c_Nat_OSuc(V_x)=c_Nat_OSuc(V_y)->V_x=V_y).
% 11.99/11.88 all V_xa_2 V_fa_2 V_ac_2 V_upd_2 T_b T_a (c_Record_Oiso__tuple__update__accessor__cong__assist(T_a,T_b,V_upd_2,V_ac_2)-> (hAPP(V_fa_2,hAPP(V_ac_2,V_xa_2))=hAPP(V_ac_2,V_xa_2)->hAPP(hAPP(V_upd_2,V_fa_2),V_xa_2)=V_xa_2)).
% 11.99/11.88 all V_fa_2 T_b T_a V_b_2 V_c_2 V_a_2 (V_a_2!=V_c_2-> (V_b_2!=V_c_2->c_Fun_Oswap(T_a,T_b,V_a_2,V_b_2,c_Fun_Oswap(T_a,T_b,V_b_2,V_c_2,c_Fun_Oswap(T_a,T_b,V_a_2,V_b_2,V_fa_2)))=c_Fun_Oswap(T_a,T_b,V_a_2,V_c_2,V_fa_2))).
% 11.99/11.88 all V_fa_2 V_b_2 V_a_2 T_b T_a (c_Fun_Oswap(T_a,T_b,V_a_2,V_b_2,c_Fun_Oswap(T_a,T_b,V_a_2,V_b_2,V_fa_2))=V_fa_2).
% 11.99/11.88 all V_fa_2 V_b_2 V_a_2 T_b T_a (c_Fun_Oswap(T_a,T_b,V_a_2,V_b_2,V_fa_2)=c_Fun_Oswap(T_a,T_b,V_b_2,V_a_2,V_fa_2)).
% 11.99/11.88 all V_fa_2 V_a_2 T_b T_a (c_Fun_Oswap(T_a,T_b,V_a_2,V_a_2,V_fa_2)=V_fa_2).
% 11.99/11.88 all V_n_2 V_m_2 T_a (class_Nat_Osemiring__char__0(T_a)-> (hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)<->V_m_2=V_n_2)).
% 11.99/11.88 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).
% 11.99/11.88 all V_n (c_Nat_OSuc(V_n)!=V_n).
% 11.99/11.88 all V_n (V_n!=c_Nat_OSuc(V_n)).
% 11.99/11.88 all V_ya_2 V_xa_2 V_fa_2 T_a T_b (class_Orderings_Oorder(T_b)&class_Orderings_Olinorder(T_a)-> (c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_fa_2)-> (hAPP(V_fa_2,V_xa_2)=hAPP(V_fa_2,V_ya_2)<->V_xa_2=V_ya_2))).
% 11.99/11.88 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)).
% 11.99/11.88 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)).
% 11.99/11.88 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))-> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->V_m=V_n)).
% 11.99/11.88 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k))).
% 11.99/11.88 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)-> (c_Nat_OSuc(V_m)!=V_n->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n))).
% 11.99/11.88 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))).
% 11.99/11.88 all V_m V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))->V_m=V_n)).
% 11.99/11.88 all V_m_2 V_n_2 (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))<->V_n_2=V_m_2)).
% 11.99/11.88 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 11.99/11.88 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2).
% 11.99/11.88 all V_n_2 V_m_2 (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))).
% 11.99/11.88 all V_n_H_2 V_n_2 V_fa_2 T_a (class_Orderings_Oorder(T_a)-> ((all B_n c_Orderings_Oord__class_Oless(T_a,hAPP(V_fa_2,B_n),hAPP(V_fa_2,c_Nat_OSuc(B_n))))-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_n_H_2)->c_Orderings_Oord__class_Oless(T_a,hAPP(V_fa_2,V_n_2),hAPP(V_fa_2,V_n_H_2))))).
% 11.99/11.88 all V_m_2 V_n_2 V_fa_2 T_a (class_Orderings_Oorder(T_a)-> ((all B_n c_Orderings_Oord__class_Oless(T_a,hAPP(V_fa_2,B_n),hAPP(V_fa_2,c_Nat_OSuc(B_n))))-> (c_Orderings_Oord__class_Oless(T_a,hAPP(V_fa_2,V_n_2),hAPP(V_fa_2,V_m_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)))).
% 11.99/11.88 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 11.99/11.88 all V_ya_2 V_xa_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_xa_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_ya_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2)).
% 11.99/11.88 all V_fa_2 V_n_2 T_a (hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),c_Nat_OSuc(V_n_2)),V_fa_2)=hAPP(c_Fun_Ocomp(T_a,T_a,T_a,V_fa_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_fa_2))).
% 11.99/11.88 all V_fa_2 T_a T_b (class_Orderings_Oorder(T_b)&class_Orderings_Oorder(T_a)-> ((all B_x B_y (c_Orderings_Oord__class_Oless(T_a,B_x,B_y)->c_Orderings_Oord__class_Oless(T_b,hAPP(V_fa_2,B_x),hAPP(V_fa_2,B_y))))->c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_fa_2))).
% 11.99/11.88 all V_i_2 V_n_2 V_inc_2 T_a (class_Rings_Osemiring__1(T_a)->c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Nat_OSuc(V_n_2),V_i_2)=c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2))).
% 11.99/11.88 all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)).
% 11.99/11.88 all V_k V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k)-> (V_k!=c_Nat_OSuc(V_i)-> -(all B_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,B_j)->V_k!=c_Nat_OSuc(B_j))))).
% 11.99/11.88 all V_k V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k)-> -(all B_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,B_j)->V_k!=c_Nat_OSuc(B_j)))).
% 11.99/11.88 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 11.99/11.88 all V_n_2 V_m_2 (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)<->V_m_2=V_n_2).
% 11.99/11.88 all V_ya_2 V_xa_2 (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_xa_2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_ya_2)<->V_xa_2=V_ya_2).
% 11.99/11.88 all V_xa_2 V_n_2 T_a V_fa_2 (hAPP(V_fa_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_fa_2),V_xa_2))=hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_fa_2),hAPP(V_fa_2,V_xa_2))).
% 11.99/11.88 all V_i_2 V_inc_2 T_a (class_Rings_Osemiring__1(T_a)->c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)=V_i_2).
% 11.99/11.88 all V_y V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x)).
% 11.99/11.89 all T_a (class_Rings_Osemiring__1(T_a)->hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.89 all V_fa_2 V_n_2 T_b T_a (hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_a,T_b),tc_fun(T_a,T_b)),V_n_2),c_Fun_Ocomp(T_b,T_b,T_a,V_fa_2))=c_Fun_Ocomp(T_b,T_b,T_a,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_fa_2))).
% 11.99/11.89 all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m)).
% 11.99/11.89 all V_nat_H (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_nat_H)).
% 11.99/11.89 all V_m (c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.89 all V_nat_H_1 (c_Nat_OSuc(V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.89 all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m)).
% 11.99/11.89 all V_m (c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.89 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 11.99/11.89 all V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 11.99/11.89 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 11.99/11.89 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.89 all V_n (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)).
% 11.99/11.89 all V_n_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))).
% 11.99/11.89 all V_m T_a (class_Rings_Olinordered__semidom(T_a)-> -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.89 all V_n_2 V_m_2 (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)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)))).
% 11.99/11.89 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.89 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)<-> (exists B_m (V_n_2=c_Nat_OSuc(B_m)))).
% 11.99/11.89 all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))->V_x=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 11.99/11.89 all T_a (c_Nat_Ofunpow(T_a)=c_Nat_Ocompow(T_a,T_a)).
% 11.99/11.89 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 11.99/11.89 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j)))).
% 11.99/11.89 all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)-> (exists B_m (V_n=c_Nat_OSuc(B_m)))).
% 11.99/11.89 all V_m V_n c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)).
% 11.99/11.89 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 11.99/11.89 all V_xa_2 T_a (class_Groups_Ozero(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=V_xa_2<->V_xa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.89 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)<-> (exists B_n (V_z_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(B_n)))))).
% 11.99/11.89 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,V_a)=V_b)).
% 11.99/11.89 all V_ya_2 V_xa_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2))=c_Groups_Ozero__class_Ozero(T_a)<->V_xa_2=c_Groups_Ozero__class_Ozero(T_a)&V_ya_2=c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.89 all V_w V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))).
% 11.99/11.89 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))).
% 11.99/11.89 all V_z3 V_z2 V_z1 (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3))).
% 11.99/11.89 all V_w V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w))).
% 11.99/11.89 all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.89 all V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.89 all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.89 all V_z2 V_z1 V_w (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))).
% 11.99/11.89 all V_z V_y V_x (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z))).
% 11.99/11.89 all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)<->c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.89 all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.89 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)).
% 11.99/11.89 all V_w V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)).
% 11.99/11.89 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).
% 11.99/11.89 all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z).
% 11.99/11.89 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).
% 11.99/11.89 all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)=V_z).
% 11.99/11.89 all V_w V_z (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))).
% 11.99/11.89 all V_z (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z))=V_z).
% 11.99/11.89 c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 11.99/11.89 all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.89 c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 11.99/11.89 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)|V_w_2=V_z_2).
% 11.99/11.89 all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.89 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint)<->V_m_2=c_Groups_Oone__class_Oone(tc_Int_Oint)&V_n_2=c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 11.99/11.89 all V_a T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)))).
% 11.99/11.89 all V_n V_m T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))))).
% 11.99/11.89 all V_n V_m T_a (class_Rings_Osemiring__1(T_a)->hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))).
% 11.99/11.89 all V_n V_m T_a (class_Rings_Osemiring__1(T_a)->hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))).
% 11.99/11.89 all T_a (class_Rings_Osemiring__1(T_a)->hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a)).
% 11.99/11.89 all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=V_a).
% 11.99/11.89 all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 11.99/11.89 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a))).
% 11.99/11.89 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).
% 11.99/11.89 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).
% 11.99/11.89 all V_xa_2 T_a (class_Groups_Oone(T_a)-> (c_Groups_Oone__class_Oone(T_a)=V_xa_2<->V_xa_2=c_Groups_Oone__class_Oone(T_a))).
% 11.99/11.89 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).
% 11.99/11.89 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).
% 11.99/11.89 all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)<->V_b_2=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))).
% 11.99/11.89 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b))=V_b).
% 11.99/11.89 all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=V_b_2<->c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)=V_a_2)).
% 11.99/11.89 all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)<->V_a_2=V_b_2)).
% 11.99/11.89 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=V_b).
% 11.99/11.89 all V_c V_b V_a T_a (class_Groups_Oab__semigroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))).
% 11.99/11.89 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))).
% 11.99/11.89 all V_c_2 V_b_2 V_a_2 T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)<->V_b_2=V_c_2)).
% 11.99/11.89 all V_c_2 V_a_2 V_b_2 T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)=c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)<->V_b_2=V_c_2)).
% 11.99/11.89 all V_c V_b V_a T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)->V_b=V_c)).
% 11.99/11.89 all V_c V_b V_a T_a (class_Groups_Ocancel__ab__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)->V_b=V_c)).
% 11.99/11.89 all V_c V_a V_b T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_b,V_a)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)->V_b=V_c)).
% 11.99/11.89 all V_c V_b V_e V_a T_a (class_Rings_Osemiring(T_a)->c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c)).
% 11.99/11.89 all V_b_2 V_a_2 T_a (class_Rings_Oidom(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)<->V_a_2=V_b_2|V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))).
% 11.99/11.89 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 11.99/11.89 all V_xa_2 T_a (class_Rings_Oring__1__no__zero__divisors(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2)=c_Groups_Oone__class_Oone(T_a)<->V_xa_2=c_Groups_Oone__class_Oone(T_a)|V_xa_2=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)))).
% 11.99/11.89 all V_b V_a T_a (class_Rings_Oring(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 11.99/11.89 all V_b V_a T_a (class_Rings_Oring(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 11.99/11.89 all V_b V_a T_a (class_Rings_Oring(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b)).
% 11.99/11.89 all V_b V_a T_a (class_Rings_Oring(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 11.99/11.89 all T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.89 all V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)<->c_Groups_Ozero__class_Ozero(T_a)=V_a_2)).
% 11.99/11.89 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.89 all V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.89 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=V_a_2<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.89 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)->c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)))).
% 11.99/11.89 all V_a_2 V_b_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2))).
% 11.99/11.89 all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2))).
% 11.99/11.89 all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)))).
% 11.99/11.89 all V_a T_a (class_Groups_Omonoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a).
% 11.99/11.89 all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a).
% 11.99/11.89 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.89 all V_a T_a (class_Groups_Omonoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 11.99/11.89 all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 11.99/11.89 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 11.99/11.89 all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 11.99/11.89 all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 11.99/11.89 all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 11.99/11.89 all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)))).
% 11.99/11.89 all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))).
% 11.99/11.89 all V_b_2 V_a_2 V_c_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2))).
% 11.99/11.89 all V_b_2 V_c_2 V_a_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2))).
% 11.99/11.89 all V_ya_2 V_xa_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2)))<->V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2!=c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.89 all V_y V_x T_a (class_Rings_Olinordered__ring(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.89 all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))).
% 11.99/11.89 all V_m T_a (class_Rings_Osemiring__1(T_a)->hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Nat_OSuc(V_m))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))).
% 11.99/11.89 all V_m (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(V_m))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))).
% 11.99/11.89 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.89 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))).
% 11.99/11.89 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)))).
% 11.99/11.89 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))).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k))).
% 11.99/11.89 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 11.99/11.89 all V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 11.99/11.89 all V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 11.99/11.89 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 11.99/11.89 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 11.99/11.89 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 11.99/11.89 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 11.99/11.89 all V_n c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.89 all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 11.99/11.89 all V_c V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 11.99/11.89 all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 11.99/11.89 all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 11.99/11.89 all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))).
% 11.99/11.89 all V_c V_b V_a T_a (class_Rings_Olinordered__comm__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 11.99/11.89 all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 11.99/11.89 all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))).
% 11.99/11.89 all V_b V_a T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))).
% 11.99/11.89 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 11.99/11.89 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)))).
% 11.99/11.89 all V_a V_b T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)))).
% 11.99/11.89 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)))).
% 11.99/11.89 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a))))).
% 11.99/11.89 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 11.99/11.89 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))).
% 11.99/11.89 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (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))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)))).
% 11.99/11.89 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)&c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2))).
% 11.99/11.89 all V_b_2 V_c_2 V_a_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)&c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2))).
% 11.99/11.89 all V_a T_a (class_Rings_Olinordered__ring(T_a)-> -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.89 all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))).
% 11.99/11.89 all T_a (class_Rings_Olinordered__semidom(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.89 all V_m_2 V_n_2 (c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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)).
% 11.99/11.89 all V_m V_n (-c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)))).
% 11.99/11.89 all V_n_2 (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.89 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 11.99/11.89 c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.89 all V_k (-c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.89 all V_x T_a (class_Rings_Ocomm__ring__1(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x)).
% 11.99/11.89 all V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_m,V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_m)).
% 11.99/11.89 all V_a V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m)).
% 11.99/11.89 all V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m)).
% 11.99/11.89 all V_ya_2 V_xa_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_ya_2=c_Groups_Ouminus__class_Ouminus(T_a,V_xa_2))).
% 11.99/11.89 all V_d V_c V_b V_a V_r T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_r!=c_Groups_Ozero__class_Ozero(T_a)-> (V_a=V_b&V_c!=V_d->c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c))!=c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d))))).
% 11.99/11.89 all V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 11.99/11.89 all V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ouminus__class_Ouminus(T_a,V_x))=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x))).
% 11.99/11.89 all V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))).
% 11.99/11.89 all V_n (c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)).
% 11.99/11.89 all V_n (c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 11.99/11.89 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)).
% 11.99/11.89 all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))).
% 11.99/11.89 all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))).
% 11.99/11.89 all V_n_2 V_k_2 V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)<->V_m_2=V_n_2).
% 11.99/11.89 all V_n_2 V_m_2 V_k_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)<->V_m_2=V_n_2).
% 11.99/11.89 all V_k V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))).
% 11.99/11.89 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))).
% 11.99/11.89 all V_k V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))).
% 11.99/11.89 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)).
% 11.99/11.89 all V_n V_m V_k (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))).
% 11.99/11.89 all V_z V_y V_x (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z))).
% 11.99/11.89 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)).
% 11.99/11.89 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)).
% 11.99/11.89 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).
% 11.99/11.89 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)).
% 11.99/11.89 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).
% 11.99/11.89 all V_n (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n).
% 11.99/11.89 all V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 11.99/11.89 all V_n_2 V_m_2 (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)).
% 11.99/11.89 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=V_m->V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))).
% 11.99/11.89 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))).
% 11.99/11.89 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))).
% 11.99/11.89 all V_j V_i (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i)).
% 11.99/11.89 all V_i V_j (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i)).
% 11.99/11.89 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 11.99/11.89 all V_m V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))).
% 11.99/11.89 all V_m V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))).
% 11.99/11.89 all V_z V_y V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 11.99/11.89 all V_y V_z V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 11.99/11.89 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))).
% 11.99/11.89 all V_l V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)))).
% 11.99/11.89 all V_n V_m V_l V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)-> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 11.99/11.89 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k)).
% 11.99/11.89 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).
% 11.99/11.89 all V_fa_2 V_m_2 V_n_2 T_a (hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_fa_2))=hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_fa_2)).
% 11.99/11.89 all V_n_2 V_m_2 (c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=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))).
% 11.99/11.89 all V_n_2 V_m_2 (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))).
% 11.99/11.89 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 11.99/11.89 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)<-> (exists B_k (V_n_2=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k))))).
% 11.99/11.89 all V_m V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))).
% 11.99/11.89 all V_m V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))).
% 11.99/11.89 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))).
% 11.99/11.89 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))).
% 11.99/11.89 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))).
% 11.99/11.89 all V_n_2 V_k_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 11.99/11.89 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 11.99/11.89 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 11.99/11.89 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 11.99/11.89 c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.89 all V_z V_n V_m (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n),V_z))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_z)).
% 11.99/11.89 all V_y V_x (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_y))).
% 11.99/11.89 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))).
% 11.99/11.89 all V_n V_m (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))).
% 11.99/11.89 all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))).
% 11.99/11.89 all V_y V_x (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y))).
% 11.99/11.89 c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 11.99/11.89 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 11.99/11.89 all V_fa_2 V_n_2 V_m_2 T_a (hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)),V_fa_2)=hAPP(c_Fun_Ocomp(T_a,T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_fa_2)),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_fa_2))).
% 11.99/11.89 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))).
% 11.99/11.89 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)))).
% 11.99/11.89 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))).
% 11.99/11.89 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))).
% 11.99/11.89 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))).
% 11.99/11.89 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)))).
% 11.99/11.89 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)).
% 11.99/11.89 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))).
% 11.99/11.89 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)).
% 11.99/11.89 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))).
% 11.99/11.89 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)).
% 11.99/11.89 all V_d V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))).
% 11.99/11.89 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b)).
% 11.99/11.89 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))).
% 11.99/11.89 all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d)).
% 11.99/11.89 all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d))).
% 11.99/11.89 all V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 all V_a_2 V_b_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_b_2=c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.89 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 11.99/11.89 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a).
% 11.99/11.89 all V_z_2 V_xa_2 V_ya_2 V_w_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_ya_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_z_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_ya_2))<->V_w_2=V_xa_2|V_ya_2=V_z_2)).
% 11.99/11.89 all V_b V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m)).
% 11.99/11.89 all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),V_ya)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya))).
% 11.99/11.89 all V_b V_a_H V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H)),V_b)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b))).
% 11.99/11.89 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 11.99/11.89 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<->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))!=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)))).
% 11.99/11.89 all V_y V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y))).
% 11.99/11.89 all V_z V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z))).
% 11.99/11.89 all V_b_H V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H))).
% 11.99/11.89 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).
% 11.99/11.89 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).
% 11.99/11.89 all V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x)),V_y)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))).
% 11.99/11.89 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)<->V_m_2=V_n_2)).
% 11.99/11.89 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))).
% 11.99/11.89 all V_k V_j V_u V_i (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k)).
% 11.99/11.89 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).
% 11.99/11.89 all V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (exists B_n (V_x=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(B_n)))))).
% 11.99/11.89 all V_k (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)-> (exists B_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B_n)&V_k=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)))).
% 11.99/11.89 all V_v V_u V_y V_a V_x T_a (class_Rings_Olinordered__semiring__1__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_a)-> (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))-> (c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)=c_Groups_Oone__class_Oone(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a))))))).
% 11.99/11.89 hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)).
% 11.99/11.89 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))).
% 11.99/11.89 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)).
% 11.99/11.89 all V_m V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))).
% 11.99/11.89 all V_n_2 V_m_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)))).
% 11.99/11.89 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)))).
% 11.99/11.89 all V_xa_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_xa_2)),hAPP(V_gb_2,V_xa_2))))).
% 11.99/11.89 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))))).
% 11.99/11.89 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))).
% 11.99/11.89 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))))).
% 11.99/11.89 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))).
% 11.99/11.89 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))))).
% 11.99/11.89 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))))).
% 11.99/11.89 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))))).
% 11.99/11.89 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))))).
% 11.99/11.89 all V_xa_2 V_ya_2 T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2),V_xa_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))<->V_xa_2=V_ya_2))).
% 11.99/11.89 all V_xa_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_xa_2)),hAPP(V_gb_2,V_xa_2))))).
% 11.99/11.89 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)))).
% 11.99/11.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Oorder(T_a)-> (V_xa_2=V_ya_2<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2),V_xa_2)))).
% 11.99/11.89 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))).
% 11.99/11.89 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)))))).
% 11.99/11.89 all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))).
% 11.99/11.89 all V_ya_2 V_xa_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_xa_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_ya_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_xa_2),V_ya_2))).
% 11.99/11.89 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))-> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 11.99/11.89 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))-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 11.99/11.89 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_z),V_y))->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 11.99/11.89 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_z))->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 11.99/11.89 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->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 11.99/11.89 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->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 11.99/11.89 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))->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y)).
% 11.99/11.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->V_xa_2=V_ya_2))).
% 11.99/11.89 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (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)))).
% 11.99/11.89 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))-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_y))).
% 11.99/11.89 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))->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 11.99/11.89 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))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 11.99/11.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))<->V_xa_2=V_ya_2))).
% 11.99/11.89 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))->c_Orderings_Oord__class_Oless(T_a,V_x,V_y))).
% 11.99/11.89 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-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)))).
% 11.99/11.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))<->c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2)).
% 11.99/11.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))& -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2),V_xa_2)))).
% 11.99/11.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))&V_xa_2!=V_ya_2)).
% 11.99/11.89 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))|c_Orderings_Oord__class_Oless(T_a,V_y,V_x)).
% 11.99/11.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))<->c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2))).
% 11.99/11.89 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2),V_xa_2)))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)),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)))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)),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)))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)))))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)),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)))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)),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)))).
% 11.99/11.89 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),c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))))).
% 11.99/11.89 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,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)),V_b_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)),V_a_2)))).
% 11.99/11.89 all V_a_2 V_b_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2)))).
% 11.99/11.89 all V_b V_a T_a (class_Groups_Oordered__ab__group__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)),c_Groups_Ouminus__class_Ouminus(T_a,V_a))))).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 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))).
% 11.99/11.89 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))).
% 11.99/11.89 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))).
% 11.99/11.89 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)))).
% 11.99/11.89 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))).
% 11.99/11.89 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)).
% 11.99/11.89 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))).
% 11.99/11.89 all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n)),V_n))).
% 11.99/11.89 all V_n V_m (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))).
% 11.99/11.89 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->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 11.99/11.89 all V_y V_x (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))).
% 11.99/11.89 all V_n V_m (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))).
% 11.99/11.89 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))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2).
% 11.99/11.89 all V_n_2 V_m_2 (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).
% 11.99/11.89 all V_m V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))).
% 11.99/11.89 all V_m V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))).
% 11.99/11.89 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=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)))).
% 11.99/11.89 all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2)),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))).
% 11.99/11.89 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)))).
% 11.99/11.89 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)))).
% 11.99/11.89 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))).
% 11.99/11.89 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))))).
% 11.99/11.89 all V_n V_k V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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))).
% 11.99/11.89 all V_n V_k V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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))).
% 11.99/11.89 all V_n V_k V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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)))).
% 11.99/11.89 all V_w_2 V_z_2 (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).
% 11.99/11.89 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))).
% 11.99/11.89 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)))).
% 11.99/11.89 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)))).
% 11.99/11.89 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)))).
% 11.99/11.89 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))))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j)))).
% 11.99/11.89 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)))).
% 11.99/11.89 all V_ya_2 V_xa_2 V_fa_2 T_a T_b (class_Orderings_Oorder(T_b)&class_Orderings_Olinorder(T_a)-> (c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_fa_2)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,V_xa_2)),hAPP(V_fa_2,V_ya_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))))).
% 11.99/11.89 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)))).
% 11.99/11.89 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))))).
% 11.99/11.89 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)))).
% 11.99/11.89 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)))))).
% 11.99/11.89 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)))))).
% 11.99/11.89 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)))))).
% 11.99/11.89 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)))))).
% 11.99/11.89 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)))))).
% 11.99/11.89 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)))))).
% 11.99/11.89 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)))))).
% 11.99/11.89 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)))))).
% 11.99/11.89 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)))))).
% 11.99/11.89 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)))))).
% 11.99/11.89 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)))))))).
% 11.99/11.89 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)))))))).
% 11.99/11.89 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))))).
% 11.99/11.89 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))))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 11.99/11.89 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),c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))).
% 11.99/11.89 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),c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)))))).
% 11.99/11.89 all V_ya_2 V_xa_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_xa_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_ya_2))-> (c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_xa_2=c_Groups_Ozero__class_Ozero(T_a)&V_ya_2=c_Groups_Ozero__class_Ozero(T_a))))).
% 11.99/11.89 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)),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))))).
% 11.99/11.89 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_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))))).
% 11.99/11.89 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)),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)))).
% 11.99/11.89 all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c),V_d))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 11.99/11.89 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))-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 11.99/11.89 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)))).
% 11.99/11.89 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)))).
% 11.99/11.89 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_Ouminus__class_Ouminus(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)))).
% 11.99/11.89 all V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)))).
% 11.99/11.89 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,V_a_2),c_Groups_Ouminus__class_Ouminus(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))))).
% 11.99/11.89 all V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))))).
% 11.99/11.89 all V_n 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)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))).
% 11.99/11.89 all V_m 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)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)))).
% 11.99/11.89 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (hBOOL(hAPP(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)))).
% 11.99/11.89 all V_m_2 V_n_2 (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))).
% 11.99/11.89 all V_n_2 V_m_2 (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))).
% 11.99/11.89 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))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 11.99/11.89 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))).
% 11.99/11.89 all V_n V_m (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))).
% 11.99/11.89 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))-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))<->V_n_2=V_m_2)).
% 11.99/11.89 all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)).
% 11.99/11.89 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))).
% 11.99/11.89 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))).
% 11.99/11.89 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_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y))))).
% 11.99/11.89 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))))).
% 11.99/11.89 all V_P_2 ((all B_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))->hBOOL(hAPP(V_P_2,B_x))))<-> (all B_x hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))))).
% 11.99/11.89 all V_P_2 ((exists B_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))&hBOOL(hAPP(V_P_2,B_x))))<-> (exists B_x hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))))).
% 11.99/11.89 all V_z hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))).
% 11.99/11.89 all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))).
% 11.99/11.89 all V_z V_z_H V_w V_w_H (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))->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)))).
% 11.99/11.89 all V_z_2 V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2))<-> (exists B_n (V_z_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n))))).
% 11.99/11.89 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_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))))).
% 11.99/11.89 all V_b_2 V_a_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (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))))).
% 11.99/11.89 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))).
% 11.99/11.89 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (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))->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))))))).
% 11.99/11.89 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (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))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))).
% 11.99/11.89 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))-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))).
% 11.99/11.89 all V_b V_c V_a T_a (class_Rings_Olinordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 11.99/11.89 all V_b V_c V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 11.99/11.89 all V_b V_a V_c T_a (class_Rings_Olinordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 11.99/11.89 all V_b V_a V_c T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 11.99/11.89 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)))-> (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))))).
% 11.99/11.89 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)))-> (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))))).
% 11.99/11.89 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)))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 11.99/11.89 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 11.99/11.89 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))-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 11.99/11.89 all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_c))->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 11.99/11.89 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))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 11.99/11.89 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 11.99/11.89 all V_ya_2 V_xa_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2))),c_Groups_Ozero__class_Ozero(T_a)))<->V_xa_2=c_Groups_Ozero__class_Ozero(T_a)&V_ya_2=c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.89 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)),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))))).
% 11.99/11.89 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)))))).
% 11.99/11.89 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)))))).
% 11.99/11.89 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))).
% 11.99/11.89 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)))<-> (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)))).
% 11.99/11.89 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)))<-> (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)))).
% 11.99/11.89 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.89 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))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)).
% 11.99/11.89 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2))).
% 11.99/11.89 all V_z_2 V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)).
% 11.99/11.89 all V_z V_w (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z))).
% 11.99/11.89 all V_m_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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)).
% 11.99/11.89 all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.89 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))-> (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,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)))))))).
% 11.99/11.89 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))->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z))).
% 11.99/11.89 all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(V_n)))))).
% 11.99/11.89 all V_q V_r V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)-> (V_a=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))-> (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)))))).
% 11.99/11.89 all V_q V_r V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)-> (V_a=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q))))).
% 11.99/11.89 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)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H))))).
% 11.99/11.89 all V_r_H V_q_H V_b_H (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H),V_q)))))).
% 11.99/11.89 all V_ya_2 V_xa_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,V_ya_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_ya_2),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_xa_2)))).
% 11.99/11.89 all V_ya_2 V_xa_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,V_ya_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_xa_2)),V_ya_2))).
% 11.99/11.89 all V_ya_2 V_xa_2 V_z_2 (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_xa_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_z_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2)))).
% 11.99/11.89 all V_ya_2 V_xa_2 V_z_2 (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_xa_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_ya_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2)))).
% 11.99/11.89 all V_x V_u hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),V_u))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)))).
% 11.99/11.89 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)).
% 11.99/11.89 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)))).
% 11.99/11.89 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))).
% 11.99/11.89 all V_w hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w),V_w)).
% 11.99/11.89 all V_ya_2 V_xa_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)|V_xa_2=V_ya_2).
% 11.99/11.89 all V_ya_2 V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2))&V_xa_2!=V_ya_2).
% 11.99/11.89 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)).
% 11.99/11.89 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)))).
% 11.99/11.89 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))).
% 11.99/11.89 all V_w hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w),V_w)).
% 11.99/11.89 all V_gb_2 V_fa_2 T_a T_b (class_Orderings_Oord(T_b)-> (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)))).
% 11.99/11.89 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)).
% 11.99/11.89 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)))).
% 11.99/11.89 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))).
% 11.99/11.89 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))).
% 11.99/11.89 all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_n)).
% 11.99/11.89 all V_y V_x V_z (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y)))).
% 11.99/11.89 all V_y V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)))).
