TSTP Solution File: SWW190+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWW190+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 13:22:04 EDT 2022
% Result : Unknown 13.77s 13.67s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW190+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 02:52:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 13.65/13.62 ----- Otter 3.3f, August 2004 -----
% 13.65/13.62 The process was started by sandbox on n004.cluster.edu,
% 13.65/13.62 Wed Jul 27 02:52:21 2022
% 13.65/13.62 The command was "./otter". The process ID is 3801.
% 13.65/13.62
% 13.65/13.62 set(prolog_style_variables).
% 13.65/13.62 set(auto).
% 13.65/13.62 dependent: set(auto1).
% 13.65/13.62 dependent: set(process_input).
% 13.65/13.62 dependent: clear(print_kept).
% 13.65/13.62 dependent: clear(print_new_demod).
% 13.65/13.62 dependent: clear(print_back_demod).
% 13.65/13.62 dependent: clear(print_back_sub).
% 13.65/13.62 dependent: set(control_memory).
% 13.65/13.62 dependent: assign(max_mem, 12000).
% 13.65/13.62 dependent: assign(pick_given_ratio, 4).
% 13.65/13.62 dependent: assign(stats_level, 1).
% 13.65/13.62 dependent: assign(max_seconds, 10800).
% 13.65/13.62 clear(print_given).
% 13.65/13.62
% 13.65/13.62 formula_list(usable).
% 13.65/13.62 all A (A=A).
% 13.65/13.62 all V_g_2 V_f_2 ((all B_x (hAPP(V_f_2,B_x)=hAPP(V_g_2,B_x)))->V_f_2=V_g_2).
% 13.65/13.62 hBOOL(hAPP(v_P,v_x____)).
% 13.65/13.62 exists B_x1 hBOOL(hAPP(v_P,B_x1)).
% 13.65/13.62 exists B_z all B_x (hBOOL(hAPP(v_P,B_x))->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,B_z)).
% 13.65/13.62 all V_xa_2 T_a hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_xa_2)).
% 13.65/13.62 all V_xa_2 T_b T_a (class_Orderings_Otop(T_a)->hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_xa_2)=c_Orderings_Otop__class_Otop(T_a)).
% 13.65/13.62 all V_x (hBOOL(hAPP(v_P,V_x))->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,v_Y____)).
% 13.65/13.62 all V_S_2 V_R_2 T_a (class_Orderings_Oord(T_a)->c_Lubs_Oubs(T_a,V_R_2,V_S_2)=c_Set_OCollect(T_a,c_Lubs_OisUb(T_a,V_R_2,V_S_2))).
% 13.65/13.62 all V_Pa_2 T_a (c_Set_OCollect(T_a,V_Pa_2)=V_Pa_2).
% 13.65/13.62 exists B_x c_member(tc_RealDef_Oreal,B_x,c_Set_OCollect(tc_RealDef_Oreal,v_P)).
% 13.65/13.62 all T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)->c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(T_a)).
% 13.65/13.62 all V_xa_2 V_S_2 V_R_2 T_a (class_Orderings_Oord(T_a)-> (hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2))-> (c_Lubs_Osetge(T_a,V_xa_2,c_Set_OCollect(T_a,c_Lubs_OisUb(T_a,V_R_2,V_S_2)))->c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)))).
% 13.65/13.62 all V_xa_2 V_S_2 V_R_2 T_a (class_Orderings_Oord(T_a)-> (hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2))->c_Lubs_Osetle(T_a,V_S_2,V_xa_2))).
% 13.65/13.62 all V_xa_2 V_S_2 V_R_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)->hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2)))).
% 13.65/13.62 all V_net_2 T_a (c_Limits_Owithin(T_a,V_net_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))=V_net_2).
% 13.65/13.62 all V_A_2 V_C_2 V_X_2 T_a (c_member(tc_fun(T_a,tc_HOL_Obool),V_X_2,V_C_2)-> (c_member(T_a,V_A_2,V_X_2)->c_member(T_a,V_A_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)))).
% 13.65/13.62 all V_c_2 T_a V_B_2 V_A_2 (V_A_2=V_B_2-> ((c_member(T_a,V_c_2,V_A_2)-> -c_member(T_a,V_c_2,V_B_2))-> -(-c_member(T_a,V_c_2,V_A_2)->c_member(T_a,V_c_2,V_B_2)))).
% 13.65/13.62 all V_xa_2 T_a c_member(T_a,V_xa_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_x T_a (class_Orderings_Opreorder(T_a)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_x)).
% 13.65/13.62 all V_y_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (V_xa_2!=V_y_2<->c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_xa_2))).
% 13.65/13.62 all V_y_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_y_2,V_xa_2)|V_xa_2=V_y_2)).
% 13.65/13.62 all V_A_2 V_xa_2 T_a (c_member(T_a,V_xa_2,V_A_2)<->hBOOL(hAPP(V_A_2,V_xa_2))).
% 13.65/13.62 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x)).
% 13.65/13.62 all V_y_2 V_xa_2 T_a (c_member(T_a,V_xa_2,c_fe_qual(V_y_2))<->V_xa_2=V_y_2).
% 13.65/13.62 all V_S_2 V_a_2 T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)&class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2))<-> (exists B_x (c_member(T_a,B_x,V_S_2)&c_Orderings_Oord__class_Oless(T_a,V_a_2,B_x))))).
% 13.65/13.62 all V_xa_2 V_y_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_y_2,V_xa_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)<->V_xa_2=V_y_2))).
% 13.65/13.62 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 13.65/13.62 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)).
% 13.65/13.62 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 13.65/13.62 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 13.65/13.62 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)).
% 13.65/13.62 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_y!=V_x)).
% 13.65/13.62 all V_xa_2 T_a V_B_2 V_A_2 (V_A_2=V_B_2-> (c_member(T_a,V_xa_2,V_A_2)<->c_member(T_a,V_xa_2,V_B_2))).
% 13.65/13.62 all V_A_2 T_a V_y_2 V_xa_2 (V_xa_2=V_y_2-> (c_member(T_a,V_xa_2,V_A_2)<->c_member(T_a,V_y_2,V_A_2))).
% 13.65/13.62 all V_b V_a T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> -c_Orderings_Oord__class_Oless(T_a,V_b,V_a))).
% 13.65/13.62 all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> -c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 13.65/13.62 all V_A_2 T_a V_b_2 V_a_2 (V_a_2=V_b_2-> (c_member(T_a,V_b_2,V_A_2)->c_member(T_a,V_a_2,V_A_2))).
% 13.65/13.62 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))).
% 13.65/13.62 all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_b)->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))).
% 13.65/13.62 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))).
% 13.65/13.62 all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))).
% 13.65/13.62 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 13.65/13.62 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 13.65/13.62 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 13.65/13.62 all V_xa_2 V_S_2 V_R_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)->c_Lubs_Osetle(T_a,V_S_2,V_xa_2))).
% 13.65/13.62 all V_xa_2 V_S_2 V_R_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)->c_member(T_a,V_xa_2,V_R_2))).
% 13.65/13.62 all V_xa_2 V_S_2 V_R_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)->c_Lubs_Osetge(T_a,V_xa_2,c_Lubs_Oubs(T_a,V_R_2,V_S_2)))).
% 13.65/13.62 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (V_x!=V_y->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 13.65/13.62 all V_R_2 V_xa_2 V_S_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_Osetle(T_a,V_S_2,V_xa_2)-> (c_member(T_a,V_xa_2,V_R_2)->hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2))))).
% 13.65/13.62 all V_xa_2 V_S_2 V_R_2 T_a (class_Orderings_Oord(T_a)-> (hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2))<->c_Lubs_Osetle(T_a,V_S_2,V_xa_2)&c_member(T_a,V_xa_2,V_R_2))).
% 13.65/13.62 all T_a (c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_xa_2 V_S_2 V_R_2 T_a (class_Orderings_Oord(T_a)-> (hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2))->c_member(T_a,V_xa_2,V_R_2))).
% 13.65/13.62 all V_xa_2 T_a c_member(T_a,V_xa_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_xa_2 V_S_2 V_R_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)->c_Lubs_OleastP(T_a,c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2))).
% 13.65/13.62 all V_xa_2 V_S_2 V_R_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_OleastP(T_a,c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2)->c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2))).
% 13.65/13.62 all V_xa_2 V_S_2 V_R_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)<->c_Lubs_OleastP(T_a,c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2))).
% 13.65/13.62 all V_xa_2 V_Pa_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_OleastP(T_a,V_Pa_2,V_xa_2)->c_Lubs_Osetge(T_a,V_xa_2,c_Set_OCollect(T_a,V_Pa_2)))).
% 13.65/13.62 all V_xa_2 V_Pa_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_OleastP(T_a,V_Pa_2,V_xa_2)<->hBOOL(hAPP(V_Pa_2,V_xa_2))&c_Lubs_Osetge(T_a,V_xa_2,c_Set_OCollect(T_a,V_Pa_2)))).