% 11.99/11.89 all V_ya_2 V_xa_2 V_z_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_z_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2))).
% 11.99/11.89 all V_ya_2 V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,V_ya_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_ya_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_xa_2))).
% 11.99/11.89 all V_ya_2 V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,V_ya_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_xa_2),V_ya_2)).
% 11.99/11.89 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 11.99/11.89 all V_ya_2 V_xa_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,V_ya_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_ya_2=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_xa_2)).
% 11.99/11.89 all V_a_2 V_xa_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_xa_2=V_a_2).
% 11.99/11.89 all V_ya_2 V_xa_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_ya_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)&V_ya_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 all V_r_H V_q_H V_b_H V_r V_q V_b (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)-> (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)))))))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q),V_q_H)))))).
% 11.99/11.89 all V_r_H V_q_H V_b_H V_r V_q V_b (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)-> (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)))))))).
% 11.99/11.89 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=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n)))).
% 11.99/11.89 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))))))).
% 11.99/11.89 all V_y V_x T_a (class_Lattices_Oboolean__algebra(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y)),c_Groups_Ouminus__class_Ouminus(T_a,V_x))))).
% 11.99/11.89 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).
% 11.99/11.89 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)).
% 11.99/11.89 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))).
% 11.99/11.89 all V_w V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2)),V_w)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w))).
% 11.99/11.89 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).
% 11.99/11.89 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).
% 11.99/11.89 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)).
% 11.99/11.89 all V_x T_a (class_Lattices_Oboolean__algebra(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x))=V_x).
% 11.99/11.89 all V_xa_2 V_A_2 T_b T_a (class_Groups_Ouminus(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_xa_2)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_xa_2))).
% 11.99/11.89 all V_ya_2 V_xa_2 T_a (class_Lattices_Oboolean__algebra(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_xa_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_ya_2)<->V_xa_2=V_ya_2)).
% 11.99/11.89 all V_ya_2 V_xa_2 T_a (class_Lattices_Oboolean__algebra(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_xa_2)),c_Groups_Ouminus__class_Ouminus(T_a,V_ya_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2),V_xa_2)))).
% 11.99/11.89 all V_xa_2 (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_xa_2))<->V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 11.99/11.89 all V_n_2 V_P_2 (-hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))-> (hBOOL(hAPP(V_P_2,V_n_2))-> (exists B_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2)& (all B_i (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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))).
% 11.99/11.89 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))))))).
% 11.99/11.89 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(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 11.99/11.89 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(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 11.99/11.89 all V_z_H V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))->hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z))),hAPP(c_Int_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z_H)))).
% 11.99/11.89 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)))).
% 11.99/11.89 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))).
% 11.99/11.89 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.89 all V_n (hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))=V_n).
% 11.99/11.89 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)))).
% 11.99/11.89 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))).
% 11.99/11.89 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.89 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 11.99/11.89 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 11.99/11.89 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.89 c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.89 all V_z_H_2 V_z_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))-> (hAPP(c_Int_Onat,V_z_2)=hAPP(c_Int_Onat,V_z_H_2)<->V_z_2=V_z_H_2))).
% 11.99/11.89 all V_ya_2 V_xa_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_xa_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ya_2))-> (hAPP(c_Int_Onat,V_xa_2)=hAPP(c_Int_Onat,V_ya_2)<->V_xa_2=V_ya_2))).
% 11.99/11.89 all V_P_2 ((all B_x1 hBOOL(hAPP(V_P_2,B_x1)))<-> (all B_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))->hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))))).
% 11.99/11.89 all V_P_2 ((exists B_x1 hBOOL(hAPP(V_P_2,B_x1)))<-> (exists B_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))&hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))))).
% 11.99/11.89 c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 all V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))->hAPP(c_Int_Onat,V_z)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.89 all V_i_2 (hAPP(c_Int_Onat,V_i_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))).
% 11.99/11.89 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.89 all V_w_2 V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2),hAPP(c_Int_Onat,V_z_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2))).
% 11.99/11.89 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2),hAPP(c_Int_Onat,V_z_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)&c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)).
% 11.99/11.89 all V_ya_2 V_xa_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_xa_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ya_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Int_Onat,V_xa_2)),hAPP(c_Int_Onat,V_ya_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_xa_2),V_ya_2))))).
% 11.99/11.89 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))->hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z))=V_z)& (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))->hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z))=c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.89 all V_z_2 V_m_2 (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)=V_z_2<->V_m_2=hAPP(c_Int_Onat,V_z_2)&hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))).
% 11.99/11.89 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))->hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z))=V_z).
% 11.99/11.89 all V_z_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onat,V_z_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),V_z_2)).
% 11.99/11.89 all V_n (hAPP(c_Int_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.89 all V_xa_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_xa_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_xa_2))).
% 11.99/11.89 all V_xa_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))).
% 11.99/11.89 all V_z_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)).
% 11.99/11.89 all V_ya_2 V_xa_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_xa_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ya_2))-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_xa_2),hAPP(c_Int_Onat,V_ya_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,V_ya_2)))).
% 11.99/11.89 all V_z_2 V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2),hAPP(c_Int_Onat,V_z_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2))).
% 11.99/11.89 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_w_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2)))).
% 11.99/11.89 all V_m_2 V_w_2 (hAPP(c_Int_Onat,V_w_2)=V_m_2<-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))->V_w_2=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))& (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 11.99/11.89 all V_w_2 V_m_2 (V_m_2=hAPP(c_Int_Onat,V_w_2)<-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))->V_w_2=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))& (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 11.99/11.89 all V_i_2 V_P_2 (hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))<-> (all B_n (V_i_2=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)->hBOOL(hAPP(V_P_2,B_n))))& (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))->hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))).
% 11.99/11.89 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))->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y))=hAPP(c_Int_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)))).
% 11.99/11.89 all V_z_H 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__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))->hAPP(c_Int_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_z_H))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Int_Onat,V_z),hAPP(c_Int_Onat,V_z_H)))).
% 11.99/11.89 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))->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)))).
% 11.99/11.89 all V_z_H V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))->hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H))).
% 11.99/11.89 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)))))).
% 11.99/11.89 all V_z_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)).
% 11.99/11.89 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))->c_Nat_OSuc(hAPP(c_Int_Onat,V_z))=hAPP(c_Int_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z))).
% 11.99/11.89 all V_m_2 V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2),V_m_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))).
% 11.99/11.89 all V_n V_i (c_Int_Onat__aux(V_i,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Int_Onat,V_i),V_n)).
% 11.99/11.89 c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.89 all V_x V_n (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),V_x)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))->c_RComplete_Onatceiling(V_x)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 11.99/11.89 all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))).
% 11.99/11.89 all V_n (c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))=V_n).
% 11.99/11.89 all V_n (c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))=V_n).
% 11.99/11.89 c_RealDef_Oreal(tc_Nat_Onat)=c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal).
% 11.99/11.89 c_RealDef_Oreal(tc_Nat_Onat)=c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal).
% 11.99/11.89 all V_m_2 V_n_2 (hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2)=hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)<->V_n_2=V_m_2).
% 11.99/11.89 hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 11.99/11.89 all V_n_2 (hAPP(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)).
% 11.99/11.89 all V_n (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 11.99/11.89 all V_m_2 V_n_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)).
% 11.99/11.89 all V_m_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2)),hAPP(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))).
% 11.99/11.89 all V_n V_m (hAPP(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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))).
% 11.99/11.89 all V_n V_m (hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))).
% 11.99/11.89 hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 11.99/11.89 all V_x hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)))).
% 11.99/11.89 all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(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)).
% 11.99/11.89 all V_n c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(V_n))).
% 11.99/11.89 hAPP(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).
% 11.99/11.89 all V_n (hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(V_n))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 11.99/11.89 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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x))),V_x))).
% 11.99/11.89 all V_a V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(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)))).
% 11.99/11.89 all V_a V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),hAPP(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))).
% 11.99/11.89 all V_n_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 11.99/11.89 all V_m_2 V_n_2 (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,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)))).
% 11.99/11.89 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))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))).
% 11.99/11.89 all V_a_2 V_xa_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_xa_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2),c_RComplete_Onatfloor(V_xa_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)),V_xa_2)))).
% 11.99/11.89 all V_a_2 V_xa_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_xa_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2)),V_a_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2))))).
% 11.99/11.89 all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 11.99/11.89 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))-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n))).
% 11.99/11.89 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(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)).
% 11.99/11.89 all V_n V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))).
% 11.99/11.89 all V_x V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),V_x))-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))->c_RComplete_Onatfloor(V_x)=V_n)).
% 11.99/11.89 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(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)).
% 11.99/11.89 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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),B_n)),V_r))&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_n)))))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n)))).
% 11.99/11.89 all V_k T_a (class_Rings_Oring__1(T_a)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k,c_Groups_Ozero__class_Ozero(tc_Int_Oint))->c_Int_Oring__1__class_Oof__int(T_a,V_k)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k)))))& (-c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k,c_Groups_Ozero__class_Ozero(tc_Int_Oint))->c_Int_Oring__1__class_Oof__int(T_a,V_k)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_k)))).
% 11.99/11.89 all V_z_2 T_a (class_Int_Oring__char__0(T_a)-> (c_Int_Oring__1__class_Oof__int(T_a,V_z_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_z_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.89 all V_z_2 T_a (class_Int_Oring__char__0(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=c_Int_Oring__1__class_Oof__int(T_a,V_z_2)<->V_z_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.89 all T_a (class_Rings_Oring__1(T_a)->c_Int_Oring__1__class_Oof__int(T_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.89 all V_z_2 V_w_2 T_a (class_Rings_Olinordered__idom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_w_2)),c_Int_Oring__1__class_Oof__int(T_a,V_z_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2)))).
% 11.99/11.89 all V_z_2 V_w_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_w_2),c_Int_Oring__1__class_Oof__int(T_a,V_z_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2))).
% 11.99/11.89 all V_z V_w T_a (class_Rings_Oring__1(T_a)->c_Int_Oring__1__class_Oof__int(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z))=c_Groups_Oplus__class_Oplus(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_w),c_Int_Oring__1__class_Oof__int(T_a,V_z))).
% 11.99/11.89 all V_z V_w T_a (class_Rings_Oring__1(T_a)->c_Int_Oring__1__class_Oof__int(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Oring__1__class_Oof__int(T_a,V_w)),c_Int_Oring__1__class_Oof__int(T_a,V_z))).
% 11.99/11.89 all T_a (class_Rings_Oring__1(T_a)->c_Int_Oring__1__class_Oof__int(T_a,c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Oone__class_Oone(T_a)).
% 11.99/11.89 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))).
% 11.99/11.89 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))).
% 11.99/11.89 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))).
% 11.99/11.89 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)).
% 11.99/11.89 all V_z T_a (class_Rings_Oring__1(T_a)->c_Int_Oring__1__class_Oof__int(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z))=c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_z))).
% 11.99/11.89 all V_q V_p V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q))).
% 11.99/11.89 all V_n T_a (class_Rings_Oring__1(T_a)->c_Int_Oring__1__class_Oof__int(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)).
% 11.99/11.89 all V_z_2 V_w_2 T_a (class_Int_Oring__char__0(T_a)-> (c_Int_Oring__1__class_Oof__int(T_a,V_w_2)=c_Int_Oring__1__class_Oof__int(T_a,V_z_2)<->V_w_2=V_z_2)).
% 11.99/11.89 all V_n V_z T_a (class_Rings_Oring__1(T_a)->c_Int_Oring__1__class_Oof__int(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Int_Oring__1__class_Oof__int(T_a,V_z)),V_n)).
% 11.99/11.89 all V_n (c_Int_Oring__1__class_Oof__int(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)).
% 11.99/11.89 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))).
% 11.99/11.89 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).
% 11.99/11.89 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))).
% 11.99/11.89 all V_ya_2 V_xa_2 T_a (class_Rings_Oidom(T_a)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ya_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))<->V_xa_2=V_ya_2|V_xa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_ya_2))).
% 11.99/11.89 all V_z_2 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)),c_Int_Oring__1__class_Oof__int(T_a,V_z_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)))).
% 11.99/11.89 all V_z_2 T_a (class_Rings_Olinordered__idom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_z_2)),c_Groups_Ozero__class_Ozero(T_a)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))).
% 11.99/11.89 all V_z_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_z_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))).
% 11.99/11.89 all V_z_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Oring__1__class_Oof__int(T_a,V_z_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2))).
% 11.99/11.89 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))))).
% 11.99/11.89 all V_z T_a (class_Rings_Oring__1(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))->hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_z))=c_Int_Oring__1__class_Oof__int(T_a,V_z))).
% 11.99/11.89 all V_n V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))))).
% 11.99/11.89 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 11.99/11.89 all V_ya_2 V_xa_2 V_b_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_xa_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_ya_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_xa_2),V_ya_2))))).
% 11.99/11.89 all V_n V_m (hAPP(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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),V_n)).
% 11.99/11.89 all V_n V_m (hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),V_n)=hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))).
% 11.99/11.89 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))).
% 11.99/11.89 all V_m_2 V_xa_2 (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_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_xa_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 11.99/11.89 all V_n V_m (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n)).
% 11.99/11.89 all V_n V_m (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))).
% 11.99/11.89 all V_n V_x (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n))).
% 11.99/11.89 all V_n V_m V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 11.99/11.89 all V_n_2 V_xa_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xa_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.89 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))).
% 11.99/11.89 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))->hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),V_n)=hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))).
% 11.99/11.89 all V_n V_z (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))->hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),V_n)).
% 11.99/11.89 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)))).
% 11.99/11.89 all V_n_2 V_xa_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_2),V_n_2))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xa_2)).
% 11.99/11.89 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)))).
% 11.99/11.89 all V_z V_y V_x (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z))).
% 11.99/11.89 all V_n V_x (V_x=hAPP(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)).
% 11.99/11.89 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))).
% 11.99/11.89 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))).
% 11.99/11.89 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))).
% 11.99/11.89 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)).
% 11.99/11.89 all V_n V_m T_a (class_Rings_Osemiring__1(T_a)->hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n)).
% 11.99/11.89 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)).
% 11.99/11.89 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).
% 11.99/11.89 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))))).
% 11.99/11.89 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)))))).
% 11.99/11.89 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))).
% 11.99/11.89 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))))).
% 11.99/11.89 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))).
% 11.99/11.89 all V_n_2 V_m_2 V_a_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)<->V_m_2=V_n_2))).
% 11.99/11.89 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)).
% 11.99/11.89 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))).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 all V_n V_m V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 11.99/11.89 all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 11.99/11.89 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))))).
% 11.99/11.89 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)))).
% 11.99/11.89 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 11.99/11.89 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 11.99/11.89 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))).
% 11.99/11.89 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))))).
% 11.99/11.89 all V_n V_a T_a (class_Rings_Oring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 11.99/11.89 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))))).
% 11.99/11.89 all V_n V_m V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))).
% 11.99/11.89 all V_ya_2 V_xa_2 V_b_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_xa_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_ya_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2)))).
% 11.99/11.89 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)))))).
% 11.99/11.89 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 11.99/11.89 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a))))).
% 11.99/11.89 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))).
% 11.99/11.89 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))-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->V_a=V_b))))).
% 11.99/11.89 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))))))).
% 11.99/11.89 all V_n V_m V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (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))))).
% 11.99/11.89 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))).
% 11.99/11.89 all V_a V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)-> (exists B_r (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r)&hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n)=V_a)))).
% 11.99/11.89 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).
% 11.99/11.89 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))).
% 11.99/11.89 all V_a V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)-> (exists B_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_x)&hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n)=V_a& (all B_y (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y)&hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n)=V_a->B_y=B_x)))))).
% 11.99/11.89 all V_x V_y (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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),B_n)),V_y)),V_x))&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(B_n))),V_y)))))).
% 11.99/11.89 all V_n V_x (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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),c_Transcendental_Oln(V_x))).
% 11.99/11.89 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (all B_y exists B_n c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),B_n)),V_x)))).
% 11.99/11.89 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),V_x)).
% 11.99/11.89 all V_ya_2 V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)-> (c_Transcendental_Oln(V_xa_2)=c_Transcendental_Oln(V_ya_2)<->V_xa_2=V_ya_2))).
% 11.99/11.89 all V_ya_2 V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_xa_2),c_Transcendental_Oln(V_ya_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)))).
% 11.99/11.89 c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 11.99/11.89 all V_ya_2 V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(V_xa_2)),c_Transcendental_Oln(V_ya_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2))))).
% 11.99/11.89 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)))).
% 11.99/11.89 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x))).
% 11.99/11.89 all V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_xa_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_xa_2))).
% 11.99/11.89 all V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)-> (c_Transcendental_Oln(V_xa_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_xa_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 11.99/11.89 all V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))).
% 11.99/11.89 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))).
% 11.99/11.89 all V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x))-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x))).
% 11.99/11.89 all V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_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_xa_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_xa_2)))).
% 11.99/11.89 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)))-> (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)))).
% 11.99/11.89 all V_y V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)->c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y)))).
% 11.99/11.89 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(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x))),V_x))).
% 11.99/11.89 all V_n V_a (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)-> (exists B_r (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r)&hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),c_Nat_OSuc(V_n))=V_a))).
% 11.99/11.89 all V_x V_n T_a (class_Groups_Omonoid__mult(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))).
% 11.99/11.89 all V_m V_n T_a (class_Rings_Oring__1(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))).
% 11.99/11.89 all V_m_2 V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 11.99/11.89 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m))).
% 11.99/11.89 all V_n V_m c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)).
% 11.99/11.89 all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.89 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))).
% 11.99/11.89 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)).
% 11.99/11.89 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))).
% 11.99/11.89 all V_k_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2)).
% 11.99/11.89 all V_n V_m (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m).
% 11.99/11.89 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_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))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)))).
% 11.99/11.89 all V_c V_b V_a (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))->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)))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)).
% 11.99/11.89 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_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))).
% 11.99/11.89 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=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2))).
% 11.99/11.89 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)=V_m).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)),V_j_2)))).
% 11.99/11.89 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_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)).
% 11.99/11.89 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k)))).
% 11.99/11.89 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j)).
% 11.99/11.89 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).
% 11.99/11.89 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)).
% 11.99/11.89 all V_n V_k V_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k)).
% 11.99/11.89 all V_l V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)))).
% 11.99/11.89 all V_n V_k V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 11.99/11.89 all V_n V_m V_k (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 11.99/11.89 all V_k V_j V_i (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))).
% 11.99/11.89 all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n)=V_m).
% 11.99/11.89 all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n)=V_m).
% 11.99/11.89 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))).
% 11.99/11.89 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))).
% 11.99/11.89 all V_xa_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_xa_2)=c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_xa_2),hAPP(V_B_2,V_xa_2))).
% 11.99/11.89 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=V_a).
% 11.99/11.89 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b)=V_a).
% 11.99/11.89 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))).
% 11.99/11.89 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))).
% 11.99/11.89 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))).
% 11.99/11.89 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))).
% 11.99/11.89 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)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2)))).
% 11.99/11.89 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))).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 11.99/11.89 all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.89 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)).
% 11.99/11.89 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)).
% 11.99/11.89 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))).
% 11.99/11.89 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)).
% 11.99/11.89 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).
% 11.99/11.89 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))))).
% 11.99/11.89 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)).
% 11.99/11.89 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)))).
% 11.99/11.89 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)))).
% 11.99/11.89 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).
% 11.99/11.89 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))).
% 11.99/11.89 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))).
% 11.99/11.89 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))))).
% 11.99/11.89 all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)).
% 11.99/11.89 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 11.99/11.89 all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 11.99/11.89 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 11.99/11.89 all V_y V_x T_a (class_Rings_Ocomm__ring__1(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)=c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y))).
% 11.99/11.89 all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a)).
% 11.99/11.89 all V_d_2 V_b_2 V_c_2 V_e_2 V_a_2 T_a (class_Rings_Oring(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)<->c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_c_2)=V_d_2)).
% 11.99/11.89 all V_d_2 V_b_2 V_c_2 V_e_2 V_a_2 T_a (class_Rings_Oring(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)<->V_c_2=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2))).
% 11.99/11.89 all V_b V_a V_y V_x T_a (class_Rings_Oring(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b))).
% 11.99/11.89 all V_b V_a V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)))).
% 11.99/11.89 all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))).
% 11.99/11.89 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))))).
% 11.99/11.89 all V_z V_w T_a (class_Rings_Oring__1(T_a)->c_Int_Oring__1__class_Oof__int(T_a,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_w,V_z))=c_Groups_Ominus__class_Ominus(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_w),c_Int_Oring__1__class_Oof__int(T_a,V_z))).
% 11.99/11.89 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,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)),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),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))))).
% 11.99/11.89 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,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)),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,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)))).
% 11.99/11.89 all V_d_2 V_b_2 V_c_2 V_e_2 V_a_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))<->c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2)))).
% 11.99/11.89 all V_d_2 V_b_2 V_c_2 V_e_2 V_a_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_c_2),V_d_2))).
% 11.99/11.89 all V_x T_a (class_Rings_Oring__1(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)))).
% 11.99/11.89 all V_i V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n)).
% 11.99/11.89 all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n).
% 11.99/11.89 all V_b_2 V_a_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))<-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)->hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))& (all B_d (V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)->hBOOL(hAPP(V_P_2,B_d))))).
% 11.99/11.89 all V_b_2 V_a_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))<-> -(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)& -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| (exists B_d (V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)& -hBOOL(hAPP(V_P_2,B_d)))))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j))).
% 11.99/11.89 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m))).
% 11.99/11.89 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,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)),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,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)))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u),V_m),V_n)).
% 11.99/11.89 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))-> (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)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)<->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2)=V_n_2)).
% 11.99/11.89 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,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)),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),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))))).
% 11.99/11.89 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u),V_n))).
% 11.99/11.89 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))-> (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)=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=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))).
% 11.99/11.89 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))).
% 11.99/11.89 all V_n (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)))).
% 11.99/11.89 all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=V_n).
% 11.99/11.89 all V_n V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=V_n)& (V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Nat_OSuc(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)))).
% 11.99/11.89 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))-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)))).
% 11.99/11.89 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))-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_n_2))).
% 11.99/11.89 all V_n V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)))).
% 11.99/11.89 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)))))).
% 11.99/11.89 all V_y V_x T_a (class_Rings_Ocomm__ring__1(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))).
% 11.99/11.89 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)))))).
% 11.99/11.89 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))->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y))=hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(V_x,V_y)))).
% 11.99/11.89 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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_r))&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,hAPP(c_RealDef_Oreal(tc_Nat_Onat),B_n))))).
% 11.99/11.89 all V_ya_2 V_xa_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_xa_2,V_ya_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))).
% 11.99/11.89 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.90 all V_w V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w)).
% 11.99/11.90 all V_w V_z (c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))).
% 11.99/11.90 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))).
% 11.99/11.90 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))).
% 11.99/11.90 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))).
% 11.99/11.90 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)).
% 11.99/11.90 all V_s V_r (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_s))).
% 11.99/11.90 all V_y V_x (c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y))).
% 11.99/11.90 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))))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)).
% 11.99/11.90 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_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))).
% 11.99/11.90 all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))->hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))).
% 11.99/11.90 all V_z V_z_H (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_H),V_z))->hAPP(c_Int_Onat,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_z_H))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Int_Onat,V_z),hAPP(c_Int_Onat,V_z_H)))).
% 11.99/11.90 all V_x V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a)),V_x))->c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)).
% 11.99/11.90 all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x))).
% 11.99/11.90 all V_x V_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a)),V_x))->c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)).
% 11.99/11.90 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))))).
% 11.99/11.90 all V_y V_x (c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_x,V_y))).
% 11.99/11.90 all V_ya_2 V_xa_2 V_P_2 (hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_xa_2,V_ya_2))))<-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ya_2),V_xa_2))->hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_xa_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_ya_2)))))& (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2)->hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))).
% 11.99/11.90 all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))).
% 11.99/11.90 all V_k V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))).
% 11.99/11.90 all V_d V_b V_c V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d))).
% 11.99/11.90 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,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b)=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))).
% 11.99/11.90 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,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b)=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)))).
% 11.99/11.90 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,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=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)))).
% 11.99/11.90 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,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b)=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)))).
% 11.99/11.90 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))).
% 11.99/11.90 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)).
% 11.99/11.90 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)).
% 11.99/11.90 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))).
% 11.99/11.90 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))).
% 11.99/11.90 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))).
% 11.99/11.90 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))))).
% 11.99/11.90 all V_b V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))).
% 11.99/11.90 all V_a_2 V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2))).
% 11.99/11.90 all V_a_2 V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))).
% 11.99/11.90 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)).
% 11.99/11.90 all V_b V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b)).
% 11.99/11.90 all V_b V_a (c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)).
% 11.99/11.90 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)).
% 11.99/11.90 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)).
% 11.99/11.90 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)).
% 11.99/11.90 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).
% 11.99/11.90 all V_b V_a V_c (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)->c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c)).
% 11.99/11.90 all V_k V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x))).
% 11.99/11.90 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))&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)))&c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2)).
% 11.99/11.90 all V_a_2 V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)-> (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)))).
% 11.99/11.90 all V_i_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)-> (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)))).
% 11.99/11.90 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))-> (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))&c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2))).
% 11.99/11.90 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))-> (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)))))).
% 11.99/11.90 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))-> (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))))).
% 11.99/11.90 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))-> (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))).
% 11.99/11.90 all V_a_2 V_b_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (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))))).
% 11.99/11.90 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)))-> (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))))).
% 11.99/11.90 all V_b V_b_H V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_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)))))).
% 11.99/11.90 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)))-> (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))).
% 11.99/11.90 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))-> (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))))).
% 11.99/11.90 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))-> (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))))).
% 11.99/11.90 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))))& (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))&c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)&V_n_2=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)))))& (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 (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=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)))))).
% 11.99/11.90 all V_r_1 V_y V_b_1 V_a_1 (V_a_1=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)-> ((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))&c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1,V_b_1))& (-c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)->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))).
% 11.99/11.90 all V_k V_l ((hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))->c_SMT_Oz3div(V_k,V_l)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,V_l))& (-hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))->c_SMT_Oz3div(V_k,V_l)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_l))))).
% 11.99/11.90 all V_k_2 V_P_2 V_d_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)-> ((all B_x (hBOOL(hAPP(V_P_2,B_x))->hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,V_d_2)))))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))-> (all B_x (hBOOL(hAPP(V_P_2,B_x))->hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2))))))))).
% 11.99/11.90 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).
% 11.99/11.90 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.90 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))).
% 11.99/11.90 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)).
% 11.99/11.90 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)))).
% 11.99/11.90 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)).
% 11.99/11.90 all V_b V_a (hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b))).
% 11.99/11.90 all V_y V_x (c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_x,V_y))).
% 11.99/11.90 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m))).
% 11.99/11.90 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n)=V_m).
% 11.99/11.90 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n)=V_m).
% 11.99/11.90 all V_n V_m V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)).
% 11.99/11.90 all V_k V_n V_m (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))))).
% 11.99/11.90 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (-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)))).
% 11.99/11.90 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)-> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,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)))).
% 11.99/11.90 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 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2)-> (V_n_2=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))))))).
% 11.99/11.90 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))->hAPP(c_Int_Onat,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y))).
% 11.99/11.90 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))->c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y))=hAPP(c_Int_Onat,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y)))).
% 11.99/11.90 all V_m_2 V_q_2 V_n_2 (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))&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))).
% 11.99/11.90 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))&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))))).
% 11.99/11.90 all T_2 T_1 (class_Lattices_Oboolean__algebra(T_1)->class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))).
% 11.99/11.90 all T_2 T_1 (class_Orderings_Opreorder(T_1)->class_Orderings_Opreorder(tc_fun(T_2,T_1))).
% 11.99/11.90 all T_2 T_1 (class_Orderings_Oorder(T_1)->class_Orderings_Oorder(tc_fun(T_2,T_1))).
% 11.99/11.90 all T_2 T_1 (class_Orderings_Oord(T_1)->class_Orderings_Oord(tc_fun(T_2,T_1))).
% 11.99/11.90 all T_2 T_1 (class_Groups_Ouminus(T_1)->class_Groups_Ouminus(tc_fun(T_2,T_1))).
% 11.99/11.90 all T_2 T_1 (class_Groups_Ominus(T_1)->class_Groups_Ominus(tc_fun(T_2,T_1))).
% 11.99/11.90 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 11.99/11.90 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 11.99/11.90 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 11.99/11.90 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 11.99/11.90 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint).
% 11.99/11.90 class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 11.99/11.90 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint).
% 11.99/11.90 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 11.99/11.90 class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 11.99/11.90 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 11.99/11.90 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 11.99/11.90 class_Rings_Oordered__cancel__semiring(tc_Int_Oint).
% 11.99/11.90 class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 11.99/11.90 class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 11.99/11.90 class_Rings_Oordered__comm__semiring(tc_Int_Oint).
% 11.99/11.90 class_Rings_Olinordered__semiring__1(tc_Int_Oint).
% 11.99/11.90 class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 11.99/11.90 class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 11.99/11.90 class_Rings_Olinordered__semiring(tc_Int_Oint).
% 11.99/11.90 class_Rings_Olinordered__semidom(tc_Int_Oint).
% 11.99/11.90 class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 11.99/11.90 class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 11.99/11.90 class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 11.99/11.90 class_Rings_Oordered__semiring(tc_Int_Oint).
% 11.99/11.90 class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 11.99/11.90 class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 11.99/11.90 class_Rings_Olinordered__ring(tc_Int_Oint).
% 11.99/11.90 class_Rings_Olinordered__idom(tc_Int_Oint).
% 11.99/11.90 class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 11.99/11.90 class_Divides_Osemiring__div(tc_Int_Oint).
% 11.99/11.90 class_Rings_Ocomm__semiring(tc_Int_Oint).
% 11.99/11.90 class_Nat_Osemiring__char__0(tc_Int_Oint).
% 11.99/11.90 class_Groups_Oab__group__add(tc_Int_Oint).
% 11.99/11.90 class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 11.99/11.90 class_Rings_Oordered__ring(tc_Int_Oint).
% 11.99/11.90 class_Orderings_Opreorder(tc_Int_Oint).
% 11.99/11.90 class_Orderings_Olinorder(tc_Int_Oint).
% 11.99/11.90 class_Groups_Omonoid__mult(tc_Int_Oint).
% 11.99/11.90 class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 11.99/11.90 class_Groups_Omonoid__add(tc_Int_Oint).
% 11.99/11.90 class_Rings_Osemiring__1(tc_Int_Oint).
% 11.99/11.90 class_Rings_Osemiring__0(tc_Int_Oint).
% 11.99/11.90 class_Groups_Ogroup__add(tc_Int_Oint).
% 11.99/11.90 class_Rings_Omult__zero(tc_Int_Oint).
% 11.99/11.90 class_Orderings_Oorder(tc_Int_Oint).
% 11.99/11.90 class_Int_Oring__char__0(tc_Int_Oint).
% 11.99/11.90 class_Rings_Osemiring(tc_Int_Oint).
% 11.99/11.90 class_Orderings_Oord(tc_Int_Oint).