% 13.65/13.62 all V_S_2 ((exists B_X c_member(tc_RealDef_Oreal,B_X,V_S_2))-> ((exists B_x1 hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),V_S_2),B_x1)))-> (exists B_x1 c_Lubs_OisLub(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),V_S_2,B_x1)))).
% 13.65/13.62 all V_S_2 ((exists B_x c_member(tc_RealDef_Oreal,B_x,V_S_2))& (exists B_x1 hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),V_S_2),B_x1)))-> (exists B_x1 c_Lubs_OisLub(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),V_S_2,B_x1))).
% 13.65/13.62 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 13.65/13.62 -((exists B_x1 hBOOL(hAPP(v_P,B_x1)))-> (all B_Y (-(all B_x (hBOOL(hAPP(v_P,B_x))->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,B_Y)))))).
% 13.65/13.62 all V_y_2 V_xa_2 V_S_2 V_R_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)-> (hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_y_2))->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)))).
% 13.65/13.62 all T_a exists B_x c_member(T_a,B_x,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_x T_a (class_Orderings_Opreorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x)).
% 13.65/13.62 all V_c_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_member(T_a,V_c_2,V_A_2)->c_member(T_a,V_c_2,V_B_2))).
% 13.65/13.62 all V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)<-> (all B_x c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x))))).
% 13.65/13.62 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)).
% 13.65/13.62 all V_y_2 V_xa_2 T_a (class_Orderings_Oorder(T_a)-> (V_xa_2=V_y_2<->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2))).
% 13.65/13.62 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (V_x=V_y->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y))).
% 13.65/13.62 all V_A_2 V_B_2 T_a (c_member(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),V_A_2,V_B_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2))).
% 13.65/13.62 all V_xa_2 V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)->c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_2)))).
% 13.65/13.62 all V_xa_2 V_y_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)<->V_xa_2=V_y_2))).
% 13.65/13.62 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)))).
% 13.65/13.62 all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a)))).
% 13.65/13.62 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (V_b=V_c->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)))).
% 13.65/13.62 all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (V_b=V_c->c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a)))).
% 13.65/13.62 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)->V_x=V_y))).
% 13.65/13.62 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_z)))).
% 13.65/13.62 all V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->V_x=V_y))).
% 13.65/13.62 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x)))).
% 13.65/13.62 all V_xa_2 V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)->c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_2)))).
% 13.65/13.62 all V_y_2 V_xa_2 V_S_2 V_R_2 (c_Lubs_OisLub(tc_RealDef_Oreal,V_R_2,V_S_2,V_xa_2)-> (c_Lubs_OisLub(tc_RealDef_Oreal,V_R_2,V_S_2,V_y_2)->V_xa_2=V_y_2)).
% 13.65/13.62 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x))).
% 13.65/13.62 all V_xa_2 V_Pa_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_OleastP(T_a,V_Pa_2,V_xa_2)->hBOOL(hAPP(V_Pa_2,V_xa_2)))).
% 13.65/13.62 all V_c_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_member(T_a,V_c_2,V_A_2)->c_member(T_a,V_c_2,V_B_2))).
% 13.65/13.62 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 13.65/13.62 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 13.65/13.62 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 13.65/13.62 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 13.65/13.62 all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (V_a!=V_b->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 13.65/13.62 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (V_a!=V_b->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 13.65/13.62 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y)).
% 13.65/13.62 all V_y_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)<->V_xa_2=V_y_2))).
% 13.65/13.62 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y))).
% 13.65/13.62 all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_y))).
% 13.65/13.62 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 13.65/13.62 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 13.65/13.62 all V_y_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)<->V_xa_2=V_y_2))).
% 13.65/13.62 all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y))).
% 13.65/13.62 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x))).
% 13.65/13.62 all V_y_2 V_xa_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|V_xa_2=V_y_2)).
% 13.65/13.62 all V_y_2 V_xa_2 T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)& -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2))).
% 13.65/13.62 all V_y_2 V_xa_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)&V_xa_2!=V_y_2)).
% 13.65/13.62 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x)).
% 13.65/13.62 all V_y_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_y_2,V_xa_2))).
% 13.65/13.62 all V_y_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2))).
% 13.65/13.62 all V_xa_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_member(T_a,V_xa_2,V_A_2)->c_member(T_a,V_xa_2,V_B_2))).
% 13.65/13.62 all V_B_2 V_A_2 V_xa_2 T_a (c_member(T_a,V_xa_2,V_A_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)->c_member(T_a,V_xa_2,V_B_2))).
% 13.65/13.62 all V_xa_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_member(T_a,V_xa_2,V_A_2)->c_member(T_a,V_xa_2,V_B_2))).
% 13.65/13.62 all V_x T_a (class_Orderings_Otop(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Orderings_Otop__class_Otop(T_a))).
% 13.65/13.62 all V_A_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_b_2 V_A_2 T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2),V_b_2)<-> (all B_x (c_member(T_a,B_x,V_A_2)->c_Orderings_Oord__class_Oless__e_q(T_a,B_x,V_b_2))))).
% 13.65/13.62 all V_y_2 V_xa_2 V_Pa_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_OleastP(T_a,V_Pa_2,V_xa_2)-> (c_member(T_a,V_y_2,c_Set_OCollect(T_a,V_Pa_2))->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)))).
% 13.65/13.62 all V_xa_2 V_S_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_Osetle(T_a,V_S_2,V_xa_2)<-> (all B_x (c_member(T_a,B_x,V_S_2)->c_Orderings_Oord__class_Oless__e_q(T_a,B_x,V_xa_2))))).
% 13.65/13.62 all V_S_2 V_xa_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_Osetge(T_a,V_xa_2,V_S_2)<-> (all B_x (c_member(T_a,B_x,V_S_2)->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,B_x))))).
% 13.65/13.62 all V_A_2 V_xa_2 T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)-> (c_member(T_a,V_xa_2,V_A_2)->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)))).
% 13.65/13.62 all V_y_2 V_xa_2 V_S_2 V_R_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)-> (c_member(T_a,V_y_2,V_S_2)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2)))).
% 13.65/13.62 all V_y_2 V_xa_2 V_S_2 V_R_2 T_a (class_Orderings_Oord(T_a)-> (hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2))-> (c_member(T_a,V_y_2,V_S_2)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2)))).
% 13.65/13.62 all V_y_2 V_xa_2 V_S_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_Osetle(T_a,V_S_2,V_xa_2)-> (c_member(T_a,V_y_2,V_S_2)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2)))).
% 13.65/13.62 all V_y_2 V_S_2 V_xa_2 T_a (class_Orderings_Oord(T_a)-> (c_Lubs_Osetge(T_a,V_xa_2,V_S_2)-> (c_member(T_a,V_y_2,V_S_2)->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)))).
% 13.65/13.62 all V_C_2 V_A_2 T_a (c_member(T_a,V_A_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))-> -(all B_X (c_member(T_a,V_A_2,B_X)-> -c_member(tc_fun(T_a,tc_HOL_Obool),B_X,V_C_2)))).
% 13.65/13.62 all V_z_2 V_A_2 T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)-> ((all B_x (c_member(T_a,B_x,V_A_2)->c_Orderings_Oord__class_Oless__e_q(T_a,B_x,V_z_2)))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2),V_z_2))).
% 13.65/13.62 all V_u_2 V_S_2 T_a (class_Orderings_Oord(T_a)-> ((all B_y (c_member(T_a,B_y,V_S_2)->c_Orderings_Oord__class_Oless__e_q(T_a,B_y,V_u_2)))->hBOOL(hAPP(c_Lubs_OisUb(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_u_2)))).
% 13.65/13.62 all V_y_2 V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2)<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2)|V_xa_2=V_y_2).
% 13.65/13.62 all V_y_2 V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2)&V_xa_2!=V_y_2).
% 13.65/13.62 all T_a (c_Set_OPow(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))).
% 13.65/13.62 all V_xa_2 V_S_2 T_a (class_Orderings_Oord(T_a)-> ((all B_x (c_member(T_a,B_x,V_S_2)->c_Orderings_Oord__class_Oless__e_q(T_a,B_x,V_xa_2)))->c_Lubs_Osetle(T_a,V_S_2,V_xa_2))).
% 13.65/13.62 all V_xa_2 V_S_2 T_a (class_Orderings_Oord(T_a)-> ((all B_x (c_member(T_a,B_x,V_S_2)->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,B_x)))->c_Lubs_Osetge(T_a,V_xa_2,V_S_2))).
% 13.65/13.62 all V_A_2 V_xa_2 T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)-> (c_member(T_a,V_xa_2,V_A_2)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2),V_xa_2))).
% 13.65/13.62 all V_C_2 V_A_2 T_a ((all B_X (c_member(tc_fun(T_a,tc_HOL_Obool),B_X,V_A_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),B_X,V_C_2)))->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2)).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)->V_A_2=V_B_2)).
% 13.65/13.62 all V_X_2 V_C_2 V_A_2 T_a (c_member(T_a,V_A_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))-> (c_member(tc_fun(T_a,tc_HOL_Obool),V_X_2,V_C_2)->c_member(T_a,V_A_2,V_X_2))).
% 13.65/13.62 all V_X_2 V_C_2 V_A_2 T_a (c_member(T_a,V_A_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))-> (c_member(tc_fun(T_a,tc_HOL_Obool),V_X_2,V_C_2)->c_member(T_a,V_A_2,V_X_2))).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)->c_member(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OPow(T_a,V_B_2))).
% 13.65/13.62 all V_A_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)&V_A_2!=V_B_2).
% 13.65/13.62 all V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)& -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2))).
% 13.65/13.62 all T_a V_B_2 V_A_2 (V_A_2=V_B_2<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)&c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)<->c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|V_A_2=V_B_2).
% 13.65/13.62 all V_Q_2 T_a V_xa_2 V_Pa_2 (hBOOL(hAPP(V_Pa_2,V_xa_2))-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_Pa_2,V_Q_2)->hBOOL(hAPP(V_Q_2,V_xa_2)))).
% 13.65/13.62 all T_a V_B_2 V_A_2 (V_A_2=V_B_2->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.62 all T_a V_B_2 V_A_2 (V_A_2=V_B_2->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Set_OPow(T_a,V_A_2),c_Set_OPow(T_a,V_B_2))).
% 13.65/13.62 all V_A_2 V_B_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),V_B_2,V_A_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))).
% 13.65/13.62 all V_xa_2 V_Q_2 V_Pa_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_Pa_2,V_Q_2)-> (hBOOL(hAPP(V_Pa_2,V_xa_2))->hBOOL(hAPP(V_Q_2,V_xa_2)))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)->c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)->c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)->c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))).
% 13.65/13.62 all T_a V_B_2 V_A_2 (V_A_2=V_B_2-> -(c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2))).
% 13.65/13.62 all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z)->V_z=V_w)).
% 13.65/13.62 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_j,V_k)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_k))).
% 13.65/13.62 all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z)).
% 13.65/13.62 all V_w c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_w).
% 13.65/13.62 all V_A_2 V_B_2 T_a (c_member(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2)).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_member(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OPow(T_a,V_B_2))->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_member(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OPow(T_a,V_B_2))<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.62 all V_A_2 T_a c_member(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OPow(T_a,V_A_2)).
% 13.65/13.62 all V_A_2 T_a (c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Set_OPow(T_a,V_A_2))=V_A_2).
% 13.65/13.62 all V_A_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),V_A_2,c_Set_OPow(T_a,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))).
% 13.65/13.62 all V_A_2 V_b_2 T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2))<-> (all B_x (c_member(T_a,B_x,V_A_2)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,B_x))))).
% 13.65/13.62 all V_a_2 V_S_2 T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)&class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2),V_a_2)<-> (exists B_x (c_member(T_a,B_x,V_S_2)&c_Orderings_Oord__class_Oless(T_a,B_x,V_a_2))))).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Predicate_OPowp(T_a,V_A_2),c_Predicate_OPowp(T_a,V_B_2))).
% 13.65/13.62 all V_z_2 V_A_2 T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)-> ((all B_x (c_member(T_a,B_x,V_A_2)->c_Orderings_Oord__class_Oless__e_q(T_a,V_z_2,B_x)))->c_Orderings_Oord__class_Oless__e_q(T_a,V_z_2,c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)))).
% 13.65/13.62 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Odecse_q(T_a,V_X_2)<-> (all B_m B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)))))).
% 13.65/13.62 all V_A_2 V_C_2 T_a ((all B_X (c_member(tc_fun(T_a,tc_HOL_Obool),B_X,V_C_2)->c_member(T_a,V_A_2,B_X)))->c_member(T_a,V_A_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))).
% 13.65/13.62 all V_B_2 V_A_2 T_a ((all B_x (c_member(T_a,B_x,V_A_2)->c_member(T_a,B_x,V_B_2)))->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.62 all T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)->c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(T_a)).
% 13.65/13.62 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Oincse_q(T_a,V_X_2)<-> (all B_m B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)))))).
% 13.65/13.62 all V_f_2 V_B_2 V_A_2 T_a T_b (class_Complete__Lattice_Ocomplete__lattice(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)->c_Orderings_Oord__class_Oless__e_q(T_b,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b,V_A_2,V_f_2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b,V_B_2,V_f_2)))).
% 13.65/13.62 all V_f_2 V_B_2 V_A_2 T_a T_b (class_Complete__Lattice_Ocomplete__lattice(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)->c_Orderings_Oord__class_Oless__e_q(T_b,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b,V_B_2,V_f_2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b,V_A_2,V_f_2)))).
% 13.65/13.62 all V_a_2 T_a (-c_member(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 13.65/13.62 all V_A_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_A_2).
% 13.65/13.62 all T_a (c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_xa_2 T_b T_a (class_Orderings_Obot(T_a)->hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_xa_2)=c_Orderings_Obot__class_Obot(T_a)).
% 13.65/13.62 all T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)->c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(T_a)).
% 13.65/13.62 all V_a_2 T_a V_A_2 (V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))-> -c_member(T_a,V_a_2,V_A_2)).
% 13.65/13.62 all V_c_2 T_a (-c_member(T_a,V_c_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 13.65/13.62 all V_A_2 T_a ((exists B_x c_member(T_a,B_x,V_A_2))<->V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_A_2 T_a ((all B_x (-c_member(T_a,B_x,V_A_2)))<->V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_Pa_2 T_a (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))=c_Set_OCollect(T_a,V_Pa_2)<-> (all B_x (-hBOOL(hAPP(V_Pa_2,B_x))))).
% 13.65/13.62 all V_Pa_2 T_a (c_Set_OCollect(T_a,V_Pa_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))<-> (all B_x (-hBOOL(hAPP(V_Pa_2,B_x))))).
% 13.65/13.62 all T_a (c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))<->V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all T_a (c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_A_2 T_a (c_Set_OPow(T_a,V_A_2)!=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))).
% 13.65/13.62 all V_A_2 T_a (-c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 13.65/13.62 all V_x T_a (class_Orderings_Obot(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Orderings_Obot__class_Obot(T_a),V_x)).
% 13.65/13.62 all T_a (c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)->c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(T_a)).
% 13.65/13.62 all V_B_2 T_a c_member(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Set_OPow(T_a,V_B_2)).
% 13.65/13.62 all V_B_2 V_A_2 T_a ((all B_X (c_member(tc_fun(T_a,tc_HOL_Obool),B_X,V_A_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),B_X,V_B_2)))-> (V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2))).
% 13.65/13.62 all V_C_2 V_A_2 T_a ((all B_X (c_member(tc_fun(T_a,tc_HOL_Obool),B_X,V_A_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,B_X)))->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2))).
% 13.65/13.62 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Omonose_q(T_a,V_X_2)<-> (all B_m B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))))| (all B_m B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)))))).
% 13.65/13.62 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__e_q(tc_Nat_Onat,V_m_2,V_n_2)&V_m_2!=V_n_2).
% 13.65/13.62 all V_n_2 V_m_2 (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).
% 13.65/13.62 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 13.65/13.62 all V_y V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)).
% 13.65/13.62 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> (V_m!=V_n->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 13.65/13.62 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 13.65/13.62 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)).
% 13.65/13.62 all V_y V_x (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x))).
% 13.65/13.62 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 13.65/13.62 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)->V_m!=V_n).
% 13.65/13.62 all V_t V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)->V_s!=V_t).
% 13.65/13.62 all V_Pa_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_Pa_2,V_n_2),V_m_2)))-> ((V_m_2=V_n_2->hBOOL(hAPP(hAPP(V_Pa_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_Pa_2,V_n_2),V_m_2)))->hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))))).
% 13.65/13.62 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Oincse_q(T_a,V_X_2)->c_SEQ_Omonose_q(T_a,V_X_2))).
% 13.65/13.62 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Odecse_q(T_a,V_X_2)->c_SEQ_Omonose_q(T_a,V_X_2))).
% 13.65/13.62 all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n).
% 13.65/13.62 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)).
% 13.65/13.62 all V_n V_m (V_m=V_n->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 13.65/13.62 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_k))).
% 13.65/13.62 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->V_m=V_n)).
% 13.65/13.62 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_m=V_n->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 13.65/13.62 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> ((all B_m B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))))->c_SEQ_Omonose_q(T_a,V_X_2))).
% 13.65/13.62 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> ((all B_m B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m))))->c_SEQ_Omonose_q(T_a,V_X_2))).
% 13.65/13.62 all T_a (c_Set_OPow(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))).
% 13.65/13.62 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y))).
% 13.65/13.62 all T_a V_Q_2 V_Pa_2 ((all B_x (hBOOL(hAPP(V_Pa_2,B_x))->hBOOL(hAPP(V_Q_2,B_x))))->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_OCollect(T_a,V_Pa_2),c_Set_OCollect(T_a,V_Q_2))).