% 11.99/11.90 class_Groups_Ouminus(tc_Int_Oint).
% 11.99/11.90 class_Rings_Oring__1(tc_Int_Oint).
% 11.99/11.91 class_Groups_Ominus(tc_Int_Oint).
% 11.99/11.91 class_Power_Opower(tc_Int_Oint).
% 11.99/11.91 class_Groups_Ozero(tc_Int_Oint).
% 11.99/11.91 class_Rings_Oring(tc_Int_Oint).
% 11.99/11.91 class_Rings_Oidom(tc_Int_Oint).
% 11.99/11.91 class_Groups_Oone(tc_Int_Oint).
% 11.99/11.91 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 11.99/11.91 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 11.99/11.91 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 11.99/11.91 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 11.99/11.91 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 11.99/11.91 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 11.99/11.91 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 11.99/11.91 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 11.99/11.91 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 11.99/11.91 class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 11.99/11.91 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 11.99/11.91 class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 11.99/11.91 class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 11.99/11.91 class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 11.99/11.91 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 11.99/11.91 class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 11.99/11.91 class_Rings_Oordered__semiring(tc_Nat_Onat).
% 11.99/11.91 class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 11.99/11.91 class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 11.99/11.91 class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 11.99/11.91 class_Divides_Osemiring__div(tc_Nat_Onat).
% 11.99/11.91 class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 11.99/11.91 class_Nat_Osemiring__char__0(tc_Nat_Onat).
% 11.99/11.91 class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 11.99/11.91 class_Orderings_Opreorder(tc_Nat_Onat).
% 11.99/11.91 class_Orderings_Olinorder(tc_Nat_Onat).
% 11.99/11.91 class_Groups_Omonoid__mult(tc_Nat_Onat).
% 11.99/11.91 class_Groups_Omonoid__add(tc_Nat_Onat).
% 11.99/11.91 class_Rings_Osemiring__1(tc_Nat_Onat).
% 11.99/11.91 class_Rings_Osemiring__0(tc_Nat_Onat).
% 11.99/11.91 class_Rings_Omult__zero(tc_Nat_Onat).
% 11.99/11.91 class_Orderings_Oorder(tc_Nat_Onat).
% 11.99/11.91 class_Rings_Osemiring(tc_Nat_Onat).
% 11.99/11.91 class_Orderings_Oord(tc_Nat_Onat).
% 11.99/11.91 class_Groups_Ominus(tc_Nat_Onat).
% 11.99/11.91 class_Power_Opower(tc_Nat_Onat).
% 11.99/11.91 class_Groups_Ozero(tc_Nat_Onat).
% 11.99/11.91 class_Groups_Oone(tc_Nat_Onat).
% 11.99/11.91 class_Lattices_Oboolean__algebra(tc_HOL_Obool).
% 11.99/11.91 class_Orderings_Opreorder(tc_HOL_Obool).
% 11.99/11.91 class_Orderings_Oorder(tc_HOL_Obool).
% 11.99/11.91 class_Orderings_Oord(tc_HOL_Obool).
% 11.99/11.91 class_Groups_Ouminus(tc_HOL_Obool).
% 11.99/11.91 class_Groups_Ominus(tc_HOL_Obool).
% 11.99/11.91 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal).
% 11.99/11.91 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Olinordered__semiring(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Olinordered__semidom(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal).
% 11.99/11.91 class_RealVector_Ometric__space(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Oordered__semiring(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Olinordered__ring(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Olinordered__idom(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Ocomm__semiring(tc_RealDef_Oreal).
% 11.99/11.91 class_Nat_Osemiring__char__0(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Oab__group__add(tc_RealDef_Oreal).
% 11.99/11.91 class_SEQ_Ocomplete__space(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Oordered__ring(tc_RealDef_Oreal).
% 11.99/11.91 class_Orderings_Opreorder(tc_RealDef_Oreal).
% 11.99/11.91 class_Orderings_Olinorder(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Omonoid__mult(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Omonoid__add(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Osemiring__1(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Osemiring__0(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Ogroup__add(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Omult__zero(tc_RealDef_Oreal).
% 11.99/11.91 class_Orderings_Oorder(tc_RealDef_Oreal).
% 11.99/11.91 class_Int_Oring__char__0(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Osemiring(tc_RealDef_Oreal).
% 11.99/11.91 class_Orderings_Oord(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Ouminus(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Oring__1(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Ominus(tc_RealDef_Oreal).
% 11.99/11.91 class_Power_Opower(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Ozero(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Oring(tc_RealDef_Oreal).
% 11.99/11.91 class_Rings_Oidom(tc_RealDef_Oreal).
% 11.99/11.91 class_Groups_Oone(tc_RealDef_Oreal).
% 11.99/11.91 -(all B_m B_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),B_m),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),B_n)))).
% 11.99/11.91 end_of_list.
% 11.99/11.91
% 11.99/11.91 -------> usable clausifies to:
% 11.99/11.91
% 11.99/11.91 list(usable).
% 11.99/11.91 0 [] A=A.
% 11.99/11.91 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.
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,B_m),hAPP(v_f____,B_n)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,B_m),hAPP(v_ga____,B_n)).
% 11.99/11.91 0 [] c_SEQ_Osubse_q(v_f____).
% 11.99/11.91 0 [] c_SEQ_Osubse_q(v_ga____).
% 11.99/11.91 0 [] hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_fa_2),hAPP(c_Fun_Ocomp(T_d,T_c,T_a,V_gb_2),V_h_2))=hAPP(c_Fun_Ocomp(T_d,T_b,T_a,hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_fa_2),V_gb_2)),V_h_2).
% 11.99/11.91 0 [] hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2),V_gb_2),V_xa_2)=hAPP(V_fa_2,hAPP(V_gb_2,V_xa_2)).
% 11.99/11.91 0 [] hAPP(V_fa_2,hAPP(V_gb_2,V_xa_2))!=hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2))|hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2),V_gb_2),V_xa_2)=hAPP(hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2),V_g_H_2),V_x_H_2).
% 11.99/11.91 0 [] hAPP(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).
% 11.99/11.91 0 [] hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2)!=hAPP(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)).
% 11.99/11.91 0 [] hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2)!=hAPP(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)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 11.99/11.91 0 [] V_m_2=V_n_2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 11.99/11.91 0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 11.99/11.91 0 [] V_x=V_y|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)|V_m!=V_n.
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)|V_s!=V_t.
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)|hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)).
% 11.99/11.91 0 [] -c_SEQ_Osubse_q(V_fa_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m),hAPP(V_fa_2,B_n)).
% 11.99/11.91 0 [] c_SEQ_Osubse_q(V_fa_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f3(V_fa_2),$f2(V_fa_2)).
% 11.99/11.91 0 [] c_SEQ_Osubse_q(V_fa_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,$f3(V_fa_2)),hAPP(V_fa_2,$f2(V_fa_2))).
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 11.99/11.91 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 11.99/11.91 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_c,V_a).
% 11.99/11.91 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_a,V_c).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_c,V_b)|c_Orderings_Oord__class_Oless(T_a,V_c,V_a).
% 11.99/11.91 0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_c).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 11.99/11.91 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_y!=V_x.
% 11.99/11.91 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_x).
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)|V_xa_2=V_ya_2|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2).
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)|V_xa_2!=V_ya_2| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2).
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)|V_xa_2!=V_ya_2| -c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2).
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)|V_xa_2=V_ya_2.
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2).
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2.
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2.
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2.
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 11.99/11.91 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 11.99/11.91 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 11.99/11.91 0 [] -class_RealVector_Ometric__space(T_a)| -c_SEQ_OCauchy(T_a,V_X_2)| -c_SEQ_Osubse_q(V_fa_2)|c_SEQ_OCauchy(T_a,hAPP(c_Fun_Ocomp(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2),V_fa_2)).
% 11.99/11.91 0 [] -class_SEQ_Ocomplete__space(T_a)| -c_SEQ_Oconvergent(T_a,V_X_2)| -c_SEQ_Osubse_q(V_fa_2)|c_SEQ_Oconvergent(T_a,hAPP(c_Fun_Ocomp(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2),V_fa_2)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__idom(T_a)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 11.99/11.91 0 [] -c_SEQ_Osubse_q(V_fa_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n),hAPP(V_fa_2,c_Nat_OSuc(B_n))).
% 11.99/11.91 0 [] c_SEQ_Osubse_q(V_fa_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,$f4(V_fa_2)),hAPP(V_fa_2,c_Nat_OSuc($f4(V_fa_2)))).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_fa_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(V_fa_2,V_xa_2),hAPP(V_fa_2,V_ya_2))|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_fa_2)|c_Orderings_Oord__class_Oless(T_b,hAPP(V_fa_2,V_xa_2),hAPP(V_fa_2,V_ya_2))| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Oorder(T_a)| -c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_fa_2)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(T_b,hAPP(V_fa_2,V_xa_2),hAPP(V_fa_2,V_ya_2)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 11.99/11.91 0 [] -c_Record_Oiso__tuple__update__accessor__cong__assist(T_a,T_b,V_upd_2,V_ac_2)|hAPP(V_fa_2,hAPP(V_ac_2,V_xa_2))!=hAPP(V_ac_2,V_xa_2)|hAPP(hAPP(V_upd_2,hAPP(c_Fun_Ocomp(T_a,T_a,T_a,V_gb_2),V_fa_2)),V_xa_2)=hAPP(hAPP(V_upd_2,V_gb_2),V_xa_2).
% 11.99/11.91 0 [] hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_fa_2),c_Fun_Oswap(T_a,T_c,V_a_2,V_b_2,V_gb_2))=c_Fun_Oswap(T_a,T_b,V_a_2,V_b_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_fa_2),V_gb_2)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)).
% 11.99/11.91 0 [] -class_RealVector_Ometric__space(T_a)| -c_SEQ_Oconvergent(T_a,V_X_2)|c_SEQ_OCauchy(T_a,V_X_2).
% 11.99/11.91 0 [] -class_SEQ_Ocomplete__space(T_a)| -c_SEQ_OCauchy(T_a,V_X_2)|c_SEQ_Oconvergent(T_a,V_X_2).
% 11.99/11.91 0 [] -class_SEQ_Ocomplete__space(T_a)| -c_SEQ_OCauchy(T_a,V_X_2)|c_SEQ_Oconvergent(T_a,V_X_2).
% 11.99/11.91 0 [] -class_SEQ_Ocomplete__space(T_a)|c_SEQ_OCauchy(T_a,V_X_2)| -c_SEQ_Oconvergent(T_a,V_X_2).
% 11.99/11.91 0 [] c_Nat_OSuc(V_x)!=c_Nat_OSuc(V_y)|V_x=V_y.
% 11.99/11.91 0 [] -c_Record_Oiso__tuple__update__accessor__cong__assist(T_a,T_b,V_upd_2,V_ac_2)|hAPP(V_fa_2,hAPP(V_ac_2,V_xa_2))!=hAPP(V_ac_2,V_xa_2)|hAPP(hAPP(V_upd_2,V_fa_2),V_xa_2)=V_xa_2.
% 11.99/11.91 0 [] V_a_2=V_c_2|V_b_2=V_c_2|c_Fun_Oswap(T_a,T_b,V_a_2,V_b_2,c_Fun_Oswap(T_a,T_b,V_b_2,V_c_2,c_Fun_Oswap(T_a,T_b,V_a_2,V_b_2,V_fa_2)))=c_Fun_Oswap(T_a,T_b,V_a_2,V_c_2,V_fa_2).
% 11.99/11.91 0 [] c_Fun_Oswap(T_a,T_b,V_a_2,V_b_2,c_Fun_Oswap(T_a,T_b,V_a_2,V_b_2,V_fa_2))=V_fa_2.
% 11.99/11.91 0 [] c_Fun_Oswap(T_a,T_b,V_a_2,V_b_2,V_fa_2)=c_Fun_Oswap(T_a,T_b,V_b_2,V_a_2,V_fa_2).
% 11.99/11.91 0 [] c_Fun_Oswap(T_a,T_b,V_a_2,V_a_2,V_fa_2)=V_fa_2.
% 11.99/11.91 0 [] -class_Nat_Osemiring__char__0(T_a)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)|V_m_2=V_n_2.
% 11.99/11.91 0 [] -class_Nat_Osemiring__char__0(T_a)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)|V_m_2!=V_n_2.
% 11.99/11.91 0 [] c_Nat_OSuc(V_nat_2)!=c_Nat_OSuc(V_nat_H_2)|V_nat_2=V_nat_H_2.
% 11.99/11.91 0 [] c_Nat_OSuc(V_nat_2)=c_Nat_OSuc(V_nat_H_2)|V_nat_2!=V_nat_H_2.
% 11.99/11.91 0 [] c_Nat_OSuc(V_n)!=V_n.
% 11.99/11.91 0 [] V_n!=c_Nat_OSuc(V_n).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_fa_2)|hAPP(V_fa_2,V_xa_2)!=hAPP(V_fa_2,V_ya_2)|V_xa_2=V_ya_2.
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_fa_2)|hAPP(V_fa_2,V_xa_2)=hAPP(V_fa_2,V_ya_2)|V_xa_2!=V_ya_2.
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_m=V_n.
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Nat_OSuc(V_m)=V_n|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))|V_m=V_n.
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))|V_n_2=V_m_2.
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))|V_n_2!=V_m_2.
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2.
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2!=V_n_2.
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(V_fa_2,$f5(V_n_H_2,V_n_2,V_fa_2,T_a)),hAPP(V_fa_2,c_Nat_OSuc($f5(V_n_H_2,V_n_2,V_fa_2,T_a))))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_n_H_2)|c_Orderings_Oord__class_Oless(T_a,hAPP(V_fa_2,V_n_2),hAPP(V_fa_2,V_n_H_2)).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(V_fa_2,$f6(V_m_2,V_n_2,V_fa_2,T_a)),hAPP(V_fa_2,c_Nat_OSuc($f6(V_m_2,V_n_2,V_fa_2,T_a))))| -c_Orderings_Oord__class_Oless(T_a,hAPP(V_fa_2,V_n_2),hAPP(V_fa_2,V_m_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(V_fa_2,$f6(V_m_2,V_n_2,V_fa_2,T_a)),hAPP(V_fa_2,c_Nat_OSuc($f6(V_m_2,V_n_2,V_fa_2,T_a))))|c_Orderings_Oord__class_Oless(T_a,hAPP(V_fa_2,V_n_2),hAPP(V_fa_2,V_m_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_xa_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_ya_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_xa_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_ya_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2).
% 11.99/11.91 0 [] hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),c_Nat_OSuc(V_n_2)),V_fa_2)=hAPP(c_Fun_Ocomp(T_a,T_a,T_a,V_fa_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_fa_2)).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless(T_a,$f8(V_fa_2,T_a,T_b),$f7(V_fa_2,T_a,T_b))|c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_fa_2).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_b,hAPP(V_fa_2,$f8(V_fa_2,T_a,T_b)),hAPP(V_fa_2,$f7(V_fa_2,T_a,T_b)))|c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_fa_2).
% 11.99/11.91 0 [] -class_Rings_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Nat_OSuc(V_n_2),V_i_2)=c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k)|V_k=c_Nat_OSuc(V_i)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,$f9(V_k,V_i)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k)|V_k=c_Nat_OSuc(V_i)|V_k=c_Nat_OSuc($f9(V_k,V_i)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,$f10(V_k,V_i)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k)|V_k=c_Nat_OSuc($f10(V_k,V_i)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.91 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)|V_m_2=V_n_2.
% 11.99/11.91 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)|V_m_2!=V_n_2.
% 11.99/11.91 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_xa_2)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_ya_2)|V_xa_2=V_ya_2.
% 11.99/11.91 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_xa_2)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_ya_2)|V_xa_2!=V_ya_2.
% 11.99/11.91 0 [] hAPP(V_fa_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_fa_2),V_xa_2))=hAPP(hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_fa_2),hAPP(V_fa_2,V_xa_2)).
% 11.99/11.91 0 [] -class_Rings_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat__aux(T_a,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)=V_i_2.
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x).
% 11.99/11.91 0 [] -class_Rings_Osemiring__1(T_a)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_a,T_b),tc_fun(T_a,T_b)),V_n_2),c_Fun_Ocomp(T_b,T_b,T_a,V_fa_2))=c_Fun_Ocomp(T_b,T_b,T_a,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_fa_2)).
% 11.99/11.91 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m).
% 11.99/11.91 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_nat_H).
% 11.99/11.91 0 [] c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.91 0 [] c_Nat_OSuc(V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.91 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m).
% 11.99/11.91 0 [] c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.91 0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 11.99/11.91 0 [] V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.91 0 [] V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -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($f11(V_n_2,V_m_2)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f11(V_n_2,V_m_2),V_n_2).
% 11.99/11.91 0 [] 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).
% 11.99/11.91 0 [] 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)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)|V_n_2=c_Nat_OSuc($f12(V_n_2)).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)|V_n_2!=c_Nat_OSuc(B_m).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.91 0 [] c_Nat_Ofunpow(T_a)=c_Nat_Ocompow(T_a,T_a).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|V_n=c_Nat_OSuc($f13(V_n)).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)).
% 11.99/11.91 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 11.99/11.91 0 [] -class_Groups_Ozero(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=V_xa_2|V_xa_2=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Groups_Ozero(T_a)|c_Groups_Ozero__class_Ozero(T_a)=V_xa_2|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)|V_z_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc($f14(V_z_2,V_w_2)))).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)|V_z_2!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(B_n))).
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)!=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a)=V_b.
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2))=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2!=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)).
% 11.99/11.91 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)).
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)).
% 11.99/11.91 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)).
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 11.99/11.91 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)).
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)).
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 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).
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z).
% 11.99/11.91 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z.
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z.
% 11.99/11.91 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)=V_z.
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)=V_z.
% 11.99/11.91 0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)).
% 11.99/11.91 0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z))=V_z.
% 11.99/11.91 0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 11.99/11.91 0 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)|V_w_2=V_z_2.
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|V_w_2!=V_z_2.
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_m_2=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_n_2=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_m_2!=c_Groups_Oone__class_Oone(tc_Int_Oint)|V_n_2!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)).
% 11.99/11.91 0 [] -class_Rings_Osemiring__1(T_a)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)).
% 11.99/11.91 0 [] -class_Rings_Osemiring__1(T_a)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)).
% 11.99/11.91 0 [] -class_Rings_Osemiring__1(T_a)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a).
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=V_a.
% 11.99/11.91 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)).
% 11.99/11.91 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.
% 11.99/11.91 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.
% 11.99/11.91 0 [] -class_Groups_Oone(T_a)|c_Groups_Oone__class_Oone(T_a)!=V_xa_2|V_xa_2=c_Groups_Oone__class_Oone(T_a).
% 11.99/11.91 0 [] -class_Groups_Oone(T_a)|c_Groups_Oone__class_Oone(T_a)=V_xa_2|V_xa_2!=c_Groups_Oone__class_Oone(T_a).
% 11.99/11.91 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.
% 11.99/11.91 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.
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_b_2=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2).
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_b_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2).
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b))=V_b.
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)!=V_b_2|c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)=V_a_2.
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=V_b_2|c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)!=V_a_2.
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_a_2=V_b_2.
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_a_2!=V_b_2.
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=V_b.
% 11.99/11.91 0 [] -class_Groups_Oab__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 11.99/11.91 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)).
% 11.99/11.91 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)!=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)|V_b_2=V_c_2.
% 11.99/11.91 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2)=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)|V_b_2!=V_c_2.
% 11.99/11.91 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)!=c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)|V_b_2=V_c_2.
% 11.99/11.91 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)=c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)|V_b_2!=V_c_2.
% 11.99/11.91 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)!=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)|V_b=V_c.
% 11.99/11.91 0 [] -class_Groups_Ocancel__ab__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)!=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)|V_b=V_c.
% 11.99/11.91 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_b,V_a)!=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)|V_b=V_c.
% 11.99/11.91 0 [] -class_Rings_Osemiring(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c).
% 11.99/11.91 0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)|V_a_2=V_b_2|V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2).
% 11.99/11.91 0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)|V_a_2!=V_b_2.
% 11.99/11.91 0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2).
% 11.99/11.91 0 [] -class_Rings_Ocomm__semiring(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 11.99/11.91 0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2)!=c_Groups_Oone__class_Oone(T_a)|V_xa_2=c_Groups_Oone__class_Oone(T_a)|V_xa_2=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)).
% 11.99/11.91 0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2)=c_Groups_Oone__class_Oone(T_a)|V_xa_2!=c_Groups_Oone__class_Oone(T_a).
% 11.99/11.91 0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2)=c_Groups_Oone__class_Oone(T_a)|V_xa_2!=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)).
% 11.99/11.91 0 [] -class_Rings_Oring(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b).
% 11.99/11.91 0 [] -class_Rings_Oring(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 11.99/11.91 0 [] -class_Rings_Oring(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b).
% 11.99/11.91 0 [] -class_Rings_Oring(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)|c_Groups_Ozero__class_Ozero(T_a)=V_a_2.
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)|c_Groups_Ozero__class_Ozero(T_a)!=V_a_2.
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|V_a_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|V_a_2=c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)!=V_a_2|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)=V_a_2|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)).
% 11.99/11.91 0 [] -class_Groups_Omonoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a.
% 11.99/11.91 0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a.
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Groups_Omonoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 11.99/11.91 0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 11.99/11.91 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 11.99/11.91 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)).
% 11.99/11.91 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2)))|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2!=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2)))|V_xa_2=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2)))|V_ya_2=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))).
% 11.99/11.91 0 [] -class_Rings_Osemiring__1(T_a)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Nat_OSuc(V_m))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)).
% 11.99/11.91 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(V_m))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a).
% 11.99/11.91 0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__comm__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -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))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|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))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.91 0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.91 0 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))).
% 11.99/11.91 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.91 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.91 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 11.99/11.91 0 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.91 0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_x)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x).
% 11.99/11.91 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_m,V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_m).
% 11.99/11.91 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m).
% 11.99/11.91 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m).
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2=c_Groups_Ouminus__class_Ouminus(T_a,V_xa_2).
% 11.99/11.91 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2)=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_xa_2).
% 11.99/11.91 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_r=c_Groups_Ozero__class_Ozero(T_a)|V_a!=V_b|V_c=V_d|c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c))!=c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)).
% 11.99/11.91 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 11.99/11.91 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ouminus__class_Ouminus(T_a,V_x))=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)).
% 11.99/11.91 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 11.99/11.91 0 [] c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n).
% 11.99/11.91 0 [] c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 11.99/11.91 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).
% 11.99/11.91 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 11.99/11.91 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)|V_m_2=V_n_2.
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)|V_m_2!=V_n_2.
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)|V_m_2=V_n_2.
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)|V_m_2!=V_n_2.
% 11.99/11.91 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)).
% 11.99/11.91 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)).
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)).
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)).
% 11.99/11.91 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).
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m).
% 11.99/11.91 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)=V_n.
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n.
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 11.99/11.91 0 [] 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).
% 11.99/11.91 0 [] 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).
% 11.99/11.91 0 [] 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).
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)!=V_m|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 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.
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 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.
% 11.99/11.91 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).
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k).
% 11.99/11.91 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.
% 11.99/11.91 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.
% 11.99/11.91 0 [] hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_fa_2))=hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_fa_2).
% 11.99/11.91 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=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).
% 11.99/11.91 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=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)).
% 11.99/11.91 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=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).
% 11.99/11.91 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=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)).
% 11.99/11.91 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=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).
% 11.99/11.91 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=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)).
% 11.99/11.91 0 [] 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).
% 11.99/11.91 0 [] 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)).
% 11.99/11.91 0 [] 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).
% 11.99/11.91 0 [] 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)).
% 11.99/11.91 0 [] 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).
% 11.99/11.91 0 [] 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)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,$f15(V_n_2,V_m_2))).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2!=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))).
% 11.99/11.91 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)).
% 11.99/11.91 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)).
% 11.99/11.91 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)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n),V_z))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_z).
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_y)).
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 11.99/11.91 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)).
% 11.99/11.91 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 11.99/11.91 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)).
% 11.99/11.91 0 [] c_Groups_Oone__class_Oone(tc_Int_Oint)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 11.99/11.91 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 11.99/11.91 0 [] hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)),V_fa_2)=hAPP(c_Fun_Ocomp(T_a,T_a,T_a,hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_m_2),V_fa_2)),hAPP(hAPP(c_Nat_Ocompow(T_a,T_a),V_n_2),V_fa_2)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)).
% 11.99/11.91 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)).
% 11.99/11.91 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)).
% 11.99/11.91 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))).
% 11.99/11.91 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).
% 11.99/11.91 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)).
% 11.99/11.91 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).
% 11.99/11.91 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)).
% 11.99/11.91 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).
% 11.99/11.91 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 11.99/11.91 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b).
% 11.99/11.91 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 11.99/11.91 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d).
% 11.99/11.91 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)).
% 11.99/11.91 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_b_2!=c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_b_2=c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 11.99/11.91 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a.
% 11.99/11.91 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_ya_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_z_2))!=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_ya_2))|V_w_2=V_xa_2|V_ya_2=V_z_2.
% 11.99/11.91 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_ya_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_z_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_ya_2))|V_w_2!=V_xa_2.
% 11.99/11.91 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_ya_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_z_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_ya_2))|V_ya_2!=V_z_2.
% 11.99/11.91 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m).
% 11.99/11.91 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),V_ya)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)).
% 11.99/11.91 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H)),V_b)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)).
% 11.99/11.91 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 11.99/11.91 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_a_2=V_b_2|V_c_2=V_d_2|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))!=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)).
% 11.99/11.91 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_a_2!=V_b_2|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)).
% 11.99/11.91 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_c_2!=V_d_2|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))=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)).
% 11.99/11.91 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)).
% 11.99/11.91 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)).
% 11.99/11.91 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)).
% 11.99/11.91 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.
% 11.99/11.91 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.
% 11.99/11.91 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x)),V_y)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2=V_n_2.
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2!=V_n_2.
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k).
% 11.99/11.91 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.
% 11.99/11.91 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).
% 11.99/11.91 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.
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|V_x=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc($f16(V_x)))).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),$f17(V_k)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)|V_k=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),$f17(V_k)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semiring__1__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_a)| -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))|c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)!=c_Groups_Oone__class_Oone(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)).
% 11.99/11.91 0 [] -class_Orderings_Opreorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_x)).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semidom(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 11.99/11.91 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)).
% 11.99/11.91 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_xa_2)),hAPP(V_gb_2,V_xa_2))).
% 11.99/11.91 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)).
% 11.99/11.91 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.
% 11.99/11.91 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)).
% 11.99/11.91 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.
% 11.99/11.91 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)).
% 11.99/11.91 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)).
% 11.99/11.91 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)).
% 11.99/11.91 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)).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2),V_xa_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))|V_xa_2=V_ya_2.
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2),V_xa_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))|V_xa_2!=V_ya_2.
% 11.99/11.91 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_xa_2)),hAPP(V_gb_2,V_xa_2))).
% 11.99/11.91 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)).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)|V_xa_2!=V_ya_2|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2)).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)|V_xa_2!=V_ya_2|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2),V_xa_2)).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)|V_xa_2=V_ya_2| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2),V_xa_2)).
% 11.99/11.91 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)).
% 11.99/11.91 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))).
% 11.99/11.91 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,$f18(V_gb_2,V_fa_2,T_a,T_b))),hAPP(V_gb_2,$f18(V_gb_2,V_fa_2,T_a,T_b)))).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_xa_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_ya_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_xa_2),V_ya_2)).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_xa_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_ya_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_xa_2),V_ya_2)).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))| -c_Orderings_Oord__class_Oless(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 11.99/11.91 0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))| -c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)| -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))|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 11.99/11.91 0 [] -class_Orderings_Opreorder(T_a)| -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))|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 11.99/11.91 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|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 11.99/11.91 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|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y.
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2.
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2.
% 11.99/11.91 0 [] -class_Orderings_Opreorder(T_a)| -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)).
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y).
% 11.99/11.91 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))|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 11.99/11.91 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))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))|V_xa_2=V_ya_2.
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))|V_xa_2!=V_ya_2.
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_y),V_x))|c_Orderings_Oord__class_Oless(T_a,V_x,V_y).
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)|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)).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2.
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))|V_xa_2!=V_ya_2.
% 11.99/11.91 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2)).
% 11.99/11.91 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2),V_xa_2)).
% 11.99/11.91 0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2),V_xa_2)).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2)).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2.
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))|V_xa_2=V_ya_2.
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2).
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2))| -c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2).
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2),V_xa_2)).
% 11.99/11.91 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2),V_xa_2)).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)),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)).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)),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)).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)),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)).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)),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)).
% 11.99/11.91 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,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))).
% 11.99/11.91 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,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))).
% 11.99/11.91 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,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b)).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)),V_b_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)),V_a_2)).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)),V_b_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)),V_a_2)).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2)).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),V_b_2)).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)),c_Groups_Ouminus__class_Ouminus(T_a,V_a))).
% 11.99/11.91 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).
% 11.99/11.91 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).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)).
% 11.99/11.91 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))).
% 11.99/11.91 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)).
% 11.99/11.91 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).
% 11.99/11.91 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))).
% 11.99/11.91 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)).
% 11.99/11.91 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)).
% 11.99/11.91 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).
% 11.99/11.91 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)).
% 11.99/11.91 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).
% 11.99/11.91 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)).
% 11.99/11.91 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)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n)),V_n)).
% 11.99/11.91 0 [] -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)).
% 11.99/11.91 0 [] V_m!=V_n|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|V_m=V_n|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 11.99/11.91 0 [] -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)).
% 11.99/11.91 0 [] -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)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2.
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 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.
% 11.99/11.91 0 [] -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)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=V_n_2.
% 11.99/11.91 0 [] 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.
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|V_n_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,$f19(V_n_2,V_m_2)).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|V_n_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2)),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)).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2)),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)).
% 11.99/11.91 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))).
% 11.99/11.91 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))).
% 11.99/11.91 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 11.99/11.91 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 11.99/11.91 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))).
% 11.99/11.91 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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)).
% 11.99/11.91 0 [] -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)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)|V_z_2!=V_w_2.
% 11.99/11.91 0 [] 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.
% 11.99/11.91 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))).
% 11.99/11.91 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)))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j))).
% 11.99/11.91 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))).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_fa_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,V_xa_2)),hAPP(V_fa_2,V_ya_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2)).
% 11.99/11.91 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_fa_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_fa_2,V_xa_2)),hAPP(V_fa_2,V_ya_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2),V_ya_2)).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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)).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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)).
% 11.99/11.91 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))).
% 11.99/11.91 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)).
% 11.99/11.91 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))).
% 11.99/11.91 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)).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 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,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.91 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),c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))).
% 11.99/11.91 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),c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))).
% 11.99/11.91 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_xa_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_ya_2))|c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 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_xa_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_ya_2))|c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 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_xa_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_ya_2))|c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2)=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2!=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 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)),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.91 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)),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)).
% 11.99/11.91 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)),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)).