% 13.65/13.62 all V_j_2 V_i_2 V_f_2 ((all B_i B_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i,B_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,B_i),hAPP(V_f_2,B_j))))-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(V_f_2,V_i_2),hAPP(V_f_2,V_j_2)))).
% 13.65/13.62 all V_A_2 T_a ((all B_x c_member(T_a,B_x,V_A_2))->c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))=V_A_2).
% 13.65/13.62 all V_b_2 V_B_2 V_a_2 T_a ((-c_member(T_a,V_a_2,V_B_2)->V_a_2=V_b_2)->c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_B_2))).
% 13.65/13.62 all V_A_2 V_b_2 V_a_2 T_a (c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2))-> (V_a_2!=V_b_2->c_member(T_a,V_a_2,V_A_2))).
% 13.65/13.62 all V_A_2 V_xa_2 T_a (c_Set_Oinsert(T_a,V_xa_2,c_Set_Oinsert(T_a,V_xa_2,V_A_2))=c_Set_Oinsert(T_a,V_xa_2,V_A_2)).
% 13.65/13.62 all V_A_2 V_y_2 V_xa_2 T_a (c_Set_Oinsert(T_a,V_xa_2,c_Set_Oinsert(T_a,V_y_2,V_A_2))=c_Set_Oinsert(T_a,V_y_2,c_Set_Oinsert(T_a,V_xa_2,V_A_2))).
% 13.65/13.62 all V_xa_2 V_A_2 V_y_2 T_a (hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_xa_2))<->V_y_2=V_xa_2|hBOOL(hAPP(V_A_2,V_xa_2))).
% 13.65/13.62 all V_A_2 V_a_2 T_a (c_member(T_a,V_a_2,V_A_2)->c_Set_Oinsert(T_a,V_a_2,V_A_2)=V_A_2).
% 13.65/13.62 all V_b_2 V_B_2 V_a_2 T_a (c_member(T_a,V_a_2,V_B_2)->c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_B_2))).
% 13.65/13.62 all V_B_2 V_A_2 V_xa_2 T_a (-c_member(T_a,V_xa_2,V_A_2)-> (-c_member(T_a,V_xa_2,V_B_2)-> (c_Set_Oinsert(T_a,V_xa_2,V_A_2)=c_Set_Oinsert(T_a,V_xa_2,V_B_2)<->V_A_2=V_B_2))).
% 13.65/13.62 all V_A_2 V_b_2 V_a_2 T_a (c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2))<->V_a_2=V_b_2|c_member(T_a,V_a_2,V_A_2)).
% 13.65/13.62 all V_B_2 V_a_2 T_a c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)).
% 13.65/13.62 all V_b_2 V_a_2 T_a (c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))->V_a_2=V_b_2).
% 13.65/13.62 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))<->V_a_2=V_c_2&V_b_2=V_d_2|V_a_2=V_d_2&V_b_2=V_c_2).
% 13.65/13.62 all V_A_2 V_a_2 T_a (c_Set_Oinsert(T_a,V_a_2,V_A_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_A_2 V_a_2 T_a (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))!=c_Set_Oinsert(T_a,V_a_2,V_A_2)).
% 13.65/13.62 all V_a_2 V_D_2 V_C_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_C_2),c_Set_Oinsert(T_a,V_a_2,V_D_2))).
% 13.65/13.62 all V_b_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_b_2,V_B_2))).
% 13.65/13.62 all V_a_2 V_B_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)).
% 13.65/13.62 all V_a_2 V_b_2 T_a (c_member(T_a,V_b_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))<->V_b_2=V_a_2).
% 13.65/13.62 all V_a_2 V_b_2 T_a (c_member(T_a,V_b_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))->V_b_2=V_a_2).
% 13.65/13.62 all V_B_2 V_A_2 V_xa_2 T_a (-c_member(T_a,V_xa_2,V_A_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 13.65/13.62 all V_B_2 V_A_2 V_xa_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_xa_2,V_A_2),V_B_2)<->c_member(T_a,V_xa_2,V_B_2)&c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.62 all V_xa_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))->V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|V_A_2=c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 13.65/13.62 all V_a_2 T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)->c_Complete__Lattice_OSup__class_OSup(T_a,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=V_a_2).
% 13.65/13.62 all V_a_2 T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)->c_Complete__Lattice_OInf__class_OInf(T_a,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=V_a_2).
% 13.65/13.62 all V_xa_2 T_a (c_Set_Othe__elem(T_a,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=V_xa_2).
% 13.65/13.62 all V_B_2 V_xa_2 V_A_2 T_a (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))<-> (c_member(T_a,V_xa_2,V_B_2)->c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))& (-c_member(T_a,V_xa_2,V_B_2)-> (c_member(T_a,V_xa_2,V_A_2)->c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2))& (-c_member(T_a,V_xa_2,V_A_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))).
% 13.65/13.62 all V_B_2 V_xa_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))<-> (c_member(T_a,V_xa_2,V_A_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2))& (-c_member(T_a,V_xa_2,V_A_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 13.65/13.62 all V_B_2 V_xa_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2)-> (c_member(T_a,V_xa_2,V_A_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2)))).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))))).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))))).
% 13.65/13.62 all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)).
% 13.65/13.62 all T_a V_A_2 V_xa_2 V_B_2 ((-hBOOL(hAPP(V_B_2,V_xa_2))->hBOOL(hAPP(V_A_2,V_xa_2)))->hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2))).
% 13.65/13.62 all V_xa_2 V_B_2 V_A_2 T_a (hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2))-> (-hBOOL(hAPP(V_A_2,V_xa_2))->hBOOL(hAPP(V_B_2,V_xa_2)))).
% 13.65/13.62 all V_xa_2 V_B_2 V_A_2 T_a (hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2))-> -(hBOOL(hAPP(V_A_2,V_xa_2))-> -hBOOL(hAPP(V_B_2,V_xa_2)))).
% 13.65/13.62 all T_a V_B_2 V_xa_2 V_A_2 (hBOOL(hAPP(V_A_2,V_xa_2))-> (hBOOL(hAPP(V_B_2,V_xa_2))->hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2)))).
% 13.65/13.62 all V_B_2 V_A_2 V_c_2 T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))-> (-c_member(T_a,V_c_2,V_A_2)->c_member(T_a,V_c_2,V_B_2))).
% 13.65/13.62 all V_A_2 V_B_2 V_c_2 T_a ((-c_member(T_a,V_c_2,V_B_2)->c_member(T_a,V_c_2,V_A_2))->c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 13.65/13.62 all V_B_2 V_A_2 V_c_2 T_a (c_member(T_a,V_c_2,V_A_2)-> (c_member(T_a,V_c_2,V_B_2)->c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))).
% 13.65/13.62 all V_B_2 V_A_2 V_c_2 T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))-> -(c_member(T_a,V_c_2,V_A_2)-> -c_member(T_a,V_c_2,V_B_2))).
% 13.65/13.62 all V_B_2 V_A_2 V_c_2 T_a (c_member(T_a,V_c_2,V_A_2)-> (-c_member(T_a,V_c_2,V_B_2)->c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))).
% 13.65/13.62 all V_B_2 V_A_2 V_c_2 T_a (c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))-> -(c_member(T_a,V_c_2,V_A_2)->c_member(T_a,V_c_2,V_B_2))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2)).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2))=V_B_2).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),V_A_2,V_B_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))).
% 13.65/13.62 all V_xa_2 V_B_2 V_A_2 T_a (hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2))->hBOOL(hAPP(V_B_2,V_xa_2))).
% 13.65/13.62 all V_xa_2 V_B_2 V_A_2 T_a (hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2))->hBOOL(hAPP(V_A_2,V_xa_2))).
% 13.65/13.62 all V_A_2 T_a V_xa_2 V_B_2 (hBOOL(hAPP(V_B_2,V_xa_2))->hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2))).
% 13.65/13.62 all V_B_2 T_a V_xa_2 V_A_2 (hBOOL(hAPP(V_A_2,V_xa_2))->hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))).
% 13.65/13.62 all V_B_2 V_C_2 V_A_2 T_a (c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))=c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),V_B_2)).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))=V_A_2).
% 13.65/13.62 all V_Pa_2 V_B_2 V_A_2 T_a ((all B_x (c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))->hBOOL(hAPP(V_Pa_2,B_x))))<-> (all B_x (c_member(T_a,B_x,V_A_2)->hBOOL(hAPP(V_Pa_2,B_x))))& (all B_x (c_member(T_a,B_x,V_B_2)->hBOOL(hAPP(V_Pa_2,B_x))))).
% 13.65/13.62 all V_Pa_2 V_B_2 V_A_2 T_a ((exists B_x (c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))&hBOOL(hAPP(V_Pa_2,B_x))))<-> (exists B_x (c_member(T_a,B_x,V_A_2)&hBOOL(hAPP(V_Pa_2,B_x))))| (exists B_x (c_member(T_a,B_x,V_B_2)&hBOOL(hAPP(V_Pa_2,B_x))))).
% 13.65/13.62 all V_A_2 V_C_2 V_B_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2),V_A_2)=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))).
% 13.65/13.62 all V_A_2 V_C_2 V_B_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2),V_A_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)=c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))).
% 13.65/13.62 all V_A_2 V_B_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2),V_A_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_B_2)=c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))).
% 13.65/13.62 all V_B_2 V_A_2 V_C_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))=c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_B_2))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2))).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)).
% 13.65/13.62 all V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)=V_A_2).
% 13.65/13.62 all V_A_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)=V_A_2).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),V_A_2,V_B_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2))).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Set_OPow(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Set_OPow(T_a,V_A_2),c_Set_OPow(T_a,V_B_2))).
% 13.65/13.62 all V_m_2 V_n_2 (c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_RealDef_Oreal(tc_Nat_Onat,V_m_2)<->V_n_2=V_m_2).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))->c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_A_2).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_B_2 V_A_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),V_A_2,V_B_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2))).
% 13.65/13.62 all V_B_2 V_A_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),V_A_2,V_B_2))).
% 13.65/13.62 all V_B_2 V_A_2 V_c_2 T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))<->c_member(T_a,V_c_2,V_A_2)|c_member(T_a,V_c_2,V_B_2)).
% 13.65/13.62 all V_B_2 V_A_2 V_c_2 T_a (c_member(T_a,V_c_2,V_A_2)->c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 13.65/13.62 all V_A_2 V_B_2 V_c_2 T_a (c_member(T_a,V_c_2,V_B_2)->c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 13.65/13.62 all V_B_2 V_A_2 V_c_2 T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))<->c_member(T_a,V_c_2,V_A_2)&c_member(T_a,V_c_2,V_B_2)).
% 13.65/13.62 all V_B_2 V_A_2 V_c_2 T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))->c_member(T_a,V_c_2,V_A_2)).
% 13.65/13.62 all V_B_2 V_A_2 V_c_2 T_a (c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))->c_member(T_a,V_c_2,V_B_2)).
% 13.65/13.62 all V_B_2 V_A_2 V_c_2 T_a (c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))<->c_member(T_a,V_c_2,V_A_2)& -c_member(T_a,V_c_2,V_B_2)).
% 13.65/13.62 all V_B_2 V_A_2 V_c_2 T_a (c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))->c_member(T_a,V_c_2,V_A_2)).
% 13.65/13.62 all V_B_2 V_A_2 V_c_2 T_a (c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))-> -c_member(T_a,V_c_2,V_B_2)).
% 13.65/13.62 all V_B_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_B_2)=V_B_2).
% 13.65/13.62 all V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=V_A_2).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))<->V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))&V_B_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_B_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_B_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_A_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))<-> (all B_x (c_member(T_a,B_x,V_A_2)-> (all B_xa (c_member(T_a,B_xa,V_B_2)->B_x!=B_xa))))).
% 13.65/13.62 all V_A_2 T_a (c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_A_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_A_2 T_a (c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=V_A_2).
% 13.65/13.62 all V_A_2 T_a (c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_C_2 V_B_2 V_a_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2)=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))).
% 13.65/13.62 all V_B_2 V_a_2 V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 13.65/13.62 all V_B_2 V_A_2 V_a_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_A_2),c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 13.65/13.62 all V_A_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_B_2 T_a (c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_B_2)=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_B_2 V_A_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.62 all V_A_2 V_B_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)<->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_B_2).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_B_2).
% 13.65/13.62 all V_A_2 V_B_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_A_2).
% 13.65/13.62 all V_B_2 V_C_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2))).
% 13.65/13.62 all V_D_2 V_B_2 V_C_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_D_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2)))).
% 13.65/13.62 all V_A_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))=V_A_2).
% 13.65/13.62 all V_B_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_B_2)=V_B_2).
% 13.65/13.62 all V_B_2 V_A_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_A_2).
% 13.65/13.62 all V_B_2 V_A_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_B_2).
% 13.65/13.62 all V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_A_2).
% 13.65/13.62 all V_A_2 V_B_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_B_2).
% 13.65/13.62 all V_B_2 V_A_2 V_C_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_B_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))).
% 13.65/13.62 all V_D_2 V_B_2 V_C_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_D_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2)))).
% 13.65/13.62 all V_B_2 V_A_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_A_2).
% 13.65/13.62 all V_B_2 V_D_2 V_C_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_D_2,V_B_2)->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2)))).
% 13.65/13.62 all V_C_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)->c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))=V_A_2)).
% 13.65/13.62 all V_B_2 V_A_2 T_a c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Set_OPow(T_a,V_A_2),c_Set_OPow(T_a,V_B_2)),c_Set_OPow(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 13.65/13.62 all V_n (c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n).
% 13.65/13.62 all V_m_2 V_n_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)).
% 13.65/13.62 all V_m_2 V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2)).
% 13.65/13.62 all V_B_2 V_C_2 V_a_2 T_a (c_member(T_a,V_a_2,V_C_2)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2)=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))).
% 13.65/13.62 all V_B_2 V_A_2 V_a_2 T_a (c_member(T_a,V_a_2,V_A_2)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 13.65/13.62 all V_B_2 V_C_2 V_a_2 T_a (-c_member(T_a,V_a_2,V_C_2)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2)=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)).
% 13.65/13.62 all V_B_2 V_A_2 V_a_2 T_a (-c_member(T_a,V_a_2,V_A_2)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.62 all V_B_2 V_C_2 V_a_2 T_a ((c_member(T_a,V_a_2,V_C_2)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2)=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)))& (-c_member(T_a,V_a_2,V_C_2)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2)=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))).
% 13.65/13.62 all V_B_2 V_A_2 V_a_2 T_a ((c_member(T_a,V_a_2,V_A_2)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))& (-c_member(T_a,V_a_2,V_A_2)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 13.65/13.62 all V_A_2 V_B_2 V_xa_2 T_a (c_member(T_a,V_xa_2,V_B_2)->c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_xa_2,V_A_2),V_B_2)=c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.62 all V_A_2 V_B_2 V_xa_2 T_a ((c_member(T_a,V_xa_2,V_B_2)->c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_xa_2,V_A_2),V_B_2)=c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))& (-c_member(T_a,V_xa_2,V_B_2)->c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_xa_2,V_A_2),V_B_2)=c_Set_Oinsert(T_a,V_xa_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))).
% 13.65/13.62 all V_A_2 V_a_2 T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)->c_Complete__Lattice_OSup__class_OSup(T_a,c_Set_Oinsert(T_a,V_a_2,V_A_2))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a_2,c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2))).
% 13.65/13.62 all V_A_2 V_a_2 T_a (c_Set_Oinsert(T_a,V_a_2,V_A_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2)).
% 13.65/13.62 all V_A_2 V_a_2 T_a (c_Set_Oinsert(T_a,V_a_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))=c_Set_Oinsert(T_a,V_a_2,V_A_2)).
% 13.65/13.62 all V_B_2 V_a_2 V_A_2 T_a (c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2)).
% 13.65/13.62 all V_B_2 V_a_2 V_A_2 T_a (c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))).
% 13.65/13.62 all V_A_2 V_a_2 T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)->c_Complete__Lattice_OInf__class_OInf(T_a,c_Set_Oinsert(T_a,V_a_2,V_A_2))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a_2,c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2))).
% 13.65/13.62 all V_A_2 T_a (c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.62 all V_A_2 V_C_2 T_a (c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2),V_A_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))<-> (all B_x (c_member(tc_fun(T_a,tc_HOL_Obool),B_x,V_C_2)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),B_x,V_A_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))).
% 13.65/13.62 all V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))).
% 13.65/13.62 all V_B_2 V_a_2 T_a (c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),V_a_2,V_B_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_a_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2))).
% 13.65/13.62 all V_B_2 V_a_2 T_a (c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),V_a_2,V_B_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_a_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2))).
% 13.65/13.62 all V_b_2 V_a_2 T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)->c_Complete__Lattice_OSup__class_OSup(T_a,c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a_2,V_b_2)).
% 13.65/13.62 all V_b_2 V_a_2 T_a (class_Complete__Lattice_Ocomplete__lattice(T_a)->c_Complete__Lattice_OInf__class_OInf(T_a,c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a_2,V_b_2)).
% 13.65/13.62 all V_A_2 V_a_2 T_a (c_member(T_a,V_a_2,V_A_2)->c_Set_Oinsert(T_a,V_a_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))=V_A_2).
% 13.65/13.62 all V_A_2 V_xa_2 T_a (-c_member(T_a,V_xa_2,V_A_2)->c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_xa_2,V_A_2),c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=V_A_2).
% 13.65/13.62 all V_z V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)))).
% 13.65/13.62 all V_z V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)),c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z)))).