% 11.99/11.91 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -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))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 11.99/11.91 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))| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 11.99/11.91 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))).
% 11.99/11.91 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))).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(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)).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(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)).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ouminus__class_Ouminus(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))).
% 11.99/11.91 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ouminus__class_Ouminus(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))).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.91 0 [] -class_Groups_Oordered__ab__group__add(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))).
% 11.99/11.91 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)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))).
% 11.99/11.91 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)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))).
% 11.99/11.91 0 [] -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)).
% 11.99/11.91 0 [] -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)).
% 11.99/11.91 0 [] -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)).
% 11.99/11.91 0 [] 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)).
% 11.99/11.91 0 [] -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)).
% 11.99/11.91 0 [] 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)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)).
% 11.99/11.91 0 [] -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)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))|V_n_2=V_m_2.
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))|V_n_2!=V_m_2.
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 11.99/11.91 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)).
% 11.99/11.91 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)).
% 11.99/11.91 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))).
% 11.99/11.91 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_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y))).
% 11.99/11.91 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))).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f20(V_P_2)))|hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))).
% 11.99/11.91 0 [] -hBOOL(hAPP(V_P_2,$f20(V_P_2)))|hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))|hBOOL(hAPP(V_P_2,X1))| -hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),$f21(V_P_2)))).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))| -hBOOL(hAPP(V_P_2,B_x))|hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),$f22(V_P_2)))).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f23(V_P_2)))| -hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))).
% 11.99/11.91 0 [] hBOOL(hAPP(V_P_2,$f23(V_P_2)))| -hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))).
% 11.99/11.91 0 [] -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))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2))|V_z_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),$f24(V_z_2,V_w_2))).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2))|V_z_2!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -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)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -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)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -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)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -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)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -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))|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)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -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))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_a),V_b))| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semiring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semiring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 11.99/11.91 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 11.99/11.91 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)))| -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)).
% 11.99/11.91 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)))| -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)).
% 11.99/11.91 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)))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.91 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))| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 11.99/11.91 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_b),V_c))|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 11.99/11.91 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))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 11.99/11.91 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2))),c_Groups_Ozero__class_Ozero(T_a)))|V_xa_2=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2))),c_Groups_Ozero__class_Ozero(T_a)))|V_ya_2=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 0 [] -class_Rings_Olinordered__ring__strict(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2))),c_Groups_Ozero__class_Ozero(T_a)))|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2!=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.91 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)),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)))).
% 11.99/11.91 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)).
% 11.99/11.91 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)).
% 11.99/11.91 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)).
% 11.99/11.91 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)).
% 11.99/11.91 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)).
% 11.99/11.91 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)))| -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)).
% 11.99/11.91 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)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 11.99/11.91 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)).
% 11.99/11.91 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)))| -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)).
% 11.99/11.91 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)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 11.99/11.91 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)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2)).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.91 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))|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,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)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(V_n))))).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)|V_a!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))| -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))).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)|V_a!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H),V_q)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,V_ya_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_ya_2),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_xa_2))).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,V_ya_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_ya_2),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_xa_2))).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,V_ya_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_xa_2)),V_ya_2)).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,V_ya_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_xa_2)),V_ya_2)).
% 11.99/11.91 0 [] -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_xa_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_z_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2)).
% 11.99/11.91 0 [] -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_xa_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_z_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2)).
% 11.99/11.91 0 [] -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_xa_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_ya_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2)).
% 11.99/11.91 0 [] -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_xa_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_ya_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2)).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),V_u))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x))).
% 11.99/11.91 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,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y))).
% 11.99/11.91 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.
% 11.99/11.91 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)).
% 11.99/11.91 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)).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w),V_w)).
% 11.99/11.91 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)|V_xa_2=V_ya_2.
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2))|V_xa_2!=V_ya_2.
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2.
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2))|V_xa_2=V_ya_2.
% 11.99/11.91 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.
% 11.99/11.91 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)).
% 11.99/11.91 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)).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w),V_w)).
% 11.99/11.91 0 [] -class_Orderings_Oord(T_b)| -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)).
% 11.99/11.91 0 [] -class_Orderings_Oord(T_b)| -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)).
% 11.99/11.91 0 [] -class_Orderings_Oord(T_b)|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)).
% 11.99/11.91 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.
% 11.99/11.91 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)).
% 11.99/11.91 0 [] V_m!=V_n|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m),V_n)).
% 11.99/11.91 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)).
% 11.99/11.91 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_n)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_z_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_z_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2).
% 11.99/11.91 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,V_ya_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_ya_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_xa_2)).
% 11.99/11.91 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,V_ya_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_ya_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_xa_2)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,V_ya_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_xa_2),V_ya_2).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,V_ya_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_xa_2),V_ya_2).
% 11.99/11.92 0 [] c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 11.99/11.92 0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,V_ya_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_ya_2=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_xa_2).
% 11.99/11.92 0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,V_ya_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_ya_2!=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_xa_2).
% 11.99/11.92 0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2=V_a_2.
% 11.99/11.92 0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_xa_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2!=V_a_2.
% 11.99/11.92 0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_ya_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 11.99/11.92 0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_ya_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_ya_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 11.99/11.92 0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_ya_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_ya_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 11.99/11.92 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.
% 11.99/11.92 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.
% 11.99/11.92 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.
% 11.99/11.92 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.
% 11.99/11.92 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)| -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)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q),V_q_H)).
% 11.99/11.92 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)| -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)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_l_2))|V_l_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,$f25(V_l_2,V_k_2)).
% 11.99/11.92 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2),V_l_2))|V_l_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n).
% 11.99/11.92 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))).
% 11.99/11.92 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,$f27(V_X_2,T_a)),$f26(V_X_2,T_a))).
% 11.99/11.92 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,$f26(V_X_2,T_a))),hAPP(V_X_2,$f27(V_X_2,T_a)))).
% 11.99/11.92 0 [] -class_Lattices_Oboolean__algebra(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y)),c_Groups_Ouminus__class_Ouminus(T_a,V_x))).
% 11.99/11.92 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z)=V_z.
% 11.99/11.92 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).
% 11.99/11.92 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)).
% 11.99/11.92 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2)),V_w)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)).
% 11.99/11.92 0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)=V_a.
% 11.99/11.92 0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)=V_x.
% 11.99/11.92 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).
% 11.99/11.92 0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x))=V_x.
% 11.99/11.92 0 [] -class_Groups_Ouminus(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_xa_2)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_xa_2)).
% 11.99/11.92 0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_xa_2)!=c_Groups_Ouminus__class_Ouminus(T_a,V_ya_2)|V_xa_2=V_ya_2.
% 11.99/11.92 0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_xa_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_ya_2)|V_xa_2!=V_ya_2.
% 11.99/11.92 0 [] -class_Lattices_Oboolean__algebra(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_xa_2)),c_Groups_Ouminus__class_Ouminus(T_a,V_ya_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2),V_xa_2)).
% 11.99/11.92 0 [] -class_Lattices_Oboolean__algebra(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_xa_2)),c_Groups_Ouminus__class_Ouminus(T_a,V_ya_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2),V_xa_2)).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_xa_2))|V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_xa_2))|V_xa_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f28(V_n_2,V_P_2),V_n_2).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i),$f28(V_n_2,V_P_2)))| -hBOOL(hAPP(V_P_2,B_i)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))|hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,$f28(V_n_2,V_P_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 11.99/11.92 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Oincse_q(T_a,V_X_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m),B_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))).
% 11.99/11.92 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Oincse_q(T_a,V_X_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f30(V_X_2,T_a)),$f29(V_X_2,T_a))).
% 11.99/11.92 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Oincse_q(T_a,V_X_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f30(V_X_2,T_a))),hAPP(V_X_2,$f29(V_X_2,T_a)))).
% 11.99/11.92 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(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 11.99/11.92 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(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z))),hAPP(c_Int_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z_H))).
% 11.99/11.92 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))).
% 11.99/11.92 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))).
% 11.99/11.92 0 [] c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 0 [] hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))=V_n.
% 11.99/11.92 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))).
% 11.99/11.92 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))).
% 11.99/11.92 0 [] c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 0 [] c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 11.99/11.92 0 [] c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 11.99/11.92 0 [] hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))|hAPP(c_Int_Onat,V_z_2)!=hAPP(c_Int_Onat,V_z_H_2)|V_z_2=V_z_H_2.
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))|hAPP(c_Int_Onat,V_z_2)=hAPP(c_Int_Onat,V_z_H_2)|V_z_2!=V_z_H_2.
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_xa_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ya_2))|hAPP(c_Int_Onat,V_xa_2)!=hAPP(c_Int_Onat,V_ya_2)|V_xa_2=V_ya_2.
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_xa_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ya_2))|hAPP(c_Int_Onat,V_xa_2)=hAPP(c_Int_Onat,V_ya_2)|V_xa_2!=V_ya_2.
% 11.99/11.92 0 [] -hBOOL(hAPP(V_P_2,$f31(V_P_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))|hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,B_x1))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f32(V_P_2))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,B_x1))| -hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,$f32(V_P_2)))).
% 11.99/11.92 0 [] -hBOOL(hAPP(V_P_2,B_x1))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f33(V_P_2))).
% 11.99/11.92 0 [] -hBOOL(hAPP(V_P_2,B_x1))|hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,$f33(V_P_2)))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,$f34(V_P_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))| -hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))).
% 11.99/11.92 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onat,V_z)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 0 [] hAPP(c_Int_Onat,V_i_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 0 [] hAPP(c_Int_Onat,V_i_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 0 [] hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2),hAPP(c_Int_Onat,V_z_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2),hAPP(c_Int_Onat,V_z_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2),hAPP(c_Int_Onat,V_z_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2),hAPP(c_Int_Onat,V_z_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2),hAPP(c_Int_Onat,V_z_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_xa_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ya_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Int_Onat,V_xa_2)),hAPP(c_Int_Onat,V_ya_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_xa_2),V_ya_2)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_xa_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ya_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Int_Onat,V_xa_2)),hAPP(c_Int_Onat,V_ya_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_xa_2),V_ya_2)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z))=V_z.
% 11.99/11.92 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 11.99/11.92 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)!=V_z_2|V_m_2=hAPP(c_Int_Onat,V_z_2).
% 11.99/11.92 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)!=V_z_2|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)).
% 11.99/11.92 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)=V_z_2|V_m_2!=hAPP(c_Int_Onat,V_z_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z))=V_z.
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onat,V_z_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),V_z_2).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onat,V_z_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),V_z_2).
% 11.99/11.92 0 [] hAPP(c_Int_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 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_xa_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_xa_2)).
% 11.99/11.92 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_xa_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_xa_2)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 11.99/11.92 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_xa_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ya_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_xa_2),hAPP(c_Int_Onat,V_ya_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,V_ya_2).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_xa_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ya_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_xa_2),hAPP(c_Int_Onat,V_ya_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,V_ya_2).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2),hAPP(c_Int_Onat,V_z_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2),hAPP(c_Int_Onat,V_z_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_w_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_w_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2)).
% 11.99/11.92 0 [] hAPP(c_Int_Onat,V_w_2)!=V_m_2| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))|V_w_2=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2).
% 11.99/11.92 0 [] hAPP(c_Int_Onat,V_w_2)!=V_m_2|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 0 [] hAPP(c_Int_Onat,V_w_2)=V_m_2|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 0 [] hAPP(c_Int_Onat,V_w_2)=V_m_2|V_w_2!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)).
% 11.99/11.92 0 [] hAPP(c_Int_Onat,V_w_2)=V_m_2|V_w_2!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 0 [] V_m_2!=hAPP(c_Int_Onat,V_w_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))|V_w_2=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2).
% 11.99/11.92 0 [] V_m_2!=hAPP(c_Int_Onat,V_w_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 0 [] V_m_2=hAPP(c_Int_Onat,V_w_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 0 [] V_m_2=hAPP(c_Int_Onat,V_w_2)|V_w_2!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)).
% 11.99/11.92 0 [] V_m_2=hAPP(c_Int_Onat,V_w_2)|V_w_2!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 0 [] -hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))|V_i_2!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)|hBOOL(hAPP(V_P_2,B_n)).
% 11.99/11.92 0 [] -hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))|V_i_2=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),$f35(V_i_2,V_P_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))|V_i_2=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),$f35(V_i_2,V_P_2))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))| -hBOOL(hAPP(V_P_2,$f35(V_i_2,V_P_2)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))| -hBOOL(hAPP(V_P_2,$f35(V_i_2,V_P_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 11.99/11.92 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))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y))=hAPP(c_Int_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)).
% 11.99/11.92 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__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))|hAPP(c_Int_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_z_H))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Int_Onat,V_z),hAPP(c_Int_Onat,V_z_H)).
% 11.99/11.92 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))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))|hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)).
% 11.99/11.92 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)))).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))|c_Nat_OSuc(hAPP(c_Int_Onat,V_z))=hAPP(c_Int_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2),V_m_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,V_w_2),V_m_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)).
% 11.99/11.92 0 [] c_Int_Onat__aux(V_i,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Int_Onat,V_i),V_n).
% 11.99/11.92 0 [] c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),V_x)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))|c_RComplete_Onatceiling(V_x)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 11.99/11.92 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))).
% 11.99/11.92 0 [] c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))=V_n.
% 11.99/11.92 0 [] c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))=V_n.
% 11.99/11.92 0 [] c_RealDef_Oreal(tc_Nat_Onat)=c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal).
% 11.99/11.92 0 [] c_RealDef_Oreal(tc_Nat_Onat)=c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal).
% 11.99/11.92 0 [] hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2)!=hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)|V_n_2=V_m_2.
% 11.99/11.92 0 [] hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2)=hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2)|V_n_2!=V_m_2.
% 11.99/11.92 0 [] hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 11.99/11.92 0 [] hAPP(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).
% 11.99/11.92 0 [] hAPP(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).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2)),hAPP(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)).
% 11.99/11.92 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2)),hAPP(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)).
% 11.99/11.92 0 [] hAPP(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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)).
% 11.99/11.92 0 [] hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)).
% 11.99/11.92 0 [] hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 11.99/11.92 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)))).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(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).
% 11.99/11.92 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(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).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(V_n))).
% 11.99/11.92 0 [] hAPP(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).
% 11.99/11.92 0 [] hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(V_n))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 11.99/11.92 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(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x))),V_x)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(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))).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x),hAPP(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)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 11.99/11.92 0 [] -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,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))).
% 11.99/11.92 0 [] 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,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),V_m_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 11.99/11.92 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2),V_m_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_xa_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2),c_RComplete_Onatfloor(V_xa_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)),V_xa_2)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_xa_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2),c_RComplete_Onatfloor(V_xa_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2)),V_xa_2)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_xa_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2)),V_a_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2))).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_xa_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2)),V_a_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a_2))).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n).
% 11.99/11.92 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(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),V_x))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatfloor(V_x)=V_n.
% 11.99/11.92 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(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a).
% 11.99/11.92 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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),$f36(V_r))),V_r)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc($f36(V_r)))).
% 11.99/11.92 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_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n))).
% 11.99/11.92 0 [] -class_Rings_Oring__1(T_a)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Int_Oring__1__class_Oof__int(T_a,V_k)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k)))).
% 11.99/11.92 0 [] -class_Rings_Oring__1(T_a)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Int_Oring__1__class_Oof__int(T_a,V_k)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_k)).
% 11.99/11.92 0 [] -class_Int_Oring__char__0(T_a)|c_Int_Oring__1__class_Oof__int(T_a,V_z_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_z_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 11.99/11.92 0 [] -class_Int_Oring__char__0(T_a)|c_Int_Oring__1__class_Oof__int(T_a,V_z_2)=c_Groups_Ozero__class_Ozero(T_a)|V_z_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 11.99/11.92 0 [] -class_Int_Oring__char__0(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Int_Oring__1__class_Oof__int(T_a,V_z_2)|V_z_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 11.99/11.92 0 [] -class_Int_Oring__char__0(T_a)|c_Groups_Ozero__class_Ozero(T_a)=c_Int_Oring__1__class_Oof__int(T_a,V_z_2)|V_z_2!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 11.99/11.92 0 [] -class_Rings_Oring__1(T_a)|c_Int_Oring__1__class_Oof__int(T_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(T_a).
% 11.99/11.92 0 [] -class_Rings_Olinordered__idom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_w_2)),c_Int_Oring__1__class_Oof__int(T_a,V_z_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2)).
% 11.99/11.92 0 [] -class_Rings_Olinordered__idom(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_w_2)),c_Int_Oring__1__class_Oof__int(T_a,V_z_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2),V_z_2)).
% 11.99/11.92 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_w_2),c_Int_Oring__1__class_Oof__int(T_a,V_z_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 11.99/11.92 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_w_2),c_Int_Oring__1__class_Oof__int(T_a,V_z_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 11.99/11.92 0 [] -class_Rings_Oring__1(T_a)|c_Int_Oring__1__class_Oof__int(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z))=c_Groups_Oplus__class_Oplus(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_w),c_Int_Oring__1__class_Oof__int(T_a,V_z)).
% 11.99/11.92 0 [] -class_Rings_Oring__1(T_a)|c_Int_Oring__1__class_Oof__int(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Oring__1__class_Oof__int(T_a,V_w)),c_Int_Oring__1__class_Oof__int(T_a,V_z)).
% 11.99/11.92 0 [] -class_Rings_Oring__1(T_a)|c_Int_Oring__1__class_Oof__int(T_a,c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Oone__class_Oone(T_a).
% 11.99/11.92 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)).
% 11.99/11.92 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)).
% 11.99/11.92 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)).
% 11.99/11.92 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).
% 11.99/11.92 0 [] -class_Rings_Oring__1(T_a)|c_Int_Oring__1__class_Oof__int(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z))=c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_z)).
% 11.99/11.92 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)).
% 11.99/11.92 0 [] -class_Rings_Oring__1(T_a)|c_Int_Oring__1__class_Oof__int(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n).
% 11.99/11.92 0 [] -class_Int_Oring__char__0(T_a)|c_Int_Oring__1__class_Oof__int(T_a,V_w_2)!=c_Int_Oring__1__class_Oof__int(T_a,V_z_2)|V_w_2=V_z_2.
% 11.99/11.92 0 [] -class_Int_Oring__char__0(T_a)|c_Int_Oring__1__class_Oof__int(T_a,V_w_2)=c_Int_Oring__1__class_Oof__int(T_a,V_z_2)|V_w_2!=V_z_2.
% 11.99/11.92 0 [] -class_Rings_Oring__1(T_a)|c_Int_Oring__1__class_Oof__int(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Int_Oring__1__class_Oof__int(T_a,V_z)),V_n).
% 11.99/11.92 0 [] c_Int_Oring__1__class_Oof__int(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n).
% 11.99/11.92 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)).
% 11.99/11.92 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.
% 11.99/11.92 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)).
% 11.99/11.92 0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))!=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ya_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_xa_2=V_ya_2|V_xa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_ya_2).
% 11.99/11.92 0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ya_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_xa_2!=V_ya_2.
% 11.99/11.92 0 [] -class_Rings_Oidom(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ya_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_xa_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_ya_2).
% 11.99/11.92 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)),c_Int_Oring__1__class_Oof__int(T_a,V_z_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)).
% 11.99/11.92 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)),c_Int_Oring__1__class_Oof__int(T_a,V_z_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)).
% 11.99/11.92 0 [] -class_Rings_Olinordered__idom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_z_2)),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 0 [] -class_Rings_Olinordered__idom(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_z_2)),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_z_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_z_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Oring__1__class_Oof__int(T_a,V_z_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2).
% 11.99/11.92 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Oring__1__class_Oof__int(T_a,V_z_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2).
% 11.99/11.92 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)).
% 11.99/11.92 0 [] -class_Rings_Oring__1(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_z))=c_Int_Oring__1__class_Oof__int(T_a,V_z).
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -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))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)).
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -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_xa_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_ya_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_xa_2),V_ya_2)).
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -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_xa_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_ya_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_xa_2),V_ya_2)).
% 11.99/11.92 0 [] hAPP(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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),V_n).
% 11.99/11.92 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m)),V_n)=hAPP(c_RealDef_Oreal(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)).
% 11.99/11.92 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)).
% 11.99/11.92 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_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_xa_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.92 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_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).
% 11.99/11.92 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_2),V_m_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_xa_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.92 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n).
% 11.99/11.92 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)).
% 11.99/11.92 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xa_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xa_2).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_2),V_n_2))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 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)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),V_n)=hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))|hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),V_n).
% 11.99/11.92 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))).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_2),V_n_2))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xa_2).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_2),V_n_2))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xa_2).
% 11.99/11.92 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))).
% 11.99/11.92 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)).
% 11.99/11.92 0 [] V_x!=hAPP(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).
% 11.99/11.92 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).
% 11.99/11.92 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)).
% 11.99/11.92 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)).
% 11.99/11.92 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).
% 11.99/11.92 0 [] -class_Rings_Osemiring__1(T_a)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n).
% 11.99/11.92 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).
% 11.99/11.92 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.
% 11.99/11.92 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))).
% 11.99/11.92 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))).
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 11.99/11.92 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))).
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2)!=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)|V_m_2=V_n_2.
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)|V_m_2!=V_n_2.
% 11.99/11.92 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).
% 11.99/11.92 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)).
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 11.99/11.92 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)).
% 11.99/11.92 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.
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))).
% 11.99/11.92 0 [] -class_Rings_Oring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)).
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_xa_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_ya_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2).
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_xa_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_ya_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2).
% 11.99/11.92 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))).
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a)).
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 11.99/11.92 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))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|V_a=V_b.
% 11.99/11.92 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))).
% 11.99/11.92 0 [] -class_Rings_Olinordered__semidom(T_a)| -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)).
% 11.99/11.92 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)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f37(V_a,V_n)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),$f37(V_a,V_n)),V_n)=V_a.
% 11.99/11.92 0 [] hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_one_2.
% 11.99/11.92 0 [] hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2))=hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f38(V_a,V_n)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),$f38(V_a,V_n)),V_n)=V_a.
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n)!=V_a|B_y=$f38(V_a,V_n).
% 11.99/11.92 0 [] -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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),$f39(V_x,V_y))),V_y)),V_x)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc($f39(V_x,V_y)))),V_y)).
% 11.99/11.92 0 [] -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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)),c_Transcendental_Oln(V_x)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),$f40(V_x,B_y))),V_x)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),V_x).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)|c_Transcendental_Oln(V_xa_2)!=c_Transcendental_Oln(V_ya_2)|V_xa_2=V_ya_2.
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)|c_Transcendental_Oln(V_xa_2)=c_Transcendental_Oln(V_ya_2)|V_xa_2!=V_ya_2.
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_xa_2),c_Transcendental_Oln(V_ya_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_xa_2),c_Transcendental_Oln(V_ya_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2).
% 11.99/11.92 0 [] c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(V_xa_2)),c_Transcendental_Oln(V_ya_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(V_xa_2)),c_Transcendental_Oln(V_ya_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2)).
% 11.99/11.92 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))).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_xa_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_xa_2).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_xa_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_xa_2).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)|c_Transcendental_Oln(V_xa_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)|c_Transcendental_Oln(V_xa_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_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_xa_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_xa_2)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_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_xa_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_xa_2)).
% 11.99/11.92 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)))| -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)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)|c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y)).
% 11.99/11.92 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(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x))),V_x)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f41(V_n,V_a)).
% 11.99/11.92 0 [] -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),$f41(V_n,V_a)),c_Nat_OSuc(V_n))=V_a.
% 11.99/11.92 0 [] -class_Groups_Omonoid__mult(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n).
% 11.99/11.92 0 [] -class_Rings_Oring__1(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)).
% 11.99/11.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 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)).
% 11.99/11.92 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)).
% 11.99/11.92 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).
% 11.99/11.92 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)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m.
% 11.99/11.92 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_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))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.92 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_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))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.92 0 [] -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))|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)).
% 11.99/11.92 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_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k).
% 11.99/11.92 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_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)).
% 11.99/11.92 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=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2).
% 11.99/11.92 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!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)=V_m.
% 11.99/11.92 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)),V_j_2)).
% 11.99/11.92 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)),V_j_2)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k),V_j))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m.
% 11.99/11.92 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k))).
% 11.99/11.92 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2))).
% 11.99/11.92 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2))).
% 11.99/11.92 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j).
% 11.99/11.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 11.99/11.92 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).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)).
% 11.99/11.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 11.99/11.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 11.99/11.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)).
% 11.99/11.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n)=V_m.
% 11.99/11.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n)=V_m.
% 11.99/11.92 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)).
% 11.99/11.92 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)).
% 11.99/11.92 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_xa_2)=c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_xa_2),hAPP(V_B_2,V_xa_2)).
% 11.99/11.92 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=V_a.
% 11.99/11.92 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b)=V_a.
% 11.99/11.92 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)).
% 11.99/11.92 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)).
% 11.99/11.92 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)).
% 11.99/11.92 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)).
% 11.99/11.92 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)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2).
% 11.99/11.92 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)|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2).
% 11.99/11.92 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.
% 11.99/11.92 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.
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 11.99/11.92 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 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.
% 11.99/11.92 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.
% 11.99/11.92 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.
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 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.
% 11.99/11.92 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)).
% 11.99/11.92 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)).
% 11.99/11.92 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)).
% 11.99/11.92 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))).
% 11.99/11.92 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))).
% 11.99/11.92 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.
% 11.99/11.92 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.
% 11.99/11.92 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.
% 11.99/11.92 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).
% 11.99/11.92 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)).
% 11.99/11.92 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)).
% 11.99/11.92 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_Groups_Ominus__class_Ominus(T_a,V_b,V_a).
% 11.99/11.92 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 11.99/11.92 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 11.99/11.92 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,V_a,V_b).
% 11.99/11.92 0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)=c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)).
% 11.99/11.92 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a).
% 11.99/11.92 0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2)!=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_c_2)=V_d_2.
% 11.99/11.92 0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_c_2)!=V_d_2.
% 11.99/11.92 0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2)!=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)|V_c_2=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2).
% 11.99/11.92 0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)|V_c_2!=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2).
% 11.99/11.92 0 [] -class_Rings_Oring(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)).
% 11.99/11.92 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))).
% 11.99/11.92 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.92 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 11.99/11.92 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))).
% 11.99/11.92 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))).
% 11.99/11.92 0 [] -class_Rings_Oring__1(T_a)|c_Int_Oring__1__class_Oof__int(T_a,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_w,V_z))=c_Groups_Ominus__class_Ominus(T_a,c_Int_Oring__1__class_Oof__int(T_a,V_w),c_Int_Oring__1__class_Oof__int(T_a,V_z)).
% 11.99/11.92 0 [] -class_Rings_Oordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2)),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2))).
% 11.99/11.92 0 [] -class_Rings_Oordered__ring(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2)),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2))).
% 11.99/11.92 0 [] -class_Rings_Oordered__ring(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2)),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_c_2)),V_d_2)).
% 11.99/11.92 0 [] -class_Rings_Oordered__ring(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2)),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_c_2)),V_d_2)).
% 11.99/11.92 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2)).
% 11.99/11.92 0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2)).
% 11.99/11.92 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_c_2),V_d_2).
% 11.99/11.92 0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_c_2),V_d_2).
% 11.99/11.92 0 [] -class_Rings_Oring__1(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n.
% 11.99/11.92 0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 11.99/11.92 0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|V_a_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f42(V_b_2,V_a_2,V_P_2)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)| -hBOOL(hAPP(V_P_2,$f42(V_b_2,V_a_2,V_P_2))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f42(V_b_2,V_a_2,V_P_2)).
% 11.99/11.92 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,$f42(V_b_2,V_a_2,V_P_2))).
% 11.99/11.92 0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 11.99/11.92 0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|V_a_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f43(V_b_2,V_a_2,V_P_2)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)| -hBOOL(hAPP(V_P_2,$f43(V_b_2,V_a_2,V_P_2))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f43(V_b_2,V_a_2,V_P_2)).
% 11.99/11.92 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,$f43(V_b_2,V_a_2,V_P_2))).
% 11.99/11.92 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j)).
% 11.99/11.92 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m)).
% 11.99/11.92 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,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)),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,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)).
% 11.99/11.92 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,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)),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,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)).
% 11.99/11.92 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u),V_m),V_n).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2)=V_n_2.
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2)!=V_n_2.
% 11.99/11.92 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,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)),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),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))).
% 11.99/11.92 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,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)),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),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))).
% 11.99/11.92 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u),V_n)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)|V_m_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)|V_m_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2).
% 11.99/11.92 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).
% 11.99/11.92 0 [] -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))).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=V_n.
% 11.99/11.92 0 [] V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=V_n.
% 11.99/11.92 0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Nat_OSuc(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)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2),V_j_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_n_2).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2),V_i_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_n_2).
% 11.99/11.92 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).
% 11.99/11.92 0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)).
% 11.99/11.92 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).
% 11.99/11.92 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)))).
% 11.99/11.92 0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)).
% 11.99/11.92 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).
% 11.99/11.92 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)))).
% 11.99/11.92 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))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y))=hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(V_x,V_y)).
% 11.99/11.92 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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,$f44(V_r),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_r)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,hAPP(c_RealDef_Oreal(tc_Nat_Onat),$f44(V_r))).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_xa_2,V_ya_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 11.99/11.92 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2),V_ya_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_xa_2,V_ya_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w).
% 11.99/11.92 0 [] c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)).
% 11.99/11.92 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)).
% 11.99/11.92 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)).
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 0 [] c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_s)).
% 11.99/11.92 0 [] c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y)).
% 11.99/11.92 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))))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 11.99/11.92 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))))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n),V_m))|hAPP(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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_H),V_z))|hAPP(c_Int_Onat,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_z_H))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(c_Int_Onat,V_z),hAPP(c_Int_Onat,V_z_H)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a)),V_x))|c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(V_x))).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a)),V_x))|c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a).
% 11.99/11.92 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))).
% 11.99/11.92 0 [] c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_x,V_y)).
% 11.99/11.92 0 [] -hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_xa_2,V_ya_2))))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ya_2),V_xa_2))|hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_xa_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_ya_2)))).
% 11.99/11.92 0 [] -hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_xa_2,V_ya_2))))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_xa_2,V_ya_2))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ya_2),V_xa_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_xa_2,V_ya_2))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_ya_2),V_xa_2))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_xa_2,V_ya_2))))| -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_xa_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_ya_2))))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_xa_2,V_ya_2))))| -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_xa_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_ya_2))))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 11.99/11.92 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)).
% 11.99/11.92 0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b)=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)).
% 11.99/11.92 0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b)=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)).
% 11.99/11.92 0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=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)).
% 11.99/11.92 0 [] -class_Divides_Osemiring__div(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b)=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)).
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 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.
% 11.99/11.92 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.
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 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))).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 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).
% 11.99/11.92 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b).
% 11.99/11.92 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b).
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 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.
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)|c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x).
% 11.99/11.92 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))).
% 11.99/11.92 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))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2).
% 11.99/11.92 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)|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))).
% 11.99/11.92 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)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2).
% 11.99/11.92 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).
% 11.99/11.92 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))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2).