% 13.65/13.62 all V_xa_2 V_g_2 V_f_2 T_b T_a (class_Lattices_Olattice(T_a)->hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a),V_f_2,V_g_2),V_xa_2)=c_Lattices_Osemilattice__inf__class_Oinf(T_a,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_2))).
% 13.65/13.62 all V_xa_2 V_g_2 V_f_2 T_b T_a (class_Lattices_Olattice(T_a)->hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a),V_f_2,V_g_2),V_xa_2)=c_Lattices_Osemilattice__sup__class_Osup(T_a,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_2))).
% 13.65/13.62 all V_x T_a (class_Lattices_Obounded__lattice__top(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Orderings_Otop__class_Otop(T_a),V_x)=V_x).
% 13.65/13.62 all V_x T_a (class_Lattices_Obounded__lattice__top(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Orderings_Otop__class_Otop(T_a))=V_x).
% 13.65/13.62 all V_y_2 V_xa_2 T_a (class_Lattices_Obounded__lattice__top(T_a)-> (c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_xa_2,V_y_2)=c_Orderings_Otop__class_Otop(T_a)<->V_xa_2=c_Orderings_Otop__class_Otop(T_a)&V_y_2=c_Orderings_Otop__class_Otop(T_a))).
% 13.65/13.62 all V_z V_y V_x T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),V_z)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))).
% 13.65/13.62 all V_z V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),V_z)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))).
% 13.65/13.62 all V_c V_b V_a T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_c)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_c))).
% 13.65/13.62 all V_z V_y V_x T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z))).
% 13.65/13.62 all V_z V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z))).
% 13.65/13.62 all V_c V_a V_b T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_c))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_c))).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)).
% 13.65/13.62 all V_b V_a T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x)).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x)).
% 13.65/13.62 all V_b V_a T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_a)).
% 13.65/13.62 all V_x T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_x)=V_x).
% 13.65/13.62 all V_a T_a (class_Lattices_Osemilattice__sup(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_a)=V_a).
% 13.65/13.62 all V_z V_y V_x T_a (class_Lattices_Osemilattice__inf(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_z)=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z))).
% 13.65/13.62 all V_z V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_z)=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z))).
% 13.65/13.62 all V_c V_b V_a T_a (class_Lattices_Osemilattice__inf(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_c)=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_c))).
% 13.65/13.62 all V_z V_y V_x T_a (class_Lattices_Osemilattice__inf(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z))).
% 13.65/13.62 all V_z V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z))).
% 13.65/13.62 all V_c V_a V_b T_a (class_Lattices_Osemilattice__inf(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_c))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_c))).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Osemilattice__inf(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)).
% 13.65/13.62 all V_b V_a T_a (class_Lattices_Osemilattice__inf(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Osemilattice__inf(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_x)).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_x)).
% 13.65/13.62 all V_b V_a T_a (class_Lattices_Osemilattice__inf(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_a)).
% 13.65/13.62 all V_x T_a (class_Lattices_Osemilattice__inf(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_x)=V_x).
% 13.65/13.62 all V_a T_a (class_Lattices_Osemilattice__inf(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_a)=V_a).
% 13.65/13.62 all V_x V_b V_a T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_x)-> -(c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_x)-> -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_x)))).
% 13.65/13.62 all V_d V_b V_c V_a T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_d)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_c,V_d))))).
% 13.65/13.62 all V_z V_x V_y T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z),V_x)))).
% 13.65/13.62 all V_b V_x V_a T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_x)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_x)))).
% 13.65/13.62 all V_x V_y T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)=V_x)).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)=V_y)).
% 13.65/13.62 all V_a V_b V_x T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)))).
% 13.65/13.62 all V_b V_a V_x T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)))).
% 13.65/13.62 all V_z_2 V_y_2 V_xa_2 T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_y_2),V_z_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_z_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_z_2))).
% 13.65/13.62 all V_y_2 V_xa_2 T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)<->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_y_2)=V_y_2)).
% 13.65/13.62 all V_x V_y T_a (class_Lattices_Osemilattice__sup(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))).
% 13.65/13.62 all V_x V_y T_a (class_Lattices_Olattice(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Osemilattice__sup(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))).
% 13.65/13.62 all V_b V_a V_x T_a (class_Lattices_Osemilattice__inf(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b))-> -(c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a)-> -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_b)))).
% 13.65/13.62 all V_d V_b V_c V_a T_a (class_Lattices_Osemilattice__inf(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_d)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_c,V_d))))).
% 13.65/13.62 all V_z V_y V_x T_a (class_Lattices_Osemilattice__inf(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_z)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z))))).
% 13.65/13.62 all V_b V_a V_x T_a (class_Lattices_Osemilattice__inf(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b))))).
% 13.65/13.62 all V_x V_y T_a (class_Lattices_Osemilattice__inf(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)=V_y)).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Osemilattice__inf(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)=V_x)).
% 13.65/13.62 all V_a V_x V_b T_a (class_Lattices_Osemilattice__inf(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_x)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x))).
% 13.65/13.62 all V_b V_x V_a T_a (class_Lattices_Osemilattice__inf(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_x)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x))).
% 13.65/13.62 all V_z_2 V_y_2 V_xa_2 T_a (class_Lattices_Osemilattice__inf(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y_2,V_z_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_z_2))).
% 13.65/13.62 all V_y_2 V_xa_2 T_a (class_Lattices_Osemilattice__inf(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)<->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_xa_2,V_y_2)=V_xa_2)).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Osemilattice__inf(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_y)).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_y)).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Osemilattice__inf(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_x)).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_x)).
% 13.65/13.62 all V_b V_a V_x T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_a)->c_Orderings_Oord__class_Oless(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)))).
% 13.65/13.62 all V_a V_b V_x T_a (class_Lattices_Osemilattice__sup(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_b)->c_Orderings_Oord__class_Oless(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)))).
% 13.65/13.62 all V_b V_x V_a T_a (class_Lattices_Osemilattice__inf(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_x)->c_Orderings_Oord__class_Oless(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x))).
% 13.65/13.62 all V_a V_x V_b T_a (class_Lattices_Osemilattice__inf(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_x)->c_Orderings_Oord__class_Oless(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x))).
% 13.65/13.62 all V_y_2 V_xa_2 T_a (class_Lattices_Obounded__lattice__bot(T_a)-> (c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_y_2)=c_Orderings_Obot__class_Obot(T_a)<->V_xa_2=c_Orderings_Obot__class_Obot(T_a)&V_y_2=c_Orderings_Obot__class_Obot(T_a))).
% 13.65/13.62 all V_x T_a (class_Lattices_Obounded__lattice__bot(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Orderings_Obot__class_Obot(T_a))=V_x).
% 13.65/13.62 all V_x T_a (class_Lattices_Obounded__lattice__bot(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Orderings_Obot__class_Obot(T_a),V_x)=V_x).
% 13.65/13.62 all V_x T_a (class_Lattices_Obounded__lattice__bot(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Orderings_Obot__class_Obot(T_a))=c_Orderings_Obot__class_Obot(T_a)).
% 13.65/13.62 all V_x T_a (class_Lattices_Obounded__lattice__bot(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Orderings_Obot__class_Obot(T_a),V_x)=c_Orderings_Obot__class_Obot(T_a)).
% 13.65/13.62 all V_x V_z V_y T_a (class_Lattices_Odistrib__lattice(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z),V_x)=c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_z,V_x))).
% 13.65/13.62 all V_x V_z V_y T_a (class_Lattices_Odistrib__lattice(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z),V_x)=c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_x),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_z,V_x))).
% 13.65/13.62 all V_z V_y V_x T_a (class_Lattices_Odistrib__lattice(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z))).
% 13.65/13.62 all V_z V_y V_x T_a (class_Lattices_Odistrib__lattice(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))=c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z))).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y))=V_x).
% 13.65/13.62 all V_y V_x T_a (class_Lattices_Olattice(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))=V_x).
% 13.65/13.62 all V_x T_a (class_Lattices_Obounded__lattice__top(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Orderings_Otop__class_Otop(T_a))=c_Orderings_Otop__class_Otop(T_a)).
% 13.65/13.62 all V_x T_a (class_Lattices_Obounded__lattice__top(T_a)->c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Orderings_Otop__class_Otop(T_a),V_x)=c_Orderings_Otop__class_Otop(T_a)).
% 13.65/13.62 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))).
% 13.65/13.62 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)))).
% 13.65/13.62 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__e_q(T_a,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_d_2)))).
% 13.65/13.62 all V_Q_2 V_Pa_2 V_B_2 V_A_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)-> ((all B_x (c_member(T_a,B_x,V_A_2)-> (hBOOL(hAPP(V_Pa_2,B_x))->hBOOL(hAPP(V_Q_2,B_x)))))->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OCollect(T_a,V_Pa_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_OCollect(T_a,V_Q_2))))).
% 13.65/13.62 all V_y_2 V_z_2 V_f_2 T_b V_A_2 V_xa_2 T_a (c_member(T_a,V_xa_2,V_A_2)-> (c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_y_2)->c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_xa_2),V_y_2)))).
% 13.65/13.62 all V_a_2 V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),V_a_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)))).
% 13.65/13.62 all V_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 13.65/13.62 all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 13.65/13.63 all V_a2_2 V_a1_2 T_b T_a c_Nitpick_Ofold__graph_H(T_a,T_b,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_a2_2).
% 13.65/13.63 all V_z_2 V_f_2 T_b T_a c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2).
% 13.65/13.63 all V_l V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)))).
% 13.65/13.63 all V_n V_k V_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k)).
% 13.65/13.63 all V_n V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m).
% 13.65/13.63 all V_l V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))).
% 13.65/13.63 all V_l V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l))).
% 13.65/13.63 all V_n V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i))=V_i).
% 13.65/13.63 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)<->V_m_2=V_n_2))).
% 13.65/13.63 all V_n V_m V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_m)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))).
% 13.65/13.63 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)))).
% 13.65/13.63 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))).
% 13.65/13.63 all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=V_b_2)).
% 13.65/13.63 all V_b_2 V_a_2 T_a (class_Groups_Oab__group__add(T_a)-> (V_a_2=V_b_2<->c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a))).
% 13.65/13.63 all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.63 all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 13.65/13.63 all V_y_2 V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_xa_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.65/13.63 all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))).
% 13.65/13.63 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)))).
% 13.65/13.63 all V_x V_a (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)->c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)).
% 13.65/13.63 all V_c V_b V_a (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_c,V_a)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)))).
% 13.65/13.63 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_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)))).
% 13.65/13.63 all V_n (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 13.65/13.63 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Groups_Oab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)-> (V_a_2=V_b_2<->V_c_2=V_d_2))).
% 13.65/13.63 all V_a5_2 V_a1_2 V_a2_2 V_a4_2 V_a3_2 T_b T_a (c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))<->V_a2_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))&hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)=V_a4_2| (exists B_x B_y (hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)=hAPP(hAPP(V_a3_2,B_x),B_y)&c_member(T_a,B_x,V_a2_2)&c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_a2_2,c_Set_Oinsert(T_a,B_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),B_y)))).
% 13.65/13.63 all V_n V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n))).
% 13.65/13.63 all V_a_2 V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_xa_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_xa_2))).
% 13.65/13.63 all V_F_2 V_xa_2 T_a (-c_member(tc_fun(T_a,tc_HOL_Obool),V_xa_2,V_F_2)-> ((all B_x (c_member(tc_fun(T_a,tc_HOL_Obool),B_x,c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),V_xa_2,V_F_2))-> (all B_xa (c_member(tc_fun(T_a,tc_HOL_Obool),B_xa,c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),V_xa_2,V_F_2))-> (B_x!=B_xa->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),B_x,B_xa)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))))->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_xa_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_F_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 13.65/13.63 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.65/13.63 all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 13.65/13.63 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_RComplete_Onatfloor(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.63 all V_x c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)).
% 13.65/13.63 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.63 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)).
% 13.65/13.63 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m))).
% 13.65/13.63 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.63 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)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)).
% 13.65/13.63 all V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.63 all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 13.65/13.63 all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.63 all V_k V_j V_i (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j)).
% 13.65/13.63 all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->V_m=V_n)).
% 13.65/13.63 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.65/13.63 all V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 13.65/13.63 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.65/13.63 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.63 all V_n (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)).
% 13.65/13.63 all V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.63 all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 13.65/13.63 all V_n (c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n).
% 13.65/13.63 all V_n_2 (c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.63 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.65/13.63 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y))).
% 13.65/13.63 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.63 all V_x V_a (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)->c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)).
% 13.65/13.63 all V_x c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)).
% 13.65/13.63 all V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.63 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_RComplete_Onatceiling(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.63 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x)).
% 13.65/13.63 all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a))).
% 13.65/13.63 all V_n_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 13.65/13.63 all V_y_2 V_xa_2 V_A_2 V_z_2 V_f_2 T_b T_a (c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_y_2)-> (c_member(T_a,V_xa_2,V_A_2)->c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_xa_2),V_y_2)))).
% 13.65/13.63 all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))).
% 13.65/13.63 all V_n_2 c_member(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Nat_Osemiring__1__class_ONats(tc_RealDef_Oreal)).
% 13.65/13.63 all T_a (class_GCD_Ogcd(T_a)->c_GCD_Ogcd__class_OGcd(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.63 all T_a (class_Rings_Ozero__ne_q__one(T_a)->c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a)).
% 13.65/13.63 all T_a (class_Rings_Ozero__ne_q__one(T_a)->c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.63 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.65/13.63 c_Orderings_Obot__class_Obot(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.63 all V_xa_2 V_z_2 V_f_2 T_b T_a (c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_xa_2)->V_xa_2=V_z_2).
% 13.65/13.63 all V_z_2 V_f_2 T_b T_a c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2).
% 13.65/13.63 all V_z_2 V_f_2 T_b T_a c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2).
% 13.65/13.63 all T_a (class_Rings_Osemiring__1(T_a)->c_member(T_a,c_Groups_Oone__class_Oone(T_a),c_Nat_Osemiring__1__class_ONats(T_a))).
% 13.65/13.63 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))).
% 13.65/13.63 all T_a (class_Rings_Olinordered__semidom(T_a)-> -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))).
% 13.65/13.63 all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))).
% 13.65/13.63 all T_a (class_Rings_Olinordered__semidom(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))).
% 13.65/13.63 all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))).
% 13.65/13.63 all V_y_2 V_z_2 V_f_2 T_b V_A_2 V_xa_2 T_a (-c_member(T_a,V_xa_2,V_A_2)-> (c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2,V_y_2)->c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Set_Oinsert(T_a,V_xa_2,V_A_2),hAPP(hAPP(V_f_2,V_xa_2),V_y_2)))).
% 13.65/13.63 all T_a (class_Rings_Osemiring__1(T_a)->c_member(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_ONats(T_a))).
% 13.65/13.63 all T_a (class_GCD_Ogcd(T_a)->c_GCD_Ogcd__class_OLcm(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(T_a)).
% 13.65/13.63 all V_xa_2 V_A_2 V_a_2 V_f_2 T_a (c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2,V_xa_2)-> (-c_member(T_a,V_a_2,V_A_2)->c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Set_Oinsert(T_a,V_a_2,V_A_2),V_xa_2))).
% 13.65/13.63 all V_x V_n (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))->c_RComplete_Onatfloor(V_x)=V_n)).
% 13.65/13.63 all V_a_2 V_xa_2 V_A_2 V_b_2 T_a (class_Groups_Oab__semigroup__mult(T_a)-> (c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2,V_xa_2)-> (c_member(T_a,V_a_2,V_A_2)-> (-c_member(T_a,V_b_2,V_A_2)->c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_xa_2))))).
% 13.65/13.63 all V_v V_u V_y V_a V_x T_a (class_Rings_Olinordered__semiring__1(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)-> (c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)=c_Groups_Oone__class_Oone(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a))))))).
% 13.65/13.63 all V_b V_a T_a (class_Rings_Ono__zero__divisors(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)=c_Groups_Ozero__class_Ozero(T_a)->V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a))).
% 13.65/13.63 all V_b V_a T_a (class_Rings_Ono__zero__divisors(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a)))).
% 13.65/13.63 all V_b_2 V_a_2 T_a (class_Rings_Oring__no__zero__divisors(T_a)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.65/13.63 all V_a T_a (class_Rings_Omult__zero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.63 all V_a T_a (class_Rings_Omult__zero(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.63 all V_a T_a (class_Groups_Omonoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a).
% 13.65/13.63 all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a).
% 13.65/13.63 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))).
% 13.65/13.63 all V_a T_a (class_Groups_Omonoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 13.65/13.63 all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 13.65/13.63 all V_b_2 V_a_2 V_c_2 (V_c_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2)<->V_a_2=V_b_2)).
% 13.65/13.63 all V_b_2 V_a_2 V_c_2 (V_c_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2)<->V_a_2=V_b_2)).
% 13.65/13.63 all V_y_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_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)&V_y_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.65/13.63 all V_n V_m (V_m=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)->V_n=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.63 all V_n_2 V_k_2 V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)<->V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.63 all V_n_2 V_m_2 V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)<->V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.63 all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.63 all V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.63 all V_n (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.63 all V_x T_a (class_Rings_Oring__1(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)))).
% 13.65/13.63 all V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z)=V_z).
% 13.65/13.63 all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a).
% 13.65/13.63 all V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a).
% 13.65/13.63 all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a).
% 13.65/13.63 all V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a).
% 13.65/13.63 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__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))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2))).
% 13.65/13.63 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__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))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)))).
% 13.65/13.63 all V_d V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 13.65/13.63 all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b))).
% 13.65/13.63 all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Groups_Oab__semigroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Groups_Oab__semigroup__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 13.65/13.63 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)).
% 13.65/13.63 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)).