% 11.99/11.92 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)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2).
% 11.99/11.92 0 [] -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)).
% 11.99/11.92 0 [] -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)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)| -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)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)|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)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))| -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)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))| -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))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))|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))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))| -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))).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))| -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))).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))| -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).
% 11.99/11.92 0 [] -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))).
% 11.99/11.92 0 [] -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))).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)|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))).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_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))).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -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).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),V_a_H))| -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))).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_a),V_a_H))| -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))).
% 11.99/11.92 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))).
% 11.99/11.92 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)|V_n_2!=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)).
% 11.99/11.92 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,X4)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_n_2!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),X3),X4)|hBOOL(hAPP(V_P_2,X3)).
% 11.99/11.92 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)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 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)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 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)|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,$f47(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)|V_n_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f48(V_k_2,V_n_2,V_P_2)),$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)| -hBOOL(hAPP(V_P_2,$f48(V_k_2,V_n_2,V_P_2))).
% 11.99/11.92 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)),$f45(V_k_2,V_n_2,V_P_2)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f45(V_k_2,V_n_2,V_P_2)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f45(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f47(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f45(V_k_2,V_n_2,V_P_2)))|V_n_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f48(V_k_2,V_n_2,V_P_2)),$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 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)),$f45(V_k_2,V_n_2,V_P_2)))| -hBOOL(hAPP(V_P_2,$f48(V_k_2,V_n_2,V_P_2))).
% 11.99/11.92 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)|c_Orderings_Oord__class_Oless(tc_Int_Oint,$f45(V_k_2,V_n_2,V_P_2),V_k_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless(tc_Int_Oint,$f45(V_k_2,V_n_2,V_P_2),V_k_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless(tc_Int_Oint,$f45(V_k_2,V_n_2,V_P_2),V_k_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f47(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Orderings_Oord__class_Oless(tc_Int_Oint,$f45(V_k_2,V_n_2,V_P_2),V_k_2)|V_n_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f48(V_k_2,V_n_2,V_P_2)),$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 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)|c_Orderings_Oord__class_Oless(tc_Int_Oint,$f45(V_k_2,V_n_2,V_P_2),V_k_2)| -hBOOL(hAPP(V_P_2,$f48(V_k_2,V_n_2,V_P_2))).
% 11.99/11.92 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=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f46(V_k_2,V_n_2,V_P_2)),$f45(V_k_2,V_n_2,V_P_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 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=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f46(V_k_2,V_n_2,V_P_2)),$f45(V_k_2,V_n_2,V_P_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f46(V_k_2,V_n_2,V_P_2)),$f45(V_k_2,V_n_2,V_P_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f47(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 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=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f46(V_k_2,V_n_2,V_P_2)),$f45(V_k_2,V_n_2,V_P_2))|V_n_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f48(V_k_2,V_n_2,V_P_2)),$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 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=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f46(V_k_2,V_n_2,V_P_2)),$f45(V_k_2,V_n_2,V_P_2))| -hBOOL(hAPP(V_P_2,$f48(V_k_2,V_n_2,V_P_2))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(V_P_2,$f46(V_k_2,V_n_2,V_P_2)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 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,$f46(V_k_2,V_n_2,V_P_2)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 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,$f46(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f47(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 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,$f46(V_k_2,V_n_2,V_P_2)))|V_n_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f48(V_k_2,V_n_2,V_P_2)),$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -hBOOL(hAPP(V_P_2,$f46(V_k_2,V_n_2,V_P_2)))| -hBOOL(hAPP(V_P_2,$f48(V_k_2,V_n_2,V_P_2))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 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)))|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,$f47(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)|V_n_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f48(V_k_2,V_n_2,V_P_2)),$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)| -hBOOL(hAPP(V_P_2,$f48(V_k_2,V_n_2,V_P_2))).
% 11.99/11.92 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)),$f45(V_k_2,V_n_2,V_P_2)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f45(V_k_2,V_n_2,V_P_2)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f45(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f47(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f45(V_k_2,V_n_2,V_P_2)))|V_n_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f48(V_k_2,V_n_2,V_P_2)),$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 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)),$f45(V_k_2,V_n_2,V_P_2)))| -hBOOL(hAPP(V_P_2,$f48(V_k_2,V_n_2,V_P_2))).
% 11.99/11.92 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)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,$f45(V_k_2,V_n_2,V_P_2),V_k_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,$f45(V_k_2,V_n_2,V_P_2),V_k_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,$f45(V_k_2,V_n_2,V_P_2),V_k_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f47(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,$f45(V_k_2,V_n_2,V_P_2),V_k_2)|V_n_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f48(V_k_2,V_n_2,V_P_2)),$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 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)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,$f45(V_k_2,V_n_2,V_P_2),V_k_2)| -hBOOL(hAPP(V_P_2,$f48(V_k_2,V_n_2,V_P_2))).
% 11.99/11.92 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=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f46(V_k_2,V_n_2,V_P_2)),$f45(V_k_2,V_n_2,V_P_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 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=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f46(V_k_2,V_n_2,V_P_2)),$f45(V_k_2,V_n_2,V_P_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|V_n_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f46(V_k_2,V_n_2,V_P_2)),$f45(V_k_2,V_n_2,V_P_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f47(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 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=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f46(V_k_2,V_n_2,V_P_2)),$f45(V_k_2,V_n_2,V_P_2))|V_n_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f48(V_k_2,V_n_2,V_P_2)),$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 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=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f46(V_k_2,V_n_2,V_P_2)),$f45(V_k_2,V_n_2,V_P_2))| -hBOOL(hAPP(V_P_2,$f48(V_k_2,V_n_2,V_P_2))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(V_P_2,$f46(V_k_2,V_n_2,V_P_2)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.92 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,$f46(V_k_2,V_n_2,V_P_2)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 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,$f46(V_k_2,V_n_2,V_P_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,$f47(V_k_2,V_n_2,V_P_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 11.99/11.92 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,$f46(V_k_2,V_n_2,V_P_2)))|V_n_2=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),$f48(V_k_2,V_n_2,V_P_2)),$f47(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))| -hBOOL(hAPP(V_P_2,$f46(V_k_2,V_n_2,V_P_2)))| -hBOOL(hAPP(V_P_2,$f48(V_k_2,V_n_2,V_P_2))).
% 11.99/11.92 0 [] V_a_1!=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)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)| -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.
% 11.99/11.92 0 [] V_a_1!=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))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1,V_b_1)| -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.
% 11.99/11.92 0 [] V_a_1!=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))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1,V_b_1)| -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.
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))|c_SMT_Oz3div(V_k,V_l)=c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,V_l).
% 11.99/11.92 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))|c_SMT_Oz3div(V_k,V_l)=c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_l))).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)|hBOOL(hAPP(V_P_2,$f49(V_k_2,V_P_2,V_d_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))| -hBOOL(hAPP(V_P_2,B_x))|hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)| -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,$f49(V_k_2,V_P_2,V_d_2),V_d_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))| -hBOOL(hAPP(V_P_2,B_x))|hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))).
% 11.99/11.92 0 [] c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=V_m.
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 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).
% 11.99/11.92 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).
% 11.99/11.92 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)).
% 11.99/11.92 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))).
% 11.99/11.92 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).
% 11.99/11.92 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b))=c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)).
% 11.99/11.92 0 [] c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_x,V_y)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n)=V_m.
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n)=V_m.
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n).
% 11.99/11.92 0 [] -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))).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,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)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,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)).
% 11.99/11.92 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))).
% 11.99/11.92 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)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2)|V_n_2!=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)).
% 11.99/11.92 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)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f50(V_k_2,V_n_2,V_P_2),V_k_2).
% 11.99/11.92 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=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),$f51(V_k_2,V_n_2,V_P_2)),$f50(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 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,$f51(V_k_2,V_n_2,V_P_2))).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.92 0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f50(V_k_2,V_n_2,V_P_2),V_k_2).
% 11.99/11.92 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=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),$f51(V_k_2,V_n_2,V_P_2)),$f50(V_k_2,V_n_2,V_P_2)).
% 11.99/11.92 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,$f51(V_k_2,V_n_2,V_P_2))).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))|hAPP(c_Int_Onat,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y))=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)).
% 11.99/11.92 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))|c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y))=hAPP(c_Int_Onat,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y)).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(V_q_2)))|V_q_2=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2))|V_q_2!=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(V_q_2)))|V_q_2!=c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2).
% 11.99/11.92 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),$f52(V_n_2,V_m_2,V_P_2))),V_m_2)).
% 11.99/11.92 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)|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($f52(V_n_2,V_m_2,V_P_2)))).
% 11.99/11.92 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(V_P_2,$f52(V_n_2,V_m_2,V_P_2))).
% 11.99/11.92 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),$f52(V_n_2,V_m_2,V_P_2))),V_m_2)).
% 11.99/11.92 0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc($f52(V_n_2,V_m_2,V_P_2)))).
% 11.99/11.92 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,$f52(V_n_2,V_m_2,V_P_2))).
% 11.99/11.92 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))).
% 11.99/11.92 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))| -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)).
% 11.99/11.92 0 [] -class_Lattices_Oboolean__algebra(T_1)|class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)).
% 11.99/11.92 0 [] -class_Orderings_Opreorder(T_1)|class_Orderings_Opreorder(tc_fun(T_2,T_1)).
% 11.99/11.92 0 [] -class_Orderings_Oorder(T_1)|class_Orderings_Oorder(tc_fun(T_2,T_1)).
% 11.99/11.92 0 [] -class_Orderings_Oord(T_1)|class_Orderings_Oord(tc_fun(T_2,T_1)).
% 11.99/11.92 0 [] -class_Groups_Ouminus(T_1)|class_Groups_Ouminus(tc_fun(T_2,T_1)).
% 11.99/11.92 0 [] -class_Groups_Ominus(T_1)|class_Groups_Ominus(tc_fun(T_2,T_1)).
% 11.99/11.92 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Oordered__cancel__semiring(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Oordered__comm__semiring(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Olinordered__semiring__1(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Olinordered__semiring(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Olinordered__semidom(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Oordered__semiring(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Olinordered__ring(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Olinordered__idom(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 11.99/11.92 0 [] class_Divides_Osemiring__div(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Ocomm__semiring(tc_Int_Oint).
% 11.99/11.92 0 [] class_Nat_Osemiring__char__0(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Oab__group__add(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Oordered__ring(tc_Int_Oint).
% 11.99/11.92 0 [] class_Orderings_Opreorder(tc_Int_Oint).
% 11.99/11.92 0 [] class_Orderings_Olinorder(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Omonoid__mult(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Omonoid__add(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Osemiring__1(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Osemiring__0(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Ogroup__add(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Omult__zero(tc_Int_Oint).
% 11.99/11.92 0 [] class_Orderings_Oorder(tc_Int_Oint).
% 11.99/11.92 0 [] class_Int_Oring__char__0(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Osemiring(tc_Int_Oint).
% 11.99/11.92 0 [] class_Orderings_Oord(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Ouminus(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Oring__1(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Ominus(tc_Int_Oint).
% 11.99/11.92 0 [] class_Power_Opower(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Ozero(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Oring(tc_Int_Oint).
% 11.99/11.92 0 [] class_Rings_Oidom(tc_Int_Oint).
% 11.99/11.92 0 [] class_Groups_Oone(tc_Int_Oint).
% 11.99/11.92 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Rings_Oordered__semiring(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Divides_Osemiring__div(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Nat_Osemiring__char__0(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Orderings_Opreorder(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Orderings_Olinorder(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Groups_Omonoid__mult(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Groups_Omonoid__add(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Rings_Osemiring__1(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Rings_Osemiring__0(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Rings_Omult__zero(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Orderings_Oorder(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Rings_Osemiring(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Orderings_Oord(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Groups_Ominus(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Power_Opower(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Groups_Ozero(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Groups_Oone(tc_Nat_Onat).
% 11.99/11.92 0 [] class_Lattices_Oboolean__algebra(tc_HOL_Obool).
% 11.99/11.92 0 [] class_Orderings_Opreorder(tc_HOL_Obool).
% 11.99/11.92 0 [] class_Orderings_Oorder(tc_HOL_Obool).
% 11.99/11.92 0 [] class_Orderings_Oord(tc_HOL_Obool).
% 11.99/11.92 0 [] class_Groups_Ouminus(tc_HOL_Obool).
% 11.99/11.92 0 [] class_Groups_Ominus(tc_HOL_Obool).
% 11.99/11.92 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Olinordered__semiring(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Olinordered__semidom(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_RealVector_Ometric__space(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Oab__semigroup__add(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Oordered__semiring(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Ono__zero__divisors(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Olinordered__ring(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Olinordered__idom(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Ocomm__semiring(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Nat_Osemiring__char__0(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Oab__group__add(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_SEQ_Ocomplete__space(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Oordered__ring(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Orderings_Opreorder(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Orderings_Olinorder(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Omonoid__mult(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Ocomm__ring__1(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Omonoid__add(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Osemiring__1(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Osemiring__0(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Ogroup__add(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Omult__zero(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Orderings_Oorder(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Int_Oring__char__0(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Osemiring(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Orderings_Oord(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Ouminus(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Oring__1(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Ominus(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Power_Opower(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Ozero(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Oring(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Rings_Oidom(tc_RealDef_Oreal).
% 11.99/11.92 0 [] class_Groups_Oone(tc_RealDef_Oreal).
% 11.99/11.92 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,$c2,$c1).
% 11.99/11.92 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),$c2),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),$c1)).
% 11.99/11.92 end_of_list.
% 11.99/11.92
% 11.99/11.92 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 11.99/11.92
% 11.99/11.92 This ia a non-Horn set with equality. The strategy will be
% 11.99/11.92 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 11.99/11.92 deletion, with positive clauses in sos and nonpositive
% 11.99/11.92 clauses in usable.
% 11.99/11.92
% 11.99/11.92 dependent: set(knuth_bendix).
% 11.99/11.92 dependent: set(anl_eq).
% 11.99/11.92 dependent: set(para_from).
% 11.99/11.92 dependent: set(para_into).
% 11.99/11.92 dependent: clear(para_from_right).
% 11.99/11.92 dependent: clear(para_into_right).
% 11.99/11.92 dependent: set(para_from_vars).
% 11.99/11.92 dependent: set(eq_units_both_ways).
% 11.99/11.92 dependent: set(dynamic_demod_all).
% 11.99/11.92 dependent: set(dynamic_demod).
% 11.99/11.92 dependent: set(order_eq).
% 11.99/11.92 dependent: set(back_demod).
% 11.99/11.92 dependent: set(lrpo).
% 11.99/11.92 dependent: set(hyper_res).
% 11.99/11.92 dependent: set(unit_deletion).
% 11.99/11.92 dependent: set(factor).
% 11.99/11.92
% 11.99/11.92 ------------> process usable:
% 11.99/11.92 ** KEPT (pick-wt=14): 1 [] hAPP(A,$f1(B,A))!=hAPP(B,$f1(B,A))|A=B.
% 11.99/11.92 ** KEPT (pick-wt=12): 2 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,A),hAPP(v_f____,B)).
% 11.99/11.92 ** KEPT (pick-wt=12): 3 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,A),hAPP(v_ga____,B)).
% 11.99/11.92 ** KEPT (pick-wt=30): 4 [] hAPP(A,hAPP(B,C))!=hAPP(D,hAPP(E,F))|hAPP(hAPP(c_Fun_Ocomp(G,H,I,A),B),C)=hAPP(hAPP(c_Fun_Ocomp(J,H,K,D),E),F).
% 11.99/11.92 ** KEPT (pick-wt=18): 5 [] hAPP(c_Fun_Ocomp(A,B,C,D),E)!=F|hAPP(D,hAPP(E,G))=hAPP(F,G).
% 11.99/11.92 ** KEPT (pick-wt=26): 6 [] hAPP(c_Fun_Ocomp(A,B,C,D),E)!=hAPP(c_Fun_Ocomp(F,B,C,G),H)|hAPP(D,hAPP(E,I))=hAPP(G,hAPP(H,I)).
% 11.99/11.92 Following clause subsumed by 6 during input processing: 0 [] hAPP(c_Fun_Ocomp(A,B,C,D),E)!=hAPP(c_Fun_Ocomp(F,B,C,G),H)|hAPP(D,hAPP(E,I))=hAPP(G,hAPP(H,I)).
% 11.99/11.92 ** KEPT (pick-wt=4): 7 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 11.99/11.92 ** KEPT (pick-wt=7): 8 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 11.99/11.92 ** KEPT (pick-wt=7): 9 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 11.99/11.92 Following clause subsumed by 7 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 11.99/11.92 Following clause subsumed by 9 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=A.
% 11.99/11.92 Following clause subsumed by 8 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 11.99/11.92 ** KEPT (pick-wt=14): 10 [] -c_SEQ_Osubse_q(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,C)).
% 11.99/11.92 ** KEPT (pick-wt=12): 11 [] c_SEQ_Osubse_q(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,$f3(A)),hAPP(A,$f2(A))).
% 11.99/11.92 ** KEPT (pick-wt=13): 12 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,C,B).
% 11.99/11.92 ** KEPT (pick-wt=10): 13 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 11.99/11.92 ** KEPT (pick-wt=14): 14 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C).
% 11.99/11.92 ** KEPT (pick-wt=14): 15 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 11.99/11.92 ** KEPT (pick-wt=13): 16 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=D|c_Orderings_Oord__class_Oless(A,D,C).
% 11.99/11.92 ** KEPT (pick-wt=13): 17 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=D|c_Orderings_Oord__class_Oless(A,B,D).
% 11.99/11.92 ** KEPT (pick-wt=13): 18 [] -class_Orderings_Oorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,D,C)|c_Orderings_Oord__class_Oless(A,D,B).
% 11.99/11.92 ** KEPT (pick-wt=13): 19 [] -class_Orderings_Oord(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 11.99/11.92 ** KEPT (pick-wt=10): 20 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 11.99/11.92 Following clause subsumed by 13 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 11.99/11.92 ** KEPT (pick-wt=9): 21 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=B.
% 11.99/11.92 ** KEPT (pick-wt=6): 22 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,B).
% 11.99/11.92 Following clause subsumed by 12 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 11.99/11.92 ** KEPT (pick-wt=9): 23 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,B,C).
% 11.99/11.92 ** KEPT (pick-wt=9): 24 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,B).
% 11.99/11.92 Following clause subsumed by 12 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B)|B=C.
% 11.99/11.92 ** KEPT (pick-wt=10): 25 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 11.99/11.92 Following clause subsumed by 23 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 11.99/11.92 Following clause subsumed by 12 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,C,B).
% 11.99/11.92 Following clause subsumed by 12 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B)|C=B.
% 11.99/11.92 Following clause subsumed by 23 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B)|C!=B.
% 11.99/11.92 Following clause subsumed by 12 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 11.99/11.92 ** KEPT (pick-wt=9): 26 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 11.99/11.92 Following clause subsumed by 13 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 11.99/11.92 Following clause subsumed by 13 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 11.99/11.92 Following clause subsumed by 26 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 11.99/11.92 ** KEPT (pick-wt=16): 27 [] -class_RealVector_Ometric__space(A)| -c_SEQ_OCauchy(A,B)| -c_SEQ_Osubse_q(C)|c_SEQ_OCauchy(A,hAPP(c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B),C)).
% 11.99/11.92 ** KEPT (pick-wt=16): 28 [] -class_SEQ_Ocomplete__space(A)| -c_SEQ_Oconvergent(A,B)| -c_SEQ_Osubse_q(C)|c_SEQ_Oconvergent(A,hAPP(c_Fun_Ocomp(tc_Nat_Onat,A,tc_Nat_Onat,B),C)).
% 11.99/11.92 ** KEPT (pick-wt=13): 29 [] -class_Rings_Olinordered__idom(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 11.99/11.92 ** KEPT (pick-wt=11): 30 [] -c_SEQ_Osubse_q(A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,c_Nat_OSuc(B))).
% 11.99/11.92 ** KEPT (pick-wt=13): 31 [] c_SEQ_Osubse_q(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,$f4(A)),hAPP(A,c_Nat_OSuc($f4(A)))).
% 11.99/11.93 ** KEPT (pick-wt=20): 32 [] -class_Orderings_Oorder(A)| -class_Orderings_Olinorder(B)| -c_Orderings_Oorder__class_Ostrict__mono(B,A,C)| -c_Orderings_Oord__class_Oless(A,hAPP(C,D),hAPP(C,E))|c_Orderings_Oord__class_Oless(B,D,E).
% 11.99/11.93 ** KEPT (pick-wt=20): 33 [] -class_Orderings_Oorder(A)| -class_Orderings_Olinorder(B)| -c_Orderings_Oorder__class_Ostrict__mono(B,A,C)|c_Orderings_Oord__class_Oless(A,hAPP(C,D),hAPP(C,E))| -c_Orderings_Oord__class_Oless(B,D,E).
% 11.99/11.93 ** KEPT (pick-wt=20): 34 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oorder__class_Ostrict__mono(B,A,C)| -c_Orderings_Oord__class_Oless(B,D,E)|c_Orderings_Oord__class_Oless(A,hAPP(C,D),hAPP(C,E)).
% 11.99/11.93 ** KEPT (pick-wt=16): 35 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 11.99/11.93 ** KEPT (pick-wt=16): 36 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 11.99/11.93 Following clause subsumed by 36 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|c_Orderings_Oord__class_Oless(A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C)).
% 11.99/11.93 Following clause subsumed by 35 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 11.99/11.93 ** KEPT (pick-wt=31): 37 [] -c_Record_Oiso__tuple__update__accessor__cong__assist(A,B,C,D)|hAPP(E,hAPP(D,F))!=hAPP(D,F)|hAPP(hAPP(C,hAPP(c_Fun_Ocomp(A,A,A,G),E)),F)=hAPP(hAPP(C,G),F).
% 11.99/11.93 ** KEPT (pick-wt=10): 38 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B)).
% 11.99/11.93 ** KEPT (pick-wt=8): 39 [] -class_RealVector_Ometric__space(A)| -c_SEQ_Oconvergent(A,B)|c_SEQ_OCauchy(A,B).
% 11.99/11.93 ** KEPT (pick-wt=8): 40 [] -class_SEQ_Ocomplete__space(A)| -c_SEQ_OCauchy(A,B)|c_SEQ_Oconvergent(A,B).
% 11.99/11.93 Following clause subsumed by 40 during input processing: 0 [] -class_SEQ_Ocomplete__space(A)| -c_SEQ_OCauchy(A,B)|c_SEQ_Oconvergent(A,B).
% 11.99/11.93 ** KEPT (pick-wt=8): 41 [] -class_SEQ_Ocomplete__space(A)|c_SEQ_OCauchy(A,B)| -c_SEQ_Oconvergent(A,B).
% 11.99/11.93 ** KEPT (pick-wt=8): 42 [] c_Nat_OSuc(A)!=c_Nat_OSuc(B)|A=B.
% 11.99/11.93 ** KEPT (pick-wt=21): 43 [] -c_Record_Oiso__tuple__update__accessor__cong__assist(A,B,C,D)|hAPP(E,hAPP(D,F))!=hAPP(D,F)|hAPP(hAPP(C,E),F)=F.
% 11.99/11.93 ** KEPT (pick-wt=14): 44 [] -class_Nat_Osemiring__char__0(A)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C)|B=C.
% 11.99/11.93 ** KEPT (pick-wt=14): 45 [] -class_Nat_Osemiring__char__0(A)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C)|B!=C.
% 11.99/11.93 Following clause subsumed by 42 during input processing: 0 [] c_Nat_OSuc(A)!=c_Nat_OSuc(B)|A=B.
% 11.99/11.93 ** KEPT (pick-wt=8): 46 [] c_Nat_OSuc(A)=c_Nat_OSuc(B)|A!=B.
% 11.99/11.93 ** KEPT (pick-wt=4): 47 [] c_Nat_OSuc(A)!=A.
% 11.99/11.93 Following clause subsumed by 47 during input processing: 0 [flip.1] c_Nat_OSuc(A)!=A.
% 11.99/11.93 ** KEPT (pick-wt=18): 48 [] -class_Orderings_Oorder(A)| -class_Orderings_Olinorder(B)| -c_Orderings_Oorder__class_Ostrict__mono(B,A,C)|hAPP(C,D)!=hAPP(C,E)|D=E.
% 11.99/11.93 ** KEPT (pick-wt=18): 49 [] -class_Orderings_Oorder(A)| -class_Orderings_Olinorder(B)| -c_Orderings_Oorder__class_Ostrict__mono(B,A,C)|hAPP(C,D)=hAPP(C,E)|D!=E.
% 11.99/11.93 ** KEPT (pick-wt=10): 50 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 11.99/11.93 ** KEPT (pick-wt=9): 51 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 11.99/11.93 ** KEPT (pick-wt=12): 52 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B.
% 11.99/11.93 ** KEPT (pick-wt=13): 53 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),C).
% 11.99/11.93 ** KEPT (pick-wt=13): 54 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Nat_OSuc(A)=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),B).
% 11.99/11.93 ** KEPT (pick-wt=9): 55 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B)).
% 11.99/11.93 ** KEPT (pick-wt=12): 56 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|B=A.
% 11.99/11.93 Following clause subsumed by 52 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A=B.
% 11.99/11.93 ** KEPT (pick-wt=12): 57 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A!=B.
% 11.99/11.93 Following clause subsumed by 50 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 11.99/11.93 Following clause subsumed by 38 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 11.99/11.93 Following clause subsumed by 52 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B.
% 11.99/11.93 Following clause subsumed by 55 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 11.99/11.93 ** KEPT (pick-wt=8): 58 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A!=B.
% 11.99/11.93 ** KEPT (pick-wt=9): 59 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Nat_OSuc(A)).
% 11.99/11.93 ** KEPT (pick-wt=31): 60 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,hAPP(B,$f5(C,D,B,A)),hAPP(B,c_Nat_OSuc($f5(C,D,B,A))))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,D,C)|c_Orderings_Oord__class_Oless(A,hAPP(B,D),hAPP(B,C)).
% 11.99/11.93 ** KEPT (pick-wt=31): 61 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,hAPP(B,$f6(C,D,B,A)),hAPP(B,c_Nat_OSuc($f6(C,D,B,A))))| -c_Orderings_Oord__class_Oless(A,hAPP(B,D),hAPP(B,C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,D,C).
% 11.99/11.93 ** KEPT (pick-wt=31): 62 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,hAPP(B,$f6(C,D,B,A)),hAPP(B,c_Nat_OSuc($f6(C,D,B,A))))|c_Orderings_Oord__class_Oless(A,hAPP(B,D),hAPP(B,C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,D,C).
% 11.99/11.93 ** KEPT (pick-wt=14): 63 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 11.99/11.93 ** KEPT (pick-wt=14): 64 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 11.99/11.93 Following clause subsumed by 63 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 11.99/11.93 Following clause subsumed by 64 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 11.99/11.93 ** KEPT (pick-wt=18): 65 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)|c_Orderings_Oord__class_Oless(B,$f8(C,B,A),$f7(C,B,A))|c_Orderings_Oorder__class_Ostrict__mono(B,A,C).
% 11.99/11.93 ** KEPT (pick-wt=22): 66 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless(A,hAPP(C,$f8(C,B,A)),hAPP(C,$f7(C,B,A)))|c_Orderings_Oorder__class_Ostrict__mono(B,A,C).
% 11.99/11.93 ** KEPT (pick-wt=16): 67 [] -class_Rings_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat__aux(A,B,c_Nat_OSuc(C),D)=c_Nat_Osemiring__1__class_Oof__nat__aux(A,B,C,hAPP(B,D)).
% 11.99/11.93 ** KEPT (pick-wt=14): 68 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B=c_Nat_OSuc(A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,$f9(B,A)).
% 11.99/11.93 ** KEPT (pick-wt=14): 70 [copy,69,flip.3] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B=c_Nat_OSuc(A)|c_Nat_OSuc($f9(B,A))=B.
% 11.99/11.93 ** KEPT (pick-wt=11): 71 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,$f10(B,A)).
% 11.99/11.93 ** KEPT (pick-wt=11): 73 [copy,72,flip.2] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),B)|c_Nat_OSuc($f10(B,A))=B.
% 11.99/11.93 ** KEPT (pick-wt=5): 74 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.93 ** KEPT (pick-wt=12): 75 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)|A=B.
% 11.99/11.93 ** KEPT (pick-wt=12): 76 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)|A!=B.
% 11.99/11.93 Following clause subsumed by 75 during input processing: 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)|A=B.
% 11.99/11.93 Following clause subsumed by 76 during input processing: 0 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)|A!=B.
% 11.99/11.93 ** KEPT (pick-wt=10): 77 [] -class_Rings_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat__aux(A,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)=C.
% 11.99/11.93 ** KEPT (pick-wt=10): 78 [] -class_Rings_Osemiring__1(A)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=5): 80 [copy,79,flip.1] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.93 Following clause subsumed by 80 during input processing: 0 [flip.1] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.93 Following clause subsumed by 80 during input processing: 0 [] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.93 Following clause subsumed by 80 during input processing: 0 [] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.93 Following clause subsumed by 80 during input processing: 0 [flip.1] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.93 Following clause subsumed by 80 during input processing: 0 [] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.93 Following clause subsumed by 74 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.93 Following clause subsumed by 9 during input processing: 0 [] A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 11.99/11.93 Following clause subsumed by 74 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 11.99/11.93 ** KEPT (pick-wt=8): 81 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.93 ** KEPT (pick-wt=15): 82 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 11.99/11.93 ** KEPT (pick-wt=15): 83 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 11.99/11.93 ** KEPT (pick-wt=10): 84 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B),c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=15): 86 [copy,85,flip.3] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nat_OSuc($f11(B,A))=A.
% 11.99/11.93 ** KEPT (pick-wt=15): 87 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f11(B,A),B).
% 11.99/11.93 ** KEPT (pick-wt=9): 88 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.93 ** KEPT (pick-wt=13): 89 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A!=c_Nat_OSuc(C)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,B).
% 11.99/11.93 ** KEPT (pick-wt=10): 90 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.93 Following clause subsumed by 88 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.93 ** KEPT (pick-wt=10): 92 [copy,91,flip.2] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Nat_OSuc($f12(A))=A.
% 11.99/11.93 ** KEPT (pick-wt=9): 93 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|A!=c_Nat_OSuc(B).
% 11.99/11.93 ** KEPT (pick-wt=16): 94 [] -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)).
% 11.99/11.93 ** KEPT (pick-wt=13): 95 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 11.99/11.93 ** KEPT (pick-wt=13): 96 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 11.99/11.93 ** KEPT (pick-wt=29): 97 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),C)),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),C)),B)).
% 11.99/11.93 ** KEPT (pick-wt=10): 99 [copy,98,flip.2] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Nat_OSuc($f13(A))=A.
% 11.99/11.93 ** KEPT (pick-wt=10): 100 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=10): 101 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=16): 103 [copy,102,flip.2] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc($f14(B,A))))=B.
% 11.99/11.93 ** KEPT (pick-wt=14): 104 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|B!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(C))).
% 11.99/11.93 ** KEPT (pick-wt=14): 105 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|c_Groups_Ouminus__class_Ouminus(A,B)=C.
% 11.99/11.93 ** KEPT (pick-wt=23): 106 [] -class_Rings_Olinordered__ring__strict(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=23): 107 [] -class_Rings_Olinordered__ring__strict(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=27): 108 [] -class_Rings_Olinordered__ring__strict(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=11): 109 [] -class_Groups_Oab__group__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),B)=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=11): 110 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),B)=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=14): 111 [] -class_Groups_Ogroup__add(A)|B!=c_Groups_Ouminus__class_Ouminus(A,C)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=14): 112 [] -class_Groups_Ogroup__add(A)|B=c_Groups_Ouminus__class_Ouminus(A,C)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=11): 113 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ouminus__class_Ouminus(A,B))=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=11): 114 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A),A)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 11.99/11.93 ** KEPT (pick-wt=5): 115 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 11.99/11.93 ** KEPT (pick-wt=15): 116 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|A=B.
% 11.99/11.93 ** KEPT (pick-wt=12): 117 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 11.99/11.93 ** KEPT (pick-wt=11): 118 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)))|A!=B.
% 11.99/11.93 ** KEPT (pick-wt=17): 119 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.93 ** KEPT (pick-wt=17): 120 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.93 ** KEPT (pick-wt=18): 121 [] -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).
% 11.99/11.93 ** KEPT (pick-wt=18): 122 [] -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).
% 11.99/11.93 ** KEPT (pick-wt=22): 123 [] -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).
% 11.99/11.93 ** KEPT (pick-wt=10): 124 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))).
% 11.99/11.93 ** KEPT (pick-wt=22): 125 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 11.99/11.93 ** KEPT (pick-wt=20): 126 [] -class_Rings_Osemiring__1(A)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C))=c_Groups_Oplus__class_Oplus(A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C)).
% 11.99/11.93 ** KEPT (pick-wt=24): 128 [copy,127,flip.2] -class_Rings_Osemiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)).
% 11.99/11.93 ** KEPT (pick-wt=10): 129 [] -class_Rings_Osemiring__1(A)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(A).
% 11.99/11.93 ** KEPT (pick-wt=9): 130 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ouminus__class_Ouminus(A,B))=B.
% 11.99/11.93 ** KEPT (pick-wt=17): 131 [] -class_Groups_Oab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oplus__class_Oplus(A,B,C))=c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C)).
% 11.99/11.93 ** KEPT (pick-wt=17): 132 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oplus__class_Oplus(A,B,C))=c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,C),c_Groups_Ouminus__class_Ouminus(A,B)).
% 11.99/11.93 ** KEPT (pick-wt=11): 133 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 11.99/11.93 ** KEPT (pick-wt=11): 134 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 11.99/11.93 ** KEPT (pick-wt=10): 135 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)!=B|B=c_Groups_Oone__class_Oone(A).
% 11.99/11.93 ** KEPT (pick-wt=10): 136 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)=B|B!=c_Groups_Oone__class_Oone(A).
% 11.99/11.93 ** KEPT (pick-wt=11): 137 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 11.99/11.93 ** KEPT (pick-wt=11): 138 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 11.99/11.93 ** KEPT (pick-wt=12): 139 [] -class_Groups_Ogroup__add(A)|B!=c_Groups_Ouminus__class_Ouminus(A,C)|C=c_Groups_Ouminus__class_Ouminus(A,B).
% 11.99/11.93 Following clause subsumed by 139 during input processing: 0 [] -class_Groups_Ogroup__add(A)|B=c_Groups_Ouminus__class_Ouminus(A,C)|C!=c_Groups_Ouminus__class_Ouminus(A,B).
% 11.99/11.93 ** KEPT (pick-wt=13): 140 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),C))=C.
% 11.99/11.93 ** KEPT (pick-wt=12): 141 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=C|c_Groups_Ouminus__class_Ouminus(A,C)=B.
% 11.99/11.93 Following clause subsumed by 141 during input processing: 0 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=C|c_Groups_Ouminus__class_Ouminus(A,C)!=B.
% 11.99/11.93 ** KEPT (pick-wt=12): 142 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=c_Groups_Ouminus__class_Ouminus(A,C)|B=C.
% 11.99/11.93 ** KEPT (pick-wt=12): 143 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=c_Groups_Ouminus__class_Ouminus(A,C)|B!=C.
% 11.99/11.93 ** KEPT (pick-wt=13): 144 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Oplus__class_Oplus(A,B,C))=C.
% 11.99/11.93 ** KEPT (pick-wt=17): 145 [] -class_Groups_Oab__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 11.99/11.93 ** KEPT (pick-wt=25): 146 [] -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)).
% 11.99/11.93 ** KEPT (pick-wt=14): 147 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 11.99/11.93 ** KEPT (pick-wt=14): 148 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,B,D)|C!=D.
% 11.99/11.93 ** KEPT (pick-wt=14): 149 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,D,C)|B=D.
% 11.99/11.93 ** KEPT (pick-wt=14): 150 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,D,C)|B!=D.
% 11.99/11.93 Following clause subsumed by 147 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 11.99/11.93 ** KEPT (pick-wt=14): 151 [] -class_Groups_Ocancel__ab__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 11.99/11.93 Following clause subsumed by 149 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,D,C)|B=D.
% 11.99/11.93 ** KEPT (pick-wt=32): 153 [copy,152,flip.2] -class_Rings_Osemiring(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D),E)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),E)).
% 11.99/11.93 ** KEPT (pick-wt=23): 154 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)|B=C|B=c_Groups_Ouminus__class_Ouminus(A,C).
% 11.99/11.93 ** KEPT (pick-wt=18): 155 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)|B!=C.
% 11.99/11.93 ** KEPT (pick-wt=20): 156 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)|B!=c_Groups_Ouminus__class_Ouminus(A,C).
% 11.99/11.93 ** KEPT (pick-wt=26): 157 [] -class_Rings_Ocomm__semiring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 11.99/11.93 ** KEPT (pick-wt=21): 158 [] -class_Rings_Oring__1__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)!=c_Groups_Oone__class_Oone(A)|B=c_Groups_Oone__class_Oone(A)|B=c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)).
% 11.99/11.93 ** KEPT (pick-wt=15): 159 [] -class_Rings_Oring__1__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=c_Groups_Oone__class_Oone(A)|B!=c_Groups_Oone__class_Oone(A).
% 11.99/11.93 ** KEPT (pick-wt=17): 160 [] -class_Rings_Oring__1__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=c_Groups_Oone__class_Oone(A)|B!=c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A)).
% 11.99/11.93 ** KEPT (pick-wt=19): 161 [] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C).
% 11.99/11.93 ** KEPT (pick-wt=19): 162 [] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,B)),C)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ouminus__class_Ouminus(A,C)).
% 11.99/11.93 ** KEPT (pick-wt=19): 164 [copy,163,flip.2] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,B)),C)=c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 11.99/11.93 ** KEPT (pick-wt=19): 166 [copy,165,flip.2] -class_Rings_Oring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ouminus__class_Ouminus(A,C))=c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 11.99/11.93 ** KEPT (pick-wt=9): 167 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=12): 168 [] -class_Groups_Ogroup__add(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Ouminus__class_Ouminus(A,B)|c_Groups_Ozero__class_Ozero(A)=B.
% 11.99/11.93 ** KEPT (pick-wt=12): 169 [] -class_Groups_Ogroup__add(A)|c_Groups_Ozero__class_Ozero(A)=c_Groups_Ouminus__class_Ouminus(A,B)|c_Groups_Ozero__class_Ozero(A)!=B.
% 11.99/11.93 ** KEPT (pick-wt=11): 171 [copy,170,flip.2] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=11): 173 [copy,172,flip.2] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=12): 174 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=12): 175 [] -class_Groups_Ogroup__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 Following clause subsumed by 171 during input processing: 0 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 Following clause subsumed by 173 during input processing: 0 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ouminus__class_Ouminus(A,B)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=23): 176 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),C)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),C),B)).
% 11.99/11.93 ** KEPT (pick-wt=14): 177 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C))|c_Orderings_Oord__class_Oless(A,C,B).
% 11.99/11.93 ** KEPT (pick-wt=14): 178 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ouminus__class_Ouminus(A,C))| -c_Orderings_Oord__class_Oless(A,C,B).
% 11.99/11.93 ** KEPT (pick-wt=14): 179 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,C),B).
% 11.99/11.93 Following clause subsumed by 179 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,C),B).
% 11.99/11.93 ** KEPT (pick-wt=14): 180 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,C))|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ouminus__class_Ouminus(A,B)).
% 11.99/11.93 Following clause subsumed by 180 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,C))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ouminus__class_Ouminus(A,B)).
% 11.99/11.93 ** KEPT (pick-wt=9): 181 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 11.99/11.93 ** KEPT (pick-wt=9): 182 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 11.99/11.93 ** KEPT (pick-wt=13): 183 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oplus__class_Oplus(A,B,B)|B=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=13): 184 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)=c_Groups_Oplus__class_Oplus(A,B,B)|B!=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=9): 185 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 11.99/11.93 ** KEPT (pick-wt=9): 186 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 11.99/11.93 ** KEPT (pick-wt=16): 187 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless(A,C,D).
% 11.99/11.93 ** KEPT (pick-wt=16): 188 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless(A,B,D).
% 11.99/11.93 ** KEPT (pick-wt=20): 189 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 11.99/11.93 ** KEPT (pick-wt=16): 190 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)).
% 11.99/11.93 ** KEPT (pick-wt=16): 191 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)).
% 11.99/11.93 Following clause subsumed by 187 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless(A,C,D).
% 11.99/11.93 ** KEPT (pick-wt=16): 192 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))| -c_Orderings_Oord__class_Oless(A,C,D).
% 11.99/11.93 Following clause subsumed by 188 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless(A,B,D).
% 11.99/11.93 ** KEPT (pick-wt=16): 193 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))| -c_Orderings_Oord__class_Oless(A,B,D).
% 11.99/11.93 ** KEPT (pick-wt=28): 194 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=24): 195 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))|B=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=24): 196 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))|C=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=20): 197 [] -class_Rings_Olinordered__ring(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)),c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=12): 198 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A))).
% 11.99/11.93 ** KEPT (pick-wt=16): 199 [] -class_Rings_Osemiring__1(A)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),c_Nat_OSuc(B))=c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)).
% 11.99/11.93 ** KEPT (pick-wt=13): 200 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Oplus__class_Oplus(A,B,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=13): 201 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Oplus__class_Oplus(A,B,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=19): 202 [] -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).
% 11.99/11.93 Following clause subsumed by 202 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).
% 11.99/11.93 ** KEPT (pick-wt=19): 203 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=15): 204 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=15): 205 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.93 ** KEPT (pick-wt=12): 206 [] -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).
% 11.99/11.93 ** KEPT (pick-wt=12): 207 [] -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).
% 11.99/11.93 ** KEPT (pick-wt=7): 208 [] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 11.99/11.93 Following clause subsumed by 208 during input processing: 0 [flip.2] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 11.99/11.93 ** KEPT (pick-wt=14): 209 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)).
% 11.99/11.93 ** KEPT (pick-wt=13): 210 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 11.99/11.93 ** KEPT (pick-wt=13): 211 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 11.99/11.93 ** KEPT (pick-wt=14): 212 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 11.99/11.93 ** KEPT (pick-wt=14): 213 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ouminus__class_Ouminus(A,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 11.99/11.93 ** KEPT (pick-wt=14): 214 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=14): 215 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ouminus__class_Ouminus(A,B))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=20): 216 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=20): 217 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 11.99/11.93 ** KEPT (pick-wt=15): 218 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=15): 219 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=15): 220 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 11.99/11.93 ** KEPT (pick-wt=15): 221 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 11.99/11.93 ** KEPT (pick-wt=13): 222 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,B))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=13): 223 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ouminus__class_Ouminus(A,B))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=18): 224 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 11.99/11.93 ** KEPT (pick-wt=15): 225 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=15): 226 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=25): 227 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)).
% 11.99/11.93 ** KEPT (pick-wt=25): 228 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 11.99/11.93 ** KEPT (pick-wt=25): 229 [] -class_Rings_Olinordered__comm__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)).
% 11.99/11.93 ** KEPT (pick-wt=25): 230 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)).
% 11.99/11.93 ** KEPT (pick-wt=25): 231 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 11.99/11.93 ** KEPT (pick-wt=22): 232 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 11.99/11.93 ** KEPT (pick-wt=22): 233 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=25): 234 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,D,C).
% 11.99/11.93 Following clause subsumed by 227 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -c_Orderings_Oord__class_Oless(A,D,C).
% 11.99/11.93 ** KEPT (pick-wt=22): 235 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 11.99/11.93 ** KEPT (pick-wt=22): 236 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C).
% 11.99/11.93 Following clause subsumed by 233 during input processing: 0 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=22): 237 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=22): 238 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 11.99/11.93 ** KEPT (pick-wt=25): 239 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,C,D).
% 11.99/11.93 ** KEPT (pick-wt=25): 240 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -c_Orderings_Oord__class_Oless(A,C,D).
% 11.99/11.93 ** KEPT (pick-wt=26): 241 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=25): 242 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,D,C).
% 11.99/11.93 ** KEPT (pick-wt=25): 243 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=24): 244 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,D,C).
% 11.99/11.93 Following clause subsumed by 240 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D).
% 11.99/11.93 Following clause subsumed by 227 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,D,C).
% 11.99/11.93 ** KEPT (pick-wt=26): 245 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=25): 246 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,D,B).
% 11.99/11.93 ** KEPT (pick-wt=25): 247 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|c_Orderings_Oord__class_Oless(A,B,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=24): 248 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|c_Orderings_Oord__class_Oless(A,B,D)|c_Orderings_Oord__class_Oless(A,D,B).
% 11.99/11.93 ** KEPT (pick-wt=25): 249 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless(A,B,D).
% 11.99/11.93 Following clause subsumed by 228 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,D,B).
% 11.99/11.93 ** KEPT (pick-wt=12): 250 [] -class_Rings_Olinordered__ring(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=8): 251 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)).
% 11.99/11.93 ** KEPT (pick-wt=8): 252 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)).
% 11.99/11.93 ** KEPT (pick-wt=15): 253 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A))!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.93 ** KEPT (pick-wt=15): 254 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A))!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.93 ** KEPT (pick-wt=19): 255 [] c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.93 ** KEPT (pick-wt=12): 256 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))).
% 11.99/11.93 ** KEPT (pick-wt=11): 257 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.93 ** KEPT (pick-wt=11): 258 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.93 ** KEPT (pick-wt=8): 259 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 11.99/11.93 ** KEPT (pick-wt=15): 261 [copy,260,flip.2] -class_Rings_Ocomm__ring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A))),B)=c_Groups_Ouminus__class_Ouminus(A,B).
% 11.99/11.93 ** KEPT (pick-wt=18): 263 [copy,262,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A))),B)=c_Groups_Oplus__class_Oplus(A,B,B).
% 11.99/11.93 ** KEPT (pick-wt=22): 265 [copy,264,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))),C)=c_Groups_Oplus__class_Oplus(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 11.99/11.93 ** KEPT (pick-wt=22): 267 [copy,266,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))),C)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),C).
% 11.99/11.93 ** KEPT (pick-wt=14): 268 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ouminus__class_Ouminus(A,B).
% 11.99/11.93 ** KEPT (pick-wt=14): 269 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ouminus__class_Ouminus(A,B).
% 11.99/11.93 ** KEPT (pick-wt=31): 270 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B=c_Groups_Ozero__class_Ozero(A)|C!=D|E=F|c_Groups_Oplus__class_Oplus(A,C,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E))!=c_Groups_Oplus__class_Oplus(A,D,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),F)).
% 11.99/11.93 ** KEPT (pick-wt=19): 271 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ouminus__class_Ouminus(A,C))=c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 11.99/11.93 Following clause subsumed by 271 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ouminus__class_Ouminus(A,C))=c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 11.99/11.93 ** KEPT (pick-wt=19): 272 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,B)),C)=c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 11.99/11.93 ** KEPT (pick-wt=16): 274 [copy,273,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).
% 11.99/11.93 ** KEPT (pick-wt=12): 275 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)|A=C.
% 11.99/11.93 ** KEPT (pick-wt=12): 276 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)|A!=C.
% 11.99/11.93 ** KEPT (pick-wt=12): 277 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)|B=C.
% 11.99/11.93 ** KEPT (pick-wt=12): 278 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)|B!=C.
% 11.99/11.93 ** KEPT (pick-wt=13): 279 [] 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).
% 11.99/11.93 ** KEPT (pick-wt=13): 280 [] 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).
% 11.99/11.93 ** KEPT (pick-wt=17): 281 [] 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).
% 11.99/11.93 Following clause subsumed by 279 during input processing: 0 [flip.1] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 11.99/11.93 Following clause subsumed by 280 during input processing: 0 [flip.1] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 11.99/11.93 Following clause subsumed by 281 during input processing: 0 [flip.1] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 11.99/11.93 ** KEPT (pick-wt=11): 282 [] 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).
% 11.99/11.93 ** KEPT (pick-wt=11): 283 [] 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).
% 11.99/11.93 ** KEPT (pick-wt=15): 284 [] 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).
% 11.99/11.93 ** KEPT (pick-wt=10): 285 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=A|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 11.99/11.93 ** KEPT (pick-wt=17): 286 [] 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).
% 11.99/11.93 ** KEPT (pick-wt=13): 287 [] 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).
% 11.99/11.93 ** KEPT (pick-wt=13): 288 [] 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).
% 11.99/11.93 ** KEPT (pick-wt=20): 289 [] 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).
% 11.99/11.93 ** KEPT (pick-wt=16): 290 [] 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.
% 11.99/11.93 ** KEPT (pick-wt=17): 291 [] 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).
% 11.99/11.93 ** KEPT (pick-wt=20): 292 [] 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).
% 11.99/11.93 ** KEPT (pick-wt=16): 293 [] 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.
% 11.99/11.93 ** KEPT (pick-wt=17): 294 [] 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).
% 11.99/11.93 ** KEPT (pick-wt=7): 295 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),A).
% 11.99/11.93 ** KEPT (pick-wt=7): 296 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),B).
% 11.99/11.93 ** KEPT (pick-wt=14): 297 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 11.99/11.93 ** KEPT (pick-wt=14): 298 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 11.99/11.93 ** KEPT (pick-wt=11): 299 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 11.99/11.93 ** KEPT (pick-wt=11): 300 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 11.99/11.93 Following clause subsumed by 299 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 11.99/11.93 Following clause subsumed by 300 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 11.99/11.93 ** KEPT (pick-wt=14): 301 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 11.99/11.93 ** KEPT (pick-wt=18): 302 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)).
% 11.99/11.93 ** KEPT (pick-wt=17): 303 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,D)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D).
% 11.99/11.94 ** KEPT (pick-wt=11): 304 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C).
% 11.99/11.94 ** KEPT (pick-wt=18): 305 [] 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.
% 11.99/11.94 Following clause subsumed by 290 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.
% 11.99/11.94 ** KEPT (pick-wt=17): 306 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=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).
% 11.99/11.94 ** KEPT (pick-wt=18): 307 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=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)).
% 11.99/11.94 ** KEPT (pick-wt=16): 308 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=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).
% 11.99/11.94 ** KEPT (pick-wt=17): 309 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=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)).
% 11.99/11.94 ** KEPT (pick-wt=17): 310 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=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).
% 11.99/11.94 ** KEPT (pick-wt=17): 311 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=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)).
% 11.99/11.94 ** KEPT (pick-wt=17): 312 [] 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).
% 11.99/11.94 ** KEPT (pick-wt=18): 313 [] 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)).
% 11.99/11.94 ** KEPT (pick-wt=16): 314 [] 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).
% 11.99/11.94 ** KEPT (pick-wt=17): 315 [] 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)).
% 11.99/11.94 ** KEPT (pick-wt=17): 316 [] 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).
% 11.99/11.94 ** KEPT (pick-wt=17): 317 [] 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)).
% 11.99/11.94 ** KEPT (pick-wt=18): 318 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 11.99/11.94 Following clause subsumed by 299 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 11.99/11.94 Following clause subsumed by 300 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 11.99/11.94 ** KEPT (pick-wt=13): 320 [copy,319,flip.2] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,$f15(B,A)))=B.
% 11.99/11.94 ** KEPT (pick-wt=11): 321 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)).
% 11.99/11.94 ** KEPT (pick-wt=15): 322 [] 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)).
% 11.99/11.94 ** KEPT (pick-wt=15): 323 [] 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)).
% 11.99/11.94 ** KEPT (pick-wt=20): 324 [] 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)).
% 11.99/11.94 ** KEPT (pick-wt=23): 325 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)).
% 11.99/11.94 ** KEPT (pick-wt=23): 326 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)).
% 11.99/11.94 ** KEPT (pick-wt=19): 327 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 11.99/11.94 ** KEPT (pick-wt=18): 328 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C).
% 11.99/11.94 Following clause subsumed by 326 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C).
% 11.99/11.94 ** KEPT (pick-wt=19): 329 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 11.99/11.94 ** KEPT (pick-wt=18): 330 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 11.99/11.94 Following clause subsumed by 325 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 11.99/11.94 ** KEPT (pick-wt=15): 331 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 11.99/11.94 ** KEPT (pick-wt=15): 332 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 11.99/11.94 ** KEPT (pick-wt=20): 333 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 11.99/11.94 Following clause subsumed by 330 during input processing: 0 [] -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))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 11.99/11.94 ** KEPT (pick-wt=20): 334 [] 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))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 11.99/11.94 ** KEPT (pick-wt=23): 335 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)|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)).
% 11.99/11.94 ** KEPT (pick-wt=21): 336 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)).
% 11.99/11.94 ** KEPT (pick-wt=21): 337 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),A)).
% 11.99/11.94 ** KEPT (pick-wt=35): 338 [] -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)).
% 11.99/11.94 ** KEPT (pick-wt=35): 339 [] -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)).
% 11.99/11.94 ** KEPT (pick-wt=35): 340 [] -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))).
% 11.99/11.94 ** KEPT (pick-wt=25): 341 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)),C).
% 11.99/11.94 ** KEPT (pick-wt=25): 342 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 11.99/11.94 Following clause subsumed by 342 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)).
% 11.99/11.94 ** KEPT (pick-wt=25): 343 [] -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)).
% 11.99/11.94 ** KEPT (pick-wt=15): 344 [] -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).
% 11.99/11.94 ** KEPT (pick-wt=23): 345 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,E))=c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 11.99/11.94 ** KEPT (pick-wt=17): 346 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,D),C).
% 11.99/11.94 ** KEPT (pick-wt=17): 347 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 11.99/11.94 Following clause subsumed by 347 during input processing: 0 [flip.2] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 11.99/11.94 ** KEPT (pick-wt=17): 348 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 11.99/11.94 ** KEPT (pick-wt=11): 349 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,C,B).
% 11.99/11.94 ** KEPT (pick-wt=12): 350 [] -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).
% 11.99/11.94 Following clause subsumed by 350 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).
% 11.99/11.94 ** KEPT (pick-wt=12): 351 [] -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).
% 11.99/11.94 ** KEPT (pick-wt=12): 352 [] -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).
% 11.99/11.94 Following clause subsumed by 352 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).
% 11.99/11.94 ** KEPT (pick-wt=12): 353 [] -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).
% 11.99/11.94 ** KEPT (pick-wt=12): 355 [copy,354,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=B|C=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.94 ** KEPT (pick-wt=12): 357 [copy,356,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,B,C)=B|C!=c_Groups_Ozero__class_Ozero(A).
% 11.99/11.94 ** KEPT (pick-wt=9): 358 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 11.99/11.94 ** KEPT (pick-wt=9): 359 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 11.99/11.94 ** KEPT (pick-wt=37): 360 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))!=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|B=D|C=E.
% 11.99/11.94 ** KEPT (pick-wt=34): 361 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|B!=D.
% 11.99/11.94 ** KEPT (pick-wt=34): 362 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),E))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|C!=E.
% 11.99/11.94 ** KEPT (pick-wt=26): 364 [copy,363,flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 11.99/11.94 ** KEPT (pick-wt=26): 365 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 11.99/11.94 Following clause subsumed by 365 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 11.99/11.94 Following clause subsumed by 364 during input processing: 0 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 11.99/11.94 Following clause subsumed by 360 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B=C|D=E|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))!=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 11.99/11.94 Following clause subsumed by 361 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B!=C|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),E),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 11.99/11.94 Following clause subsumed by 362 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B!=C|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B)).
% 11.99/11.94 ** KEPT (pick-wt=26): 366 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 11.99/11.94 ** KEPT (pick-wt=26): 367 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 11.99/11.94 Following clause subsumed by 366 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 11.99/11.94 ** KEPT (pick-wt=11): 368 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 11.99/11.94 ** KEPT (pick-wt=11): 369 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 11.99/11.94 Following clause subsumed by 272 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ouminus__class_Ouminus(A,B)),C)=c_Groups_Ouminus__class_Ouminus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 11.99/11.94 ** KEPT (pick-wt=21): 370 [] -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.
% 11.99/11.94 Following clause subsumed by 290 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B!=C.
% 11.99/11.94 Following clause subsumed by 330 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 11.99/11.94 Following clause subsumed by 325 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 12.07/11.94 Following clause subsumed by 289 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=C.
% 12.07/11.94 Following clause subsumed by 291 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.94 Following clause subsumed by 290 during input processing: 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B!=C.
% 12.07/11.94 ** KEPT (pick-wt=15): 372 [copy,371,flip.2] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc($f16(A))))=A.
% 12.07/11.94 ** KEPT (pick-wt=11): 373 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),$f17(A)).
% 12.07/11.94 ** KEPT (pick-wt=12): 375 [copy,374,flip.2] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),$f17(A))=A.
% 12.07/11.94 ** KEPT (pick-wt=48): 376 [] -class_Rings_Olinordered__semiring__1__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -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))|c_Groups_Oplus__class_Oplus(A,E,F)!=c_Groups_Oone__class_Oone(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D)),C).
% 12.07/11.94 ** KEPT (pick-wt=8): 377 [] -class_Orderings_Opreorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),B)).
% 12.07/11.94 ** KEPT (pick-wt=20): 378 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 12.07/11.94 ** KEPT (pick-wt=20): 379 [] -class_Rings_Olinordered__semidom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 12.07/11.94 ** KEPT (pick-wt=14): 380 [] -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)).
% 12.07/11.94 ** KEPT (pick-wt=20): 381 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=20): 382 [] -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)).
% 12.07/11.94 ** KEPT (pick-wt=17): 383 [] -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.
% 12.07/11.94 ** KEPT (pick-wt=20): 384 [] -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)).
% 12.07/11.94 Following clause subsumed by 383 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.
% 12.07/11.94 ** KEPT (pick-wt=17): 385 [] -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)).
% 12.07/11.94 ** KEPT (pick-wt=17): 386 [] -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)).
% 12.07/11.94 ** KEPT (pick-wt=17): 387 [] -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)).
% 12.07/11.94 ** KEPT (pick-wt=17): 388 [] -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)).
% 12.07/11.94 Following clause subsumed by 383 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.
% 12.07/11.94 ** KEPT (pick-wt=17): 389 [] -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.
% 12.07/11.94 Following clause subsumed by 381 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))).
% 12.07/11.94 ** KEPT (pick-wt=11): 390 [] -class_Orderings_Opreorder(A)|B!=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C)).
% 12.07/11.94 ** KEPT (pick-wt=11): 391 [] -class_Orderings_Oorder(A)|B!=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C)).
% 12.07/11.94 ** KEPT (pick-wt=11): 392 [] -class_Orderings_Oorder(A)|B!=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 12.07/11.94 Following clause subsumed by 383 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__e_q(A,C),B)).
% 12.07/11.94 Following clause subsumed by 380 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)).
% 12.07/11.94 Following clause subsumed by 381 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))).
% 12.07/11.94 ** KEPT (pick-wt=28): 393 [] -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,$f18(D,C,B,A))),hAPP(D,$f18(D,C,B,A)))).
% 12.07/11.94 ** KEPT (pick-wt=18): 394 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 12.07/11.94 ** KEPT (pick-wt=18): 395 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 12.07/11.94 Following clause subsumed by 394 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 12.07/11.94 Following clause subsumed by 395 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 12.07/11.94 ** KEPT (pick-wt=16): 396 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -c_Orderings_Oord__class_Oless(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C).
% 12.07/11.94 ** KEPT (pick-wt=16): 397 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 12.07/11.94 ** KEPT (pick-wt=16): 398 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),B))|c_Orderings_Oord__class_Oless(A,D,C).
% 12.07/11.94 ** KEPT (pick-wt=16): 399 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D))|c_Orderings_Oord__class_Oless(A,B,D).
% 12.07/11.94 ** KEPT (pick-wt=15): 400 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|C=B|c_Orderings_Oord__class_Oless(A,B,C).
% 12.07/11.94 ** KEPT (pick-wt=15): 401 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|B=C|c_Orderings_Oord__class_Oless(A,B,C).
% 12.07/11.94 Following clause subsumed by 401 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 12.07/11.94 ** KEPT (pick-wt=15): 402 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 12.07/11.94 Following clause subsumed by 23 during input processing: 0 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 12.07/11.94 ** KEPT (pick-wt=12): 403 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C)).
% 12.07/11.94 ** KEPT (pick-wt=12): 404 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.07/11.94 Following clause subsumed by 400 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B))|c_Orderings_Oord__class_Oless(A,C,B).
% 12.07/11.94 Following clause subsumed by 401 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|c_Orderings_Oord__class_Oless(A,B,C).
% 12.07/11.94 Following clause subsumed by 402 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|B=C.
% 12.07/11.94 ** KEPT (pick-wt=15): 405 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|B!=C.
% 12.07/11.94 ** KEPT (pick-wt=12): 406 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|c_Orderings_Oord__class_Oless(A,C,B).
% 12.07/11.94 Following clause subsumed by 406 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 12.07/11.94 Following clause subsumed by 401 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 12.07/11.94 ** KEPT (pick-wt=12): 407 [] -class_Orderings_Oorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -c_Orderings_Oord__class_Oless(A,B,C).
% 12.07/11.94 Following clause subsumed by 391 during input processing: 0 [] -class_Orderings_Oorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|B!=C.
% 12.07/11.94 Following clause subsumed by 403 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C)).
% 12.07/11.94 ** KEPT (pick-wt=12): 408 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 12.07/11.94 ** KEPT (pick-wt=18): 409 [] -class_Orderings_Opreorder(A)|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)).
% 12.07/11.94 Following clause subsumed by 407 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C)).
% 12.07/11.94 Following clause subsumed by 26 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 12.07/11.94 Following clause subsumed by 401 during input processing: 0 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|B=C.
% 12.07/11.94 Following clause subsumed by 406 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|c_Orderings_Oord__class_Oless(A,C,B).
% 12.07/11.94 Following clause subsumed by 406 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|c_Orderings_Oord__class_Oless(A,C,B).
% 12.07/11.94 Following clause subsumed by 404 during input processing: 0 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.07/11.94 Following clause subsumed by 406 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 12.07/11.94 Following clause subsumed by 404 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 12.07/11.94 ** KEPT (pick-wt=20): 410 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Groups_Oplus__class_Oplus(A,D,C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 12.07/11.94 ** KEPT (pick-wt=20): 411 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Groups_Oplus__class_Oplus(A,D,C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 12.07/11.94 ** KEPT (pick-wt=20): 412 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Groups_Oplus__class_Oplus(A,B,D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D)).
% 12.07/11.94 ** KEPT (pick-wt=20): 413 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Groups_Oplus__class_Oplus(A,B,D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D)).
% 12.07/11.94 ** KEPT (pick-wt=20): 414 [] -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,c_Groups_Oplus__class_Oplus(A,B,D)),c_Groups_Oplus__class_Oplus(A,C,D))).
% 12.07/11.94 ** KEPT (pick-wt=20): 415 [] -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,c_Groups_Oplus__class_Oplus(A,D,B)),c_Groups_Oplus__class_Oplus(A,D,C))).
% 12.07/11.94 ** KEPT (pick-wt=26): 416 [] -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,c_Groups_Oplus__class_Oplus(A,B,D)),c_Groups_Oplus__class_Oplus(A,C,E))).
% 12.07/11.94 Following clause subsumed by 410 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Groups_Oplus__class_Oplus(A,D,C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),D)).
% 12.07/11.94 Following clause subsumed by 412 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Groups_Oplus__class_Oplus(A,B,D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D)).
% 12.07/11.94 ** KEPT (pick-wt=18): 417 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ouminus__class_Ouminus(A,C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ouminus__class_Ouminus(A,B))).
% 12.07/11.94 Following clause subsumed by 417 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ouminus__class_Ouminus(A,C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ouminus__class_Ouminus(A,B))).
% 12.07/11.94 ** KEPT (pick-wt=18): 418 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,C)),B)).
% 12.07/11.94 Following clause subsumed by 418 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,C)),B)).
% 12.07/11.94 ** KEPT (pick-wt=18): 419 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 12.07/11.94 ** KEPT (pick-wt=18): 420 [] -class_Groups_Oordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 12.07/11.94 Following clause subsumed by 420 during input processing: 0 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,C)),c_Groups_Ouminus__class_Ouminus(A,B))).
% 12.07/11.94 ** KEPT (pick-wt=11): 421 [] -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).
% 12.07/11.94 ** KEPT (pick-wt=11): 422 [] 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).
% 12.07/11.94 ** KEPT (pick-wt=13): 423 [] -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)).
% 12.07/11.94 ** KEPT (pick-wt=17): 424 [] -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).
% 12.07/11.94 ** KEPT (pick-wt=13): 425 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=14): 426 [] -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)).
% 12.07/11.94 ** KEPT (pick-wt=14): 427 [] 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)).
% 12.07/11.94 Following clause subsumed by 424 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).
% 12.07/11.94 Following clause subsumed by 425 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)).
% 12.07/11.94 ** KEPT (pick-wt=11): 428 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),c_Nat_OSuc(B)))|A!=c_Nat_OSuc(B).
% 12.07/11.94 ** KEPT (pick-wt=13): 429 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(B)),A)).
% 12.07/11.94 ** KEPT (pick-wt=7): 430 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A)),A)).
% 12.07/11.94 ** KEPT (pick-wt=10): 431 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 12.07/11.94 ** KEPT (pick-wt=9): 432 [] A!=B|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 12.07/11.94 ** KEPT (pick-wt=13): 433 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|A=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.07/11.94 Following clause subsumed by 431 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 12.07/11.94 Following clause subsumed by 431 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 12.07/11.94 Following clause subsumed by 433 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B.
% 12.07/11.94 Following clause subsumed by 431 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.07/11.94 Following clause subsumed by 432 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|A!=B.
% 12.07/11.94 Following clause subsumed by 431 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 12.07/11.94 Following clause subsumed by 8 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 12.07/11.94 Following clause subsumed by 433 during input processing: 0 [] 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.
% 12.07/11.94 ** KEPT (pick-wt=14): 435 [copy,434,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,$f19(B,A))=B.
% 12.07/11.94 ** KEPT (pick-wt=12): 436 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C).
% 12.07/11.94 ** KEPT (pick-wt=18): 437 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 12.07/11.94 ** KEPT (pick-wt=18): 438 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C)).
% 12.07/11.94 ** KEPT (pick-wt=15): 439 [] -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_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C))).
% 12.07/11.94 ** KEPT (pick-wt=15): 440 [] -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_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B))).
% 12.07/11.94 Following clause subsumed by 439 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C))).
% 12.07/11.94 Following clause subsumed by 440 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B))).
% 12.07/11.94 ** KEPT (pick-wt=18): 441 [] -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_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C))).
% 12.07/11.94 ** KEPT (pick-wt=24): 442 [] -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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D))).
% 12.07/11.94 ** KEPT (pick-wt=15): 443 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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)).
% 12.07/11.94 ** KEPT (pick-wt=15): 444 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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)).
% 12.07/11.94 Following clause subsumed by 444 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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)).
% 12.07/11.94 Following clause subsumed by 443 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,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)).
% 12.07/11.94 ** KEPT (pick-wt=10): 445 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B)).
% 12.07/11.94 ** KEPT (pick-wt=7): 446 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|A!=B.
% 12.07/11.94 ** KEPT (pick-wt=13): 447 [] 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.
% 12.07/11.94 ** KEPT (pick-wt=22): 448 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=22): 449 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=28): 450 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=18): 451 [] -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,c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,A)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,C,B))).
% 12.07/11.94 ** KEPT (pick-wt=10): 452 [] -c_SEQ_Osubse_q(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),hAPP(A,B))).
% 12.07/11.94 ** KEPT (pick-wt=24): 453 [] -class_Orderings_Oorder(A)| -class_Orderings_Olinorder(B)| -c_Orderings_Oorder__class_Ostrict__mono(B,A,C)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,D)),hAPP(C,E)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(B,D),E)).
% 12.07/11.94 ** KEPT (pick-wt=24): 454 [] -class_Orderings_Oorder(A)| -class_Orderings_Olinorder(B)| -c_Orderings_Oorder__class_Ostrict__mono(B,A,C)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,D)),hAPP(C,E)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(B,D),E)).
% 12.07/11.94 ** KEPT (pick-wt=14): 455 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=28): 456 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=28): 457 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=28): 458 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=28): 459 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=28): 460 [] -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)).
% 12.07/11.94 ** KEPT (pick-wt=28): 461 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=28): 462 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=28): 463 [] -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)).
% 12.07/11.94 ** KEPT (pick-wt=28): 464 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=28): 465 [] -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)).
% 12.07/11.94 ** KEPT (pick-wt=28): 466 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=28): 467 [] -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)).
% 12.07/11.94 ** KEPT (pick-wt=28): 468 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=28): 469 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=28): 470 [] -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))).
% 12.07/11.94 Following clause subsumed by 470 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))).
% 12.07/11.94 ** KEPT (pick-wt=28): 471 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=31): 472 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=31): 473 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=31): 474 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=31): 475 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=31): 476 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=44): 477 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=44): 478 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=28): 479 [] -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))).
% 12.07/11.94 Following clause subsumed by 471 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))).
% 12.07/11.94 Following clause subsumed by 469 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))).
% 12.07/11.94 Following clause subsumed by 470 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))).
% 12.07/11.94 ** KEPT (pick-wt=26): 480 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C)),c_Groups_Ozero__class_Ozero(A))).
% 12.07/11.94 ** KEPT (pick-wt=24): 481 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Oplus__class_Oplus(A,D,B))).
% 12.07/11.94 ** KEPT (pick-wt=24): 482 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),c_Groups_Oplus__class_Oplus(A,B,D))).
% 12.07/11.94 ** KEPT (pick-wt=27): 483 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 12.07/11.94 ** KEPT (pick-wt=27): 484 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 12.07/11.94 ** KEPT (pick-wt=31): 485 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 12.07/11.94 Following clause subsumed by 482 during input processing: 0 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Oplus__class_Oplus(A,B,C))).
% 12.07/11.94 ** KEPT (pick-wt=19): 486 [] -class_Groups_Olinordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,B)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 12.07/11.94 ** KEPT (pick-wt=19): 487 [] -class_Groups_Olinordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,B)),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 12.07/11.94 ** KEPT (pick-wt=19): 488 [] -class_Groups_Olinordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Oplus__class_Oplus(A,B,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 12.07/11.94 ** KEPT (pick-wt=19): 489 [] -class_Groups_Olinordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Oplus__class_Oplus(A,B,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 12.07/11.94 ** KEPT (pick-wt=22): 490 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),E))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 12.07/11.94 ** KEPT (pick-wt=22): 491 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -c_Orderings_Oord__class_Oless(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 12.07/11.94 ** KEPT (pick-wt=10): 492 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=10): 493 [] -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))).
% 12.07/11.94 ** KEPT (pick-wt=17): 494 [] -class_Groups_Olinordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 12.07/11.94 ** KEPT (pick-wt=17): 495 [] -class_Groups_Olinordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 12.07/11.94 ** KEPT (pick-wt=18): 496 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 12.07/11.94 ** KEPT (pick-wt=18): 497 [] -class_Groups_Oordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 12.07/11.94 ** KEPT (pick-wt=17): 498 [] -class_Groups_Olinordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ouminus__class_Ouminus(A,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 12.07/11.94 ** KEPT (pick-wt=17): 499 [] -class_Groups_Olinordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ouminus__class_Ouminus(A,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 12.07/11.94 ** KEPT (pick-wt=18): 500 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Ouminus__class_Ouminus(A,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 12.07/11.94 ** KEPT (pick-wt=18): 501 [] -class_Groups_Oordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Ouminus__class_Ouminus(A,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A))).
% 12.07/11.94 ** KEPT (pick-wt=12): 502 [] -class_Rings_Olinordered__semidom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B))).
% 12.07/11.94 Following clause subsumed by 502 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B))).
% 12.07/11.94 ** KEPT (pick-wt=27): 503 [] -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)).
% 12.07/11.94 Following clause subsumed by 449 during input processing: 0 [] -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)).
% 12.07/11.94 ** KEPT (pick-wt=11): 504 [] -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)).
% 12.07/11.94 ** KEPT (pick-wt=11): 505 [] 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)).
% 12.07/11.94 ** KEPT (pick-wt=11): 506 [] -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)).
% 12.07/11.94 ** KEPT (pick-wt=11): 507 [] 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)).
% 12.07/11.94 Following clause subsumed by 505 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A)),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.07/11.94 Following clause subsumed by 504 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A)),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.07/11.94 Following clause subsumed by 507 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B)).
% 12.07/11.94 Following clause subsumed by 504 during input processing: 0 [] -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)).
% 12.07/11.94 ** KEPT (pick-wt=14): 508 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Nat_OSuc(A))|B=A.
% 12.07/11.94 Following clause subsumed by 58 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Nat_OSuc(A))|B!=A.
% 12.07/11.94 Following clause subsumed by 505 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A)),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.07/11.94 ** KEPT (pick-wt=24): 509 [] -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)).
% 12.07/11.94 Following clause subsumed by 449 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)).
% 12.07/11.94 ** KEPT (pick-wt=24): 510 [] -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)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B))).
% 12.07/11.95 ** KEPT (pick-wt=26): 511 [] -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))).
% 12.07/11.95 ** KEPT (pick-wt=12): 512 [] -hBOOL(hAPP(A,$f20(A)))|hBOOL(hAPP(A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))).
% 12.07/11.95 ** KEPT (pick-wt=19): 513 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hBOOL(hAPP(B,A))| -hBOOL(hAPP(B,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),$f21(B)))).
% 12.07/11.95 ** KEPT (pick-wt=19): 514 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))| -hBOOL(hAPP(B,A))|hBOOL(hAPP(B,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),$f22(B)))).
% 12.07/11.95 ** KEPT (pick-wt=15): 515 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f23(A)))| -hBOOL(hAPP(A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))).
% 12.07/11.95 ** KEPT (pick-wt=12): 516 [] hBOOL(hAPP(A,$f23(A)))| -hBOOL(hAPP(A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))).
% 12.07/11.95 ** KEPT (pick-wt=20): 517 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,C),D))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,C),c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,D)).
% 12.07/11.95 ** KEPT (pick-wt=17): 519 [copy,518,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B))|c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),$f24(B,A)))=B.
% 12.07/11.95 ** KEPT (pick-wt=15): 520 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B))|B!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),C)).
% 12.07/11.95 ** KEPT (pick-wt=29): 521 [] -class_Rings_Olinordered__ring__strict(A)| -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)).
% 12.07/11.95 ** KEPT (pick-wt=29): 522 [] -class_Rings_Olinordered__ring__strict(A)| -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)).
% 12.07/11.95 ** KEPT (pick-wt=29): 523 [] -class_Rings_Olinordered__ring__strict(A)| -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)).
% 12.07/11.95 ** KEPT (pick-wt=29): 524 [] -class_Rings_Olinordered__ring__strict(A)| -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)).
% 12.07/11.95 ** KEPT (pick-wt=36): 525 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 12.07/11.95 ** KEPT (pick-wt=38): 526 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -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))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 12.07/11.95 ** KEPT (pick-wt=38): 527 [] -class_Rings_Olinordered__semiring__strict(A)| -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))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 12.07/11.95 ** KEPT (pick-wt=38): 528 [] -class_Rings_Olinordered__semiring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -c_Orderings_Oord__class_Oless(A,D,E)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 12.07/11.95 ** KEPT (pick-wt=27): 529 [] -class_Rings_Olinordered__semiring(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|c_Orderings_Oord__class_Oless(A,B,D).
% 12.07/11.95 ** KEPT (pick-wt=27): 530 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|c_Orderings_Oord__class_Oless(A,B,D).
% 12.07/11.95 ** KEPT (pick-wt=27): 531 [] -class_Rings_Olinordered__semiring(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|c_Orderings_Oord__class_Oless(A,C,D).
% 12.07/11.95 ** KEPT (pick-wt=27): 532 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))|c_Orderings_Oord__class_Oless(A,C,D).
% 12.07/11.95 ** KEPT (pick-wt=29): 533 [] -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)))| -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)).
% 12.07/11.95 ** KEPT (pick-wt=29): 534 [] -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)))| -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)).
% 12.07/11.95 ** KEPT (pick-wt=22): 535 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),c_Groups_Ozero__class_Ozero(A)))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 12.07/11.95 ** KEPT (pick-wt=22): 536 [] -class_Groups_Oordered__comm__monoid__add(A)| -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)))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 12.07/11.95 ** KEPT (pick-wt=20): 537 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 12.07/11.95 ** KEPT (pick-wt=20): 538 [] -class_Groups_Oordered__comm__monoid__add(A)| -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))|c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 12.07/11.95 Following clause subsumed by 537 during input processing: 0 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),B))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 12.07/11.95 Following clause subsumed by 538 during input processing: 0 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),C))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 12.07/11.95 ** KEPT (pick-wt=26): 539 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))),c_Groups_Ozero__class_Ozero(A)))|B=c_Groups_Ozero__class_Ozero(A).
% 12.07/11.95 ** KEPT (pick-wt=26): 540 [] -class_Rings_Olinordered__ring__strict(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))),c_Groups_Ozero__class_Ozero(A)))|C=c_Groups_Ozero__class_Ozero(A).
% 12.07/11.95 ** KEPT (pick-wt=30): 541 [] -class_Rings_Olinordered__ring__strict(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C))),c_Groups_Ozero__class_Ozero(A)))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 12.07/11.95 ** KEPT (pick-wt=22): 542 [] -class_Rings_Olinordered__ring(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),C)))).
% 12.07/11.95 ** KEPT (pick-wt=34): 543 [] -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)).
% 12.07/11.95 ** KEPT (pick-wt=34): 544 [] -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)).
% 12.07/11.95 ** KEPT (pick-wt=21): 545 [] -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)).
% 12.07/11.95 ** KEPT (pick-wt=21): 546 [] -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)).
% 12.07/11.95 ** KEPT (pick-wt=29): 547 [] 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)).
% 12.07/11.95 Following clause subsumed by 503 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)))| -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)).
% 12.07/11.95 Following clause subsumed by 449 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)).
% 12.07/11.95 ** KEPT (pick-wt=27): 548 [] -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)))| -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)).
% 12.07/11.95 Following clause subsumed by 448 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)).
% 12.07/11.95 ** KEPT (pick-wt=14): 549 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.95 ** KEPT (pick-wt=14): 550 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.95 ** KEPT (pick-wt=12): 551 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A).
% 12.07/11.95 ** KEPT (pick-wt=12): 552 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),A))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A).
% 12.07/11.95 ** KEPT (pick-wt=14): 553 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B)).
% 12.07/11.95 ** KEPT (pick-wt=14): 554 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B)).
% 12.07/11.95 ** KEPT (pick-wt=14): 555 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint))),B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 12.07/11.95 ** KEPT (pick-wt=14): 556 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint))),B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 12.07/11.95 Following clause subsumed by 556 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint))),B)).
% 12.07/11.95 ** KEPT (pick-wt=18): 557 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.95 ** KEPT (pick-wt=18): 558 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.95 ** KEPT (pick-wt=22): 559 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.95 ** KEPT (pick-wt=54): 560 [] -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))|c_Groups_Oplus__class_Oplus(A,E,F)!=c_Groups_Oone__class_Oone(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D))),C)).
% 12.07/11.95 ** KEPT (pick-wt=16): 561 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A)).
% 12.07/11.95 ** KEPT (pick-wt=13): 562 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(A))))).
% 12.07/11.95 ** KEPT (pick-wt=30): 564 [copy,563,flip.2] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))!=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))).
% 12.07/11.95 ** KEPT (pick-wt=27): 566 [copy,565,flip.2] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),C))!=A| -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)).
% 12.07/11.95 ** KEPT (pick-wt=31): 567 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,A)| -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)).
% 12.07/11.95 ** KEPT (pick-wt=32): 568 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),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))| -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))).
% 12.07/11.95 ** KEPT (pick-wt=43): 569 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C)),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))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,C,A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,E,A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B),D)).
% 12.07/11.95 ** KEPT (pick-wt=18): 570 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A))).
% 12.07/11.95 ** KEPT (pick-wt=18): 571 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A))).
% 12.07/11.95 ** KEPT (pick-wt=18): 572 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)),B)).
% 12.07/11.95 ** KEPT (pick-wt=18): 573 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)),B)).
% 12.07/11.95 ** KEPT (pick-wt=27): 574 [] -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)).
% 12.07/11.95 ** KEPT (pick-wt=27): 575 [] -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)).
% 12.07/11.95 ** KEPT (pick-wt=27): 576 [] -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)).
% 12.07/11.95 ** KEPT (pick-wt=27): 577 [] -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)).
% 12.07/11.95 ** KEPT (pick-wt=18): 578 [] -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,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,A)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B))).
% 12.07/11.95 ** KEPT (pick-wt=15): 579 [] -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.
% 12.07/11.95 ** KEPT (pick-wt=18): 580 [] -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)).
% 12.07/11.95 ** KEPT (pick-wt=13): 581 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),B))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|A=B.
% 12.07/11.95 ** KEPT (pick-wt=10): 582 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),B))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B).
% 12.07/11.95 ** KEPT (pick-wt=9): 583 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),B))|A!=B.
% 12.07/11.95 Following clause subsumed by 582 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),B)).
% 12.07/11.95 ** KEPT (pick-wt=7): 584 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|A!=B.
% 12.07/11.95 Following clause subsumed by 581 during input processing: 0 [] 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.
% 12.07/11.95 ** KEPT (pick-wt=15): 585 [] -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.
% 12.07/11.95 ** KEPT (pick-wt=18): 586 [] -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)).
% 12.07/11.95 ** KEPT (pick-wt=16): 587 [] -class_Orderings_Oord(A)| -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)).
% 12.07/11.95 ** KEPT (pick-wt=16): 588 [] -class_Orderings_Oord(A)| -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)).
% 12.07/11.95 ** KEPT (pick-wt=24): 589 [] -class_Orderings_Oord(A)|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)).
% 12.07/11.95 ** KEPT (pick-wt=15): 590 [] -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.
% 12.07/11.95 ** KEPT (pick-wt=18): 591 [] -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)).
% 12.07/11.95 Following clause subsumed by 432 during input processing: 0 [] A!=B|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 12.07/11.95 ** KEPT (pick-wt=23): 592 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)).
% 12.07/11.95 ** KEPT (pick-wt=20): 593 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)).
% 12.07/11.95 ** KEPT (pick-wt=23): 594 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C).
% 12.07/11.95 ** KEPT (pick-wt=23): 595 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,C).
% 12.07/11.95 ** KEPT (pick-wt=14): 596 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)).
% 12.07/11.95 ** KEPT (pick-wt=14): 597 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A)).
% 12.07/11.95 ** KEPT (pick-wt=14): 598 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B).
% 12.07/11.95 ** KEPT (pick-wt=14): 599 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A),B).
% 12.07/11.95 ** KEPT (pick-wt=5): 600 [] c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.07/11.95 ** KEPT (pick-wt=12): 601 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A).
% 12.07/11.95 ** KEPT (pick-wt=12): 602 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,B)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,A).
% 12.07/11.95 ** KEPT (pick-wt=12): 603 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=B.
% 12.07/11.95 ** KEPT (pick-wt=12): 604 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,B))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=B.
% 12.07/11.95 ** KEPT (pick-wt=21): 605 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.07/11.95 ** KEPT (pick-wt=21): 606 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.07/11.95 ** KEPT (pick-wt=25): 607 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.07/11.95 ** KEPT (pick-wt=20): 608 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)|B=C.
% 12.07/11.95 ** KEPT (pick-wt=20): 609 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)|B!=C.
% 12.07/11.95 ** KEPT (pick-wt=20): 610 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)|B=C.
% 12.07/11.95 ** KEPT (pick-wt=20): 611 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)|B!=C.
% 12.07/11.95 ** KEPT (pick-wt=60): 612 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),E),F)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),E),F),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -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))| -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)).
% 12.07/11.95 ** KEPT (pick-wt=43): 613 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C)),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)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,E)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,C)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,D),B)).
% 12.07/11.95 ** KEPT (pick-wt=62): 614 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B),C)!=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)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),D),E),F)))| -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))| -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)).
% 12.07/11.95 ** KEPT (pick-wt=14): 616 [copy,615,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,$f25(B,A))=B.
% 12.07/11.95 Following clause subsumed by 436 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C).
% 12.07/11.95 ** KEPT (pick-wt=21): 617 [] -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))).
% 12.07/11.95 ** KEPT (pick-wt=15): 618 [] -class_Orderings_Oorder(A)|c_SEQ_Odecse_q(A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f27(B,A)),$f26(B,A))).
% 12.07/11.95 ** KEPT (pick-wt=19): 619 [] -class_Orderings_Oorder(A)|c_SEQ_Odecse_q(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f26(B,A))),hAPP(B,$f27(B,A)))).
% 12.07/11.95 ** KEPT (pick-wt=18): 620 [] -class_Lattices_Oboolean__algebra(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,C)),c_Groups_Ouminus__class_Ouminus(A,B))).
% 12.07/11.95 ** KEPT (pick-wt=10): 621 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=B.
% 12.07/11.95 Following clause subsumed by 621 during input processing: 0 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=B.
% 12.07/11.95 ** KEPT (pick-wt=20): 622 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C).
% 12.07/11.95 ** KEPT (pick-wt=9): 623 [] -class_Lattices_Oboolean__algebra(A)|c_Groups_Ouminus__class_Ouminus(A,c_Groups_Ouminus__class_Ouminus(A,B))=B.
% 12.07/11.95 ** KEPT (pick-wt=15): 624 [] -class_Groups_Ouminus(A)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(B,A),C),D)=c_Groups_Ouminus__class_Ouminus(A,hAPP(C,D)).
% 12.07/11.95 ** KEPT (pick-wt=12): 625 [] -class_Lattices_Oboolean__algebra(A)|c_Groups_Ouminus__class_Ouminus(A,B)!=c_Groups_Ouminus__class_Ouminus(A,C)|B=C.
% 12.07/11.95 ** KEPT (pick-wt=12): 626 [] -class_Lattices_Oboolean__algebra(A)|c_Groups_Ouminus__class_Ouminus(A,B)=c_Groups_Ouminus__class_Ouminus(A,C)|B!=C.
% 12.07/11.95 ** KEPT (pick-wt=18): 627 [] -class_Lattices_Oboolean__algebra(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 12.07/11.95 Following clause subsumed by 620 during input processing: 0 [] -class_Lattices_Oboolean__algebra(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ouminus__class_Ouminus(A,B)),c_Groups_Ouminus__class_Ouminus(A,C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,C),B)).
% 12.07/11.95 ** KEPT (pick-wt=14): 628 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A))|A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.07/11.95 ** KEPT (pick-wt=15): 629 [] hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f28(B,A),B).
% 12.07/11.95 ** KEPT (pick-wt=21): 630 [] hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C),$f28(B,A)))| -hBOOL(hAPP(A,C)).
% 12.07/11.95 ** KEPT (pick-wt=19): 631 [] hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,$f28(B,A),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 12.07/11.95 ** KEPT (pick-wt=21): 632 [] -class_Orderings_Oorder(A)| -c_SEQ_Oincse_q(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,C)),hAPP(B,D))).
% 12.07/11.95 ** KEPT (pick-wt=15): 633 [] -class_Orderings_Oorder(A)|c_SEQ_Oincse_q(A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f30(B,A)),$f29(B,A))).
% 12.07/11.95 ** KEPT (pick-wt=19): 634 [] -class_Orderings_Oorder(A)|c_SEQ_Oincse_q(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f30(B,A))),hAPP(B,$f29(B,A)))).
% 12.07/11.95 ** KEPT (pick-wt=20): 635 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(A),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 12.07/11.95 ** KEPT (pick-wt=20): 636 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(A),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 12.07/11.95 ** KEPT (pick-wt=30): 638 [copy,637,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,A))),hAPP(c_Int_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B)))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)).
% 12.07/11.95 ** KEPT (pick-wt=14): 639 [] -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))).
% 12.07/11.95 ** KEPT (pick-wt=14): 640 [] -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))).
% 12.07/11.95 ** KEPT (pick-wt=24): 641 [] -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))|hAPP(c_Int_Onat,A)!=hAPP(c_Int_Onat,B)|A=B.
% 12.07/11.95 ** KEPT (pick-wt=24): 642 [] -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))|hAPP(c_Int_Onat,A)=hAPP(c_Int_Onat,B)|A!=B.
% 12.07/11.95 Following clause subsumed by 641 during input processing: 0 [] -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))|hAPP(c_Int_Onat,A)!=hAPP(c_Int_Onat,B)|A=B.
% 12.07/11.95 Following clause subsumed by 642 during input processing: 0 [] -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))|hAPP(c_Int_Onat,A)=hAPP(c_Int_Onat,B)|A!=B.
% 12.07/11.95 ** KEPT (pick-wt=18): 643 [] -hBOOL(hAPP(A,$f31(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B))|hBOOL(hAPP(A,hAPP(c_Int_Onat,B))).
% 12.07/11.95 ** KEPT (pick-wt=11): 644 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,hAPP(c_Int_Onat,$f32(A)))).
% 12.07/11.95 ** KEPT (pick-wt=12): 645 [] -hBOOL(hAPP(A,B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),$f33(A))).
% 12.07/11.95 ** KEPT (pick-wt=11): 646 [] -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,hAPP(c_Int_Onat,$f33(A)))).
% 12.07/11.95 ** KEPT (pick-wt=18): 647 [] hBOOL(hAPP(A,$f34(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B))| -hBOOL(hAPP(A,hAPP(c_Int_Onat,B))).
% 12.07/11.95 ** KEPT (pick-wt=12): 648 [] -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).
% 12.07/11.95 ** KEPT (pick-wt=12): 649 [] -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).
% 12.07/11.95 ** KEPT (pick-wt=13): 650 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))|hAPP(c_Int_Onat,A)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.95 ** KEPT (pick-wt=13): 651 [] hAPP(c_Int_Onat,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 12.07/11.95 Following clause subsumed by 650 during input processing: 0 [] hAPP(c_Int_Onat,A)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 12.07/11.95 ** KEPT (pick-wt=17): 652 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,B),hAPP(c_Int_Onat,A))|c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A).
% 12.07/11.95 ** KEPT (pick-wt=17): 653 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,B),hAPP(c_Int_Onat,A))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A).
% 12.07/11.95 ** KEPT (pick-wt=13): 654 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,A),hAPP(c_Int_Onat,B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B).
% 12.07/11.95 ** KEPT (pick-wt=12): 655 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,A),hAPP(c_Int_Onat,B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 12.07/11.95 Following clause subsumed by 653 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,A),hAPP(c_Int_Onat,B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 12.07/11.95 ** KEPT (pick-wt=30): 656 [] -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_Nat_Onat,hAPP(c_Int_Onat,A)),hAPP(c_Int_Onat,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B)).
% 12.07/11.95 ** KEPT (pick-wt=30): 657 [] -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_Nat_Onat,hAPP(c_Int_Onat,A)),hAPP(c_Int_Onat,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B)).
% 12.07/11.95 ** KEPT (pick-wt=15): 658 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,A))=A.
% 12.07/11.95 ** KEPT (pick-wt=11): 659 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)!=B|A=hAPP(c_Int_Onat,B).
% 12.07/11.95 ** KEPT (pick-wt=13): 660 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)!=B|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)).
% 12.07/11.95 ** KEPT (pick-wt=18): 661 [] hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)=B|A!=hAPP(c_Int_Onat,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)).
% 12.07/11.95 Following clause subsumed by 658 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,A))=A.
% 12.07/11.95 ** KEPT (pick-wt=13): 662 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Int_Onat,B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A),B).
% 12.07/11.95 ** KEPT (pick-wt=13): 663 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Int_Onat,B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A),B).
% 12.07/11.95 ** KEPT (pick-wt=15): 664 [] -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)).
% 12.07/11.95 ** KEPT (pick-wt=15): 665 [] 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)).
% 12.07/11.95 ** KEPT (pick-wt=15): 666 [] -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))).
% 12.07/11.95 ** KEPT (pick-wt=15): 667 [] 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))).
% 12.07/11.95 ** KEPT (pick-wt=12): 668 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onat,A))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A).
% 12.07/11.95 ** KEPT (pick-wt=12): 669 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onat,A))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A).
% 12.07/11.95 Following clause subsumed by 655 during input processing: 0 [] -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))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,A),hAPP(c_Int_Onat,B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 12.07/11.95 ** KEPT (pick-wt=26): 670 [] -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))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,A),hAPP(c_Int_Onat,B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 12.07/11.95 Following clause subsumed by 655 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,A),hAPP(c_Int_Onat,B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 12.07/11.95 ** KEPT (pick-wt=19): 671 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,A),hAPP(c_Int_Onat,B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 12.07/11.95 ** KEPT (pick-wt=21): 672 [] -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_Nat_Onat,hAPP(c_Int_Onat,A)),hAPP(c_Int_Onat,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B)).
% 12.07/11.95 ** KEPT (pick-wt=21): 673 [] -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_Nat_Onat,hAPP(c_Int_Onat,A)),hAPP(c_Int_Onat,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,A),B)).
% 12.07/11.95 ** KEPT (pick-wt=23): 674 [] -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_Nat_Onat,hAPP(c_Int_Onat,B)),hAPP(c_Int_Onat,A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B),A)).
% 12.07/11.96 ** KEPT (pick-wt=23): 675 [] -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_Nat_Onat,hAPP(c_Int_Onat,B)),hAPP(c_Int_Onat,A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B),A)).
% 12.07/11.96 ** KEPT (pick-wt=18): 676 [] hAPP(c_Int_Onat,A)!=B| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|A=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B).
% 12.07/11.96 ** KEPT (pick-wt=16): 677 [] hAPP(c_Int_Onat,A)!=B|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.96 ** KEPT (pick-wt=16): 678 [] hAPP(c_Int_Onat,A)=B|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.96 ** KEPT (pick-wt=18): 679 [] hAPP(c_Int_Onat,A)=B|A!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A)).
% 12.07/11.96 ** KEPT (pick-wt=15): 680 [] hAPP(c_Int_Onat,A)=B|A!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.96 ** KEPT (pick-wt=18): 681 [] A!=hAPP(c_Int_Onat,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B))|B=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A).
% 12.07/11.96 ** KEPT (pick-wt=16): 682 [] A!=hAPP(c_Int_Onat,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.96 ** KEPT (pick-wt=16): 683 [] A=hAPP(c_Int_Onat,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.96 ** KEPT (pick-wt=18): 684 [] A=hAPP(c_Int_Onat,B)|B!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(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)).
% 12.07/11.96 ** KEPT (pick-wt=15): 685 [] A=hAPP(c_Int_Onat,B)|B!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),A)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.96 ** KEPT (pick-wt=16): 686 [] -hBOOL(hAPP(A,hAPP(c_Int_Onat,B)))|B!=hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),C)|hBOOL(hAPP(A,C)).
% 12.07/11.96 ** KEPT (pick-wt=16): 687 [] -hBOOL(hAPP(A,hAPP(c_Int_Onat,B)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.07/11.96 ** KEPT (pick-wt=19): 689 [copy,688,flip.2] hBOOL(hAPP(A,hAPP(c_Int_Onat,B)))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),$f35(B,A))=B| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.07/11.96 ** KEPT (pick-wt=17): 690 [] hBOOL(hAPP(A,hAPP(c_Int_Onat,B)))| -hBOOL(hAPP(A,$f35(B,A)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.07/11.96 ** KEPT (pick-wt=17): 691 [] hBOOL(hAPP(A,hAPP(c_Int_Onat,B)))| -hBOOL(hAPP(A,$f35(B,A)))| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.07/11.96 ** KEPT (pick-wt=29): 693 [copy,692,flip.3] -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))|hAPP(c_Int_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Int_Onat,A),hAPP(c_Int_Onat,B)).
% 12.07/11.96 Following clause subsumed by 693 during input processing: 0 [] -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))|hAPP(c_Int_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Int_Onat,A),hAPP(c_Int_Onat,B)).
% 12.07/11.96 ** KEPT (pick-wt=33): 694 [] -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))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,A)),hAPP(c_Int_Onat,B))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)).
% 12.07/11.96 ** KEPT (pick-wt=26): 696 [copy,695,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,A)),hAPP(c_Int_Onat,B))=hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),A),B)).
% 12.07/11.96 ** KEPT (pick-wt=33): 697 [] -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)))).
% 12.07/11.96 ** KEPT (pick-wt=13): 698 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,A))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A).
% 12.07/11.96 ** KEPT (pick-wt=13): 699 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,A))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A).
% 12.07/11.96 ** KEPT (pick-wt=19): 700 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|c_Nat_OSuc(hAPP(c_Int_Onat,A))=hAPP(c_Int_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A)).
% 12.07/11.96 ** KEPT (pick-wt=20): 701 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,A),B)|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)).
% 12.07/11.96 ** KEPT (pick-wt=20): 702 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Int_Onat,A),B)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B)).
% 12.07/11.96 ** KEPT (pick-wt=28): 703 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),A),B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))|c_RComplete_Onatceiling(B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 12.07/11.96 ** KEPT (pick-wt=12): 704 [] hAPP(c_RealDef_Oreal(tc_Nat_Onat),A)!=hAPP(c_RealDef_Oreal(tc_Nat_Onat),B)|A=B.
% 12.07/11.96 ** KEPT (pick-wt=12): 705 [] hAPP(c_RealDef_Oreal(tc_Nat_Onat),A)=hAPP(c_RealDef_Oreal(tc_Nat_Onat),B)|A!=B.
% 12.07/11.96 ** KEPT (pick-wt=11): 706 [] hAPP(c_RealDef_Oreal(tc_Nat_Onat),A)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.96 ** KEPT (pick-wt=11): 707 [] hAPP(c_RealDef_Oreal(tc_Nat_Onat),A)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.96 ** KEPT (pick-wt=8): 708 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.07/11.96 ** KEPT (pick-wt=14): 709 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),A),hAPP(c_RealDef_Oreal(tc_Nat_Onat),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.07/11.96 ** KEPT (pick-wt=14): 710 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),A),hAPP(c_RealDef_Oreal(tc_Nat_Onat),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.07/11.96 ** KEPT (pick-wt=18): 711 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),A)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 12.07/11.96 ** KEPT (pick-wt=18): 712 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),A)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 12.07/11.96 ** KEPT (pick-wt=14): 713 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.96 ** KEPT (pick-wt=14): 714 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),A)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.96 ** KEPT (pick-wt=17): 715 [] -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(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(A))),A)).
% 12.07/11.96 ** KEPT (pick-wt=16): 716 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(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))).
% 12.07/11.96 ** KEPT (pick-wt=16): 717 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A),hAPP(c_RealDef_Oreal(tc_Nat_Onat),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A)),B)).
% 12.07/11.96 ** KEPT (pick-wt=13): 718 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),A))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 12.07/11.96 ** KEPT (pick-wt=13): 719 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),A))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 12.07/11.96 ** KEPT (pick-wt=20): 720 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),B))).
% 12.07/11.96 ** KEPT (pick-wt=20): 721 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),B))).
% 12.07/11.96 ** KEPT (pick-wt=20): 722 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),A),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),B),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 12.07/11.96 ** KEPT (pick-wt=20): 723 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),A),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),B),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 12.07/11.96 ** KEPT (pick-wt=23): 724 [] -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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),B)),A)).
% 12.07/11.96 Following clause subsumed by 716 during input processing: 0 [] -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,hAPP(c_RealDef_Oreal(tc_Nat_Onat),B)),A)).
% 12.07/11.96 ** KEPT (pick-wt=23): 725 [] -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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),B))).
% 12.07/11.96 Following clause subsumed by 717 during input processing: 0 [] -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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),B))).
% 12.07/11.96 ** KEPT (pick-wt=19): 726 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(c_RealDef_Oreal(tc_Nat_Onat),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(A),B).
% 12.07/11.96 ** KEPT (pick-wt=21): 727 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,hAPP(c_RealDef_Oreal(tc_Nat_Onat),B)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(A),B).
% 12.07/11.96 ** KEPT (pick-wt=18): 728 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(A),c_Groups_Oone__class_Oone(tc_Nat_Onat))),B))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(c_RealDef_Oreal(tc_Nat_Onat),B)).
% 12.07/11.96 ** KEPT (pick-wt=24): 729 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),A)),B))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatfloor(B)=A.
% 12.07/11.96 ** KEPT (pick-wt=21): 730 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,hAPP(c_RealDef_Oreal(tc_Nat_Onat),B)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(A),B).
% 12.07/11.96 ** KEPT (pick-wt=17): 731 [] -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(c_RealDef_Oreal(tc_Nat_Onat),$f36(A))),A)).
% 12.07/11.96 ** KEPT (pick-wt=16): 732 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc($f36(A)))).
% 12.07/11.96 ** KEPT (pick-wt=34): 733 [] -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_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(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),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),B))).
% 12.07/11.96 ** KEPT (pick-wt=21): 735 [copy,734,flip.3] -class_Rings_Oring__1(A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Groups_Ouminus__class_Ouminus(A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(c_Int_Onat,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B))))=c_Int_Oring__1__class_Oof__int(A,B).
% 12.07/11.96 ** KEPT (pick-wt=17): 737 [copy,736,flip.3] -class_Rings_Oring__1(A)|c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(c_Int_Onat,B))=c_Int_Oring__1__class_Oof__int(A,B).
% 12.07/11.96 ** KEPT (pick-wt=12): 738 [] -class_Int_Oring__char__0(A)|c_Int_Oring__1__class_Oof__int(A,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.07/11.96 ** KEPT (pick-wt=12): 739 [] -class_Int_Oring__char__0(A)|c_Int_Oring__1__class_Oof__int(A,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.07/11.96 ** KEPT (pick-wt=12): 740 [] -class_Int_Oring__char__0(A)|c_Groups_Ozero__class_Ozero(A)!=c_Int_Oring__1__class_Oof__int(A,B)|B=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.07/11.96 ** KEPT (pick-wt=12): 741 [] -class_Int_Oring__char__0(A)|c_Groups_Ozero__class_Ozero(A)=c_Int_Oring__1__class_Oof__int(A,B)|B!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.07/11.96 ** KEPT (pick-wt=9): 742 [] -class_Rings_Oring__1(A)|c_Int_Oring__1__class_Oof__int(A,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=c_Groups_Ozero__class_Ozero(A).
% 12.07/11.96 ** KEPT (pick-wt=18): 743 [] -class_Rings_Olinordered__idom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Int_Oring__1__class_Oof__int(A,B)),c_Int_Oring__1__class_Oof__int(A,C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B),C)).
% 12.07/11.96 ** KEPT (pick-wt=18): 744 [] -class_Rings_Olinordered__idom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Int_Oring__1__class_Oof__int(A,B)),c_Int_Oring__1__class_Oof__int(A,C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B),C)).
% 12.07/11.96 ** KEPT (pick-wt=14): 745 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Int_Oring__1__class_Oof__int(A,B),c_Int_Oring__1__class_Oof__int(A,C))|c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C).
% 12.07/11.96 ** KEPT (pick-wt=14): 746 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Int_Oring__1__class_Oof__int(A,B),c_Int_Oring__1__class_Oof__int(A,C))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,C).
% 12.07/11.96 ** KEPT (pick-wt=17): 747 [] -class_Rings_Oring__1(A)|c_Int_Oring__1__class_Oof__int(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C))=c_Groups_Oplus__class_Oplus(A,c_Int_Oring__1__class_Oof__int(A,B),c_Int_Oring__1__class_Oof__int(A,C)).
% 12.07/11.96 ** KEPT (pick-wt=21): 748 [] -class_Rings_Oring__1(A)|c_Int_Oring__1__class_Oof__int(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Int_Oring__1__class_Oof__int(A,B)),c_Int_Oring__1__class_Oof__int(A,C)).
% 12.07/11.96 ** KEPT (pick-wt=9): 749 [] -class_Rings_Oring__1(A)|c_Int_Oring__1__class_Oof__int(A,c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Groups_Oone__class_Oone(A).
% 12.07/11.96 ** KEPT (pick-wt=21): 750 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 12.07/11.96 Following clause subsumed by 750 during input processing: 0 [flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 12.07/11.96 ** KEPT (pick-wt=21): 751 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C)).
% 12.07/11.96 ** KEPT (pick-wt=12): 752 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(A).
% 12.07/11.96 ** KEPT (pick-wt=13): 753 [] -class_Rings_Oring__1(A)|c_Int_Oring__1__class_Oof__int(A,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,B))=c_Groups_Ouminus__class_Ouminus(A,c_Int_Oring__1__class_Oof__int(A,B)).
% 12.07/11.96 ** KEPT (pick-wt=28): 754 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)).
% 12.07/11.96 ** KEPT (pick-wt=13): 755 [] -class_Rings_Oring__1(A)|c_Int_Oring__1__class_Oof__int(A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B))=hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B).
% 12.07/11.96 ** KEPT (pick-wt=12): 756 [] -class_Int_Oring__char__0(A)|c_Int_Oring__1__class_Oof__int(A,B)!=c_Int_Oring__1__class_Oof__int(A,C)|B=C.
% 12.07/11.96 ** KEPT (pick-wt=12): 757 [] -class_Int_Oring__char__0(A)|c_Int_Oring__1__class_Oof__int(A,B)=c_Int_Oring__1__class_Oof__int(A,C)|B!=C.
% 12.07/11.96 ** KEPT (pick-wt=19): 758 [] -class_Rings_Oring__1(A)|c_Int_Oring__1__class_Oof__int(A,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C))=hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Int_Oring__1__class_Oof__int(A,B)),C).
% 12.07/11.96 ** KEPT (pick-wt=30): 759 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)).
% 12.07/11.96 ** KEPT (pick-wt=11): 760 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat))=B.
% 12.07/11.96 ** KEPT (pick-wt=25): 761 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)).
% 12.07/11.96 ** KEPT (pick-wt=29): 762 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))!=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|B=C|B=c_Groups_Ouminus__class_Ouminus(A,C).
% 12.07/11.96 ** KEPT (pick-wt=24): 763 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|B!=C.
% 12.07/11.96 ** KEPT (pick-wt=26): 764 [] -class_Rings_Oidom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|B!=c_Groups_Ouminus__class_Ouminus(A,C).
% 12.07/11.96 ** KEPT (pick-wt=18): 765 [] -class_Rings_Olinordered__idom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),c_Int_Oring__1__class_Oof__int(A,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)).
% 12.07/11.96 ** KEPT (pick-wt=18): 766 [] -class_Rings_Olinordered__idom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),c_Int_Oring__1__class_Oof__int(A,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B)).
% 12.07/11.96 ** KEPT (pick-wt=18): 767 [] -class_Rings_Olinordered__idom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Int_Oring__1__class_Oof__int(A,B)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 12.07/11.96 ** KEPT (pick-wt=18): 768 [] -class_Rings_Olinordered__idom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Int_Oring__1__class_Oof__int(A,B)),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,B),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 12.07/11.96 ** KEPT (pick-wt=14): 769 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Int_Oring__1__class_Oof__int(A,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.07/11.96 ** KEPT (pick-wt=14): 770 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Int_Oring__1__class_Oof__int(A,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.07/11.96 ** KEPT (pick-wt=14): 771 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Oring__1__class_Oof__int(A,B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B).
% 12.07/11.96 ** KEPT (pick-wt=14): 772 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Int_Oring__1__class_Oof__int(A,B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B).
% 12.07/11.96 ** KEPT (pick-wt=28): 773 [] -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)).
% 12.07/11.96 ** KEPT (pick-wt=19): 774 [] -class_Rings_Oring__1(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(c_Int_Onat,B))=c_Int_Oring__1__class_Oof__int(A,B).
% 12.07/11.96 ** KEPT (pick-wt=32): 775 [] -class_Rings_Olinordered__semidom(A)| -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))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)).
% 12.07/11.96 ** KEPT (pick-wt=22): 776 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 12.07/11.96 ** KEPT (pick-wt=29): 777 [] -class_Rings_Olinordered__semidom(A)| -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)).
% 12.07/11.96 ** KEPT (pick-wt=29): 778 [] -class_Rings_Olinordered__semidom(A)| -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)).
% 12.07/11.96 ** KEPT (pick-wt=19): 779 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.07/11.96 ** KEPT (pick-wt=14): 780 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.96 ** KEPT (pick-wt=15): 781 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.07/11.96 ** KEPT (pick-wt=23): 782 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 12.07/11.96 ** KEPT (pick-wt=19): 783 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.96 ** KEPT (pick-wt=15): 784 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 12.07/11.96 ** KEPT (pick-wt=14): 785 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.96 ** KEPT (pick-wt=24): 786 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,A)),B)=hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)).
% 12.07/11.96 Following clause subsumed by 786 during input processing: 0 [flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),A))|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,A)),B)=hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)).
% 12.07/11.96 ** KEPT (pick-wt=21): 787 [] -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))).
% 12.07/11.96 Following clause subsumed by 783 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 12.07/11.96 Following clause subsumed by 785 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.96 Following clause subsumed by 784 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),A),B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 12.07/11.96 ** KEPT (pick-wt=19): 788 [] -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))).
% 12.07/11.96 ** KEPT (pick-wt=22): 790 [copy,789,flip.1] hAPP(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).
% 12.07/11.96 ** KEPT (pick-wt=15): 791 [] -class_Rings_Oring__1__no__zero__divisors(A)|B=c_Groups_Ozero__class_Ozero(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=c_Groups_Ozero__class_Ozero(A).
% 12.07/11.96 ** KEPT (pick-wt=25): 792 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 12.07/11.96 ** KEPT (pick-wt=30): 793 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)).
% 12.07/11.96 ** KEPT (pick-wt=12): 794 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Oone__class_Oone(A)),B)=c_Groups_Oone__class_Oone(A).
% 12.07/11.96 ** KEPT (pick-wt=21): 795 [] -class_Rings_Osemiring__1(A)|hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),B),C))=hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)),C).
% 12.07/11.96 ** KEPT (pick-wt=25): 797 [copy,796,flip.2] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),D)).
% 12.07/11.96 ** KEPT (pick-wt=11): 798 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oone__class_Oone(tc_Nat_Onat))=B.
% 12.07/11.96 ** KEPT (pick-wt=21): 799 [] -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))).
% 12.07/11.96 ** KEPT (pick-wt=31): 800 [] -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))).
% 12.07/11.96 ** KEPT (pick-wt=17): 801 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 12.07/11.96 ** KEPT (pick-wt=21): 802 [] -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))).
% 12.07/11.96 ** KEPT (pick-wt=21): 803 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 12.07/11.96 ** KEPT (pick-wt=21): 804 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.96 ** KEPT (pick-wt=25): 805 [] -class_Power_Opower(A)| -class_Rings_Omult__zero(A)| -class_Rings_Ono__zero__divisors(A)| -class_Rings_Ozero__ne_q__one(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.07/11.96 ** KEPT (pick-wt=23): 806 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)!=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)|C=D.
% 12.07/11.96 ** KEPT (pick-wt=23): 807 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)|C!=D.
% 12.07/11.96 ** KEPT (pick-wt=15): 808 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),c_Nat_OSuc(B))=c_Groups_Ozero__class_Ozero(A).
% 12.07/11.96 ** KEPT (pick-wt=21): 809 [] -class_Power_Opower(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 12.07/11.96 ** KEPT (pick-wt=21): 810 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B).
% 12.07/11.96 ** KEPT (pick-wt=12): 811 [] -class_Power_Opower(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(A).
% 12.07/11.96 ** KEPT (pick-wt=28): 813 [copy,812,flip.2] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)).
% 12.07/11.96 ** KEPT (pick-wt=27): 814 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A)),D))|c_Orderings_Oord__class_Oless(A,B,D).
% 12.07/11.96 ** KEPT (pick-wt=33): 815 [] -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)).
% 12.07/11.96 ** KEPT (pick-wt=34): 816 [] -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.
% 12.10/11.96 ** KEPT (pick-wt=22): 817 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))).
% 12.10/11.96 ** KEPT (pick-wt=26): 818 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))).
% 12.10/11.96 ** KEPT (pick-wt=18): 819 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Oone__class_Oone(A).
% 12.10/11.96 ** KEPT (pick-wt=18): 820 [] -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 12.10/11.96 ** KEPT (pick-wt=18): 821 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C))).
% 12.10/11.96 ** KEPT (pick-wt=30): 822 [] -class_Rings_Oring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ouminus__class_Ouminus(A,B)),C)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Groups_Ouminus__class_Ouminus(A,c_Groups_Oone__class_Oone(A))),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 12.10/11.96 ** KEPT (pick-wt=25): 823 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C)).
% 12.10/11.96 ** KEPT (pick-wt=25): 824 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D).
% 12.10/11.96 Following clause subsumed by 824 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D).
% 12.10/11.96 Following clause subsumed by 823 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D).
% 12.10/11.96 ** KEPT (pick-wt=31): 825 [] -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))).
% 12.10/11.96 ** KEPT (pick-wt=31): 826 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 12.10/11.96 ** KEPT (pick-wt=23): 827 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Nat_OSuc(C)),c_Groups_Oone__class_Oone(A)).
% 12.10/11.96 ** KEPT (pick-wt=30): 828 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)).
% 12.10/11.96 ** KEPT (pick-wt=37): 829 [] -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))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|B=D.
% 12.10/11.96 ** KEPT (pick-wt=38): 830 [] -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))).
% 12.10/11.96 Following clause subsumed by 777 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -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)).
% 12.10/11.96 ** KEPT (pick-wt=11): 831 [] -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)).
% 12.10/11.96 ** KEPT (pick-wt=17): 832 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f37(B,A)).
% 12.10/11.96 ** KEPT (pick-wt=20): 833 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -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),$f37(B,A)),A)=B.
% 12.10/11.96 ** KEPT (pick-wt=17): 834 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f38(B,A)).
% 12.10/11.96 ** KEPT (pick-wt=20): 835 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -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),$f38(B,A)),A)=B.
% 12.10/11.96 ** KEPT (pick-wt=28): 836 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),C)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),C),A)!=B|C=$f38(B,A).
% 12.10/11.96 ** KEPT (pick-wt=28): 837 [] -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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),$f39(B,A))),A)),B)).
% 12.10/11.96 ** KEPT (pick-wt=27): 838 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc($f39(B,A)))),A)).
% 12.10/11.96 ** KEPT (pick-wt=23): 839 [] -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),hAPP(c_RealDef_Oreal(tc_Nat_Onat),B)),c_Transcendental_Oln(A)).
% 12.10/11.96 ** KEPT (pick-wt=19): 840 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),$f40(A,B))),A)).
% 12.10/11.96 ** KEPT (pick-wt=10): 841 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(A),A).
% 12.10/11.96 ** KEPT (pick-wt=18): 842 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)|c_Transcendental_Oln(A)!=c_Transcendental_Oln(B)|A=B.
% 12.10/11.96 ** KEPT (pick-wt=18): 843 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)|c_Transcendental_Oln(A)=c_Transcendental_Oln(B)|A!=B.
% 12.10/11.96 ** KEPT (pick-wt=20): 844 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(A),c_Transcendental_Oln(B))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B).
% 12.10/11.96 ** KEPT (pick-wt=20): 845 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(A),c_Transcendental_Oln(B))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B).
% 12.10/11.96 ** KEPT (pick-wt=24): 846 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)| -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)).
% 12.10/11.96 ** KEPT (pick-wt=24): 847 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)|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)).
% 12.10/11.96 ** KEPT (pick-wt=15): 848 [] -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))).
% 12.10/11.96 ** KEPT (pick-wt=11): 849 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(A)).
% 12.10/11.96 ** KEPT (pick-wt=16): 850 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A).
% 12.10/11.96 Following clause subsumed by 849 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(A))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A).
% 12.10/11.97 ** KEPT (pick-wt=14): 851 [] -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).
% 12.10/11.97 ** KEPT (pick-wt=14): 852 [] -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).
% 12.10/11.97 ** KEPT (pick-wt=16): 853 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.10/11.97 ** KEPT (pick-wt=16): 854 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.10/11.97 Following clause subsumed by 854 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.10/11.97 Following clause subsumed by 850 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(A))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A).
% 12.10/11.97 ** KEPT (pick-wt=20): 855 [] -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)).
% 12.10/11.97 Following clause subsumed by 848 during input processing: 0 [] -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)).
% 12.10/11.97 Following clause subsumed by 855 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)))| -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)).
% 12.10/11.97 ** KEPT (pick-wt=24): 856 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B)|c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oln(A),c_Transcendental_Oln(B)).
% 12.10/11.97 ** KEPT (pick-wt=18): 857 [] -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_Transcendental_Oln(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),A))),A)).
% 12.10/11.97 ** KEPT (pick-wt=12): 858 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),$f41(B,A)).
% 12.10/11.97 ** KEPT (pick-wt=16): 859 [] -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),$f41(B,A)),c_Nat_OSuc(B))=A.
% 12.10/11.97 ** KEPT (pick-wt=29): 860 [] -class_Groups_Omonoid__mult(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),C)=hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B).
% 12.10/11.97 ** KEPT (pick-wt=26): 861 [] -class_Rings_Oring__1(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B),C))|hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,B))=c_Groups_Ominus__class_Ominus(A,hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),C),hAPP(c_Nat_Osemiring__1__class_Oof__nat(A),B)).
% 12.10/11.97 ** KEPT (pick-wt=12): 862 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 12.10/11.97 ** KEPT (pick-wt=12): 863 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 12.10/11.97 ** KEPT (pick-wt=17): 864 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),B).
% 12.10/11.97 ** KEPT (pick-wt=13): 865 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 12.10/11.97 ** KEPT (pick-wt=13): 866 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B)).
% 12.10/11.97 Following clause subsumed by 866 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.10/11.97 ** KEPT (pick-wt=17): 868 [copy,867,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(B),A).
% 12.10/11.97 ** KEPT (pick-wt=14): 869 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),B).
% 12.10/11.97 ** KEPT (pick-wt=14): 870 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),B).
% 12.10/11.97 ** KEPT (pick-wt=26): 871 [] -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))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 12.10/11.97 ** KEPT (pick-wt=26): 872 [] -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))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 12.10/11.97 ** KEPT (pick-wt=20): 873 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C),A))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)).
% 12.10/11.97 ** KEPT (pick-wt=21): 875 [copy,874,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C),A).
% 12.10/11.97 Following clause subsumed by 875 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C),A).
% 12.10/11.97 ** KEPT (pick-wt=21): 877 [copy,876,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B),A).
% 12.10/11.97 ** KEPT (pick-wt=18): 878 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=C|B=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A).
% 12.10/11.97 ** KEPT (pick-wt=18): 879 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)=C|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A).
% 12.10/11.97 ** KEPT (pick-wt=15): 880 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),A)=B.
% 12.10/11.97 ** KEPT (pick-wt=24): 881 [] -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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A)),B)).
% 12.10/11.97 ** KEPT (pick-wt=24): 882 [] -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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A)),B)).
% 12.10/11.97 Following clause subsumed by 877 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B),A).
% 12.10/11.97 ** KEPT (pick-wt=15): 883 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=B.
% 12.10/11.97 ** KEPT (pick-wt=18): 884 [] -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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C),A))).
% 12.10/11.97 ** KEPT (pick-wt=18): 885 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B))).
% 12.10/11.97 ** KEPT (pick-wt=18): 886 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B))).
% 12.10/11.97 ** KEPT (pick-wt=21): 887 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A),B).
% 12.10/11.97 ** KEPT (pick-wt=11): 888 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),B).
% 12.10/11.97 ** KEPT (pick-wt=18): 889 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)).
% 12.10/11.97 ** KEPT (pick-wt=19): 890 [] -class_Groups_Ominus(A)|hAPP(c_Groups_Ominus__class_Ominus(tc_fun(B,A),C,D),E)=c_Groups_Ominus__class_Ominus(A,hAPP(C,E),hAPP(D,E)).
% 12.10/11.97 ** KEPT (pick-wt=11): 891 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,C),C)=B.
% 12.10/11.97 ** KEPT (pick-wt=11): 892 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,B,C),C)=B.
% 12.10/11.97 ** KEPT (pick-wt=26): 893 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ominus__class_Ominus(A,C,D))=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 12.10/11.97 Following clause subsumed by 893 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ominus__class_Ominus(A,C,D))=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 12.10/11.97 ** KEPT (pick-wt=26): 894 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,C)),D)=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 12.10/11.97 Following clause subsumed by 894 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,C)),D)=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 12.10/11.97 ** KEPT (pick-wt=19): 895 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,D,E).
% 12.10/11.97 ** KEPT (pick-wt=19): 896 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E).
% 12.10/11.97 ** KEPT (pick-wt=17): 897 [] -class_Groups_Oab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|B!=C|D=E.
% 12.10/11.97 ** KEPT (pick-wt=17): 898 [] -class_Groups_Oab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|B=C|D!=E.
% 12.10/11.97 ** KEPT (pick-wt=17): 899 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=B.
% 12.10/11.97 ** KEPT (pick-wt=12): 900 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|B=C.
% 12.10/11.97 ** KEPT (pick-wt=12): 901 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)=c_Groups_Ozero__class_Ozero(A)|B!=C.
% 12.10/11.97 ** KEPT (pick-wt=12): 902 [] -class_Groups_Oab__group__add(A)|B!=C|c_Groups_Ominus__class_Ominus(A,B,C)=c_Groups_Ozero__class_Ozero(A).
% 12.10/11.97 ** KEPT (pick-wt=12): 903 [] -class_Groups_Oab__group__add(A)|B=C|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ozero__class_Ozero(A).
% 12.10/11.97 ** KEPT (pick-wt=9): 904 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,B)=c_Groups_Ozero__class_Ozero(A).
% 12.10/11.97 ** KEPT (pick-wt=9): 905 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 12.10/11.97 ** KEPT (pick-wt=23): 906 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),E)).
% 12.10/11.97 ** KEPT (pick-wt=23): 907 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(A,D),E)).
% 12.10/11.97 ** KEPT (pick-wt=18): 908 [] -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_Groups_Ominu
% 12.10/11.97 Search stopped in tp_alloc by max_mem option.
% 12.10/11.97 s__class_Ominus(tc_Nat_Onat,C,B)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))).
% 12.10/11.97 ** KEPT (pick-wt=18): 909 [] -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_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C))).
% 12.10/11.97 ** KEPT (pick-wt=15): 910 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A),B))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=A.
% 12.10/11.97 ** KEPT (pick-wt=24): 911 [] -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))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)|B=C.
% 12.10/11.97 ** KEPT (pick-wt=24): 912 [] -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))|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)|B!=C.
% 12.10/11.97
% 12.10/11.97 Search stopped in tp_alloc by max_mem option.
% 12.10/11.97
% 12.10/11.97 ============ end of search ============
% 12.10/11.97
% 12.10/11.97 -------------- statistics -------------
% 12.10/11.97 clauses given 0
% 12.10/11.97 clauses generated 0
% 12.10/11.97 clauses kept 871
% 12.10/11.97 clauses forward subsumed 182
% 12.10/11.97 clauses back subsumed 0
% 12.10/11.97 Kbytes malloced 11718
% 12.10/11.97
% 12.10/11.97 ----------- times (seconds) -----------
% 12.10/11.97 user CPU time 0.19 (0 hr, 0 min, 0 sec)
% 12.10/11.97 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 12.10/11.97 wall-clock time 12 (0 hr, 0 min, 12 sec)
% 12.10/11.97
% 12.10/11.97 Process 21470 finished Wed Jul 27 02:52:07 2022
% 12.10/11.97 Otter interrupted
% 12.10/11.97 PROOF NOT FOUND
%------------------------------------------------------------------------------