% 13.65/13.63 all V_c V_b V_a T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)->V_b=V_c)).
% 13.65/13.63 all V_c V_b V_a T_a (class_Groups_Ocancel__ab__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)->V_b=V_c)).
% 13.65/13.63 all V_c V_a V_b T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_b,V_a)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)->V_b=V_c)).
% 13.65/13.63 all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 13.65/13.63 all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 13.65/13.63 all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))).
% 13.65/13.63 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))).
% 13.65/13.63 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))).
% 13.65/13.63 all V_l V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l)))).
% 13.65/13.63 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))).
% 13.65/13.63 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))).
% 13.65/13.63 all V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))).
% 13.65/13.63 all V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)).
% 13.65/13.63 all V_n V_m (c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 13.65/13.63 all V_w V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2)),V_w)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 13.65/13.63 all V_c V_b V_e V_a T_a (class_Rings_Osemiring(T_a)->c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c)).
% 13.65/13.63 all V_z V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y))).
% 13.65/13.63 all V_a T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)=V_a).
% 13.65/13.63 all V_x T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)=V_x).
% 13.65/13.63 all V_b V_a T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 13.65/13.63 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)).
% 13.65/13.63 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))).
% 13.65/13.63 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b)=V_a).
% 13.65/13.63 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=V_a).
% 13.65/13.63 all V_b V_a V_y V_x T_a (class_Rings_Oring(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b))).
% 13.65/13.63 all V_k V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))).
% 13.65/13.63 all V_n V_m V_k (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))).
% 13.65/13.63 all V_d V_b V_c V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d))).
% 13.65/13.63 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))).
% 13.65/13.63 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)))).
% 13.65/13.63 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__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))<->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))).
% 13.65/13.63 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__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))<->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)))).
% 13.65/13.63 all V_v V_u V_y V_a V_x T_a (class_Rings_Olinordered__semiring__1__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)-> (c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)=c_Groups_Oone__class_Oone(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a))))))).
% 13.65/13.63 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 13.65/13.63 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 13.65/13.63 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 13.65/13.63 all V_y_2 V_xa_2 T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_xa_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)-> (c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_xa_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 13.65/13.63 all V_a V_b V_c T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 13.65/13.63 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.65/13.63 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))).
% 13.65/13.63 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)))).
% 13.65/13.63 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 13.65/13.63 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.65/13.63 all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 13.65/13.63 all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 13.65/13.63 all V_a T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)))).
% 13.65/13.63 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)&c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))).
% 13.65/13.63 all V_b V_a T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))).
% 13.65/13.63 all V_d V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))).
% 13.65/13.63 all V_d V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))).
% 13.65/13.63 all V_c V_a V_b T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 13.65/13.63 all V_c V_a V_b T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Rings_Oordered__comm__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))).
% 13.65/13.63 all V_b V_a T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))).
% 13.65/13.63 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.65/13.63 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.65/13.63 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.65/13.63 all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))).
% 13.65/13.63 all V_b_2 V_a_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2))).
% 13.65/13.63 all V_b_2 V_a_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 13.65/13.63 all V_a T_a (class_Rings_Olinordered__ring(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))).
% 13.65/13.63 all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 13.65/13.63 all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Rings_Olinordered__comm__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))))).
% 13.65/13.63 all V_b V_a T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))).
% 13.65/13.63 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.65/13.63 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)))).
% 13.65/13.63 all V_a V_b T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)))).
% 13.65/13.63 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)))).
% 13.65/13.63 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.65/13.63 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.65/13.63 all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))))).
% 13.65/13.63 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)))).
% 13.65/13.63 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))).
% 13.65/13.63 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))).
% 13.65/13.63 all V_a T_a (class_Rings_Olinordered__ring(T_a)-> -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a))).
% 13.65/13.63 all V_b V_a (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b))))).
% 13.65/13.63 all V_n V_m T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))))).
% 13.65/13.63 all V_xa_2 V_A_2 V_f_2 T_a (c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2,V_xa_2)->V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.63 all V_xa_2 V_f_2 T_a (-c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_xa_2)).
% 13.65/13.63 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)).
% 13.65/13.63 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)).
% 13.65/13.63 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)).
% 13.65/13.63 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))).
% 13.65/13.63 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))).
% 13.65/13.63 all V_y_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_y_2),V_z_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2))).
% 13.65/13.63 all V_y V_x (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)))).
% 13.65/13.63 all V_y V_x V_z (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y)))).
% 13.65/13.63 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.65/13.63 all V_b_2 V_a_2 T_a (class_Rings_Osemiring__1(T_a)-> (c_member(T_a,V_a_2,c_Nat_Osemiring__1__class_ONats(T_a))-> (c_member(T_a,V_b_2,c_Nat_Osemiring__1__class_ONats(T_a))->c_member(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))))).
% 13.65/13.63 all V_b_2 V_a_2 T_a (class_Rings_Osemiring__1(T_a)-> (c_member(T_a,V_a_2,c_Nat_Osemiring__1__class_ONats(T_a))-> (c_member(T_a,V_b_2,c_Nat_Osemiring__1__class_ONats(T_a))->c_member(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))))).
% 13.65/13.63 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.65/13.63 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.65/13.63 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 13.65/13.63 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 13.65/13.63 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.65/13.63 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 13.65/13.63 all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))).
% 13.65/13.63 all V_b V_a V_c T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)))).
% 13.65/13.63 all V_b V_c V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)))).
% 13.65/13.63 all V_b V_a V_c T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 13.65/13.63 all V_b V_a V_c T_a (class_Rings_Olinordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 13.65/13.63 all V_b V_c V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 13.65/13.63 all V_b V_c V_a T_a (class_Rings_Olinordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 13.65/13.63 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))).
% 13.65/13.63 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))).
% 13.65/13.63 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))).
% 13.65/13.63 all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))))))).
% 13.65/13.63 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__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))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2)))).
% 13.65/13.63 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__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))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)))).
% 13.65/13.63 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x))))).
% 13.65/13.63 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x))))).
% 13.65/13.63 all V_y_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__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_y_2),V_z_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2))).
% 13.65/13.63 all V_y_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__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_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2))).
% 13.65/13.63 all V_n_2 V_k_2 V_m_2 (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)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2))).
% 13.65/13.63 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_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__e_q(tc_Nat_Onat,V_m_2,V_n_2))).
% 13.65/13.63 all V_z_2 V_y_2 V_A_2 V_b_2 T_a (class_Groups_Oab__semigroup__mult(T_a)-> (c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2,V_y_2)-> (-c_member(T_a,V_b_2,V_A_2)->c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_z_2,c_Set_Oinsert(T_a,V_b_2,V_A_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2),V_y_2))))).
% 13.65/13.63 all V_b_2 V_a_2 V_f_2 T_a (c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_b_2)<->V_a_2=V_b_2).
% 13.65/13.63 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__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))).
% 13.65/13.63 all V_m_2 V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2)<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))).
% 13.65/13.63 all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.65/13.63 all V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_xa_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_xa_2)).
% 13.65/13.63 all V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.65/13.63 all V_y_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_y_2),V_y_2)))<->V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a))).
% 13.65/13.63 all V_y V_x T_a (class_Rings_Olinordered__ring(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a))).
% 13.65/13.63 all V_y_2 V_xa_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))<->V_xa_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.65/13.63 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=V_m->V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.63 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)).
% 13.65/13.63 all V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 13.65/13.63 all V_n (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n).
% 13.65/13.63 all V_n V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)))).
% 13.65/13.63 all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)<->V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)&V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.65/13.63 all V_n (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n).
% 13.65/13.63 all V_n_2 V_m_2 (c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)<->V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)&V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.65/13.63 all V_n (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)=V_n).
% 13.65/13.63 all V_j V_i (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i)).
% 13.65/13.63 all V_i V_j (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i)).
% 13.65/13.63 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)).
% 13.65/13.63 all V_m V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))).
% 13.65/13.63 all V_m V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))).
% 13.65/13.63 all V_z V_y V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 13.65/13.63 all V_y V_z V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 13.65/13.63 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))).
% 13.65/13.63 all V_l V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)))).
% 13.65/13.63 all V_n V_m V_l V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)-> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 13.65/13.63 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k)).
% 13.65/13.63 all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)-> -(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n))).
% 13.65/13.63 all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 13.65/13.63 all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)).
% 13.65/13.63 all V_l V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)))).
% 13.65/13.63 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))).
% 13.65/13.63 all V_y V_z V_x (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_z)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 13.65/13.63 all V_z V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 13.65/13.63 all V_m V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))).
% 13.65/13.63 all V_m V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))).
% 13.65/13.63 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)).
% 13.65/13.63 all V_n_2 V_m_2 (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)))).
% 13.65/13.63 all V_m V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)).
% 13.65/13.63 all V_m V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 13.65/13.63 all V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)).
% 13.65/13.63 all V_n V_m V_k (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))).
% 13.65/13.63 all V_k V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))).
% 13.65/13.63 all V_k V_n V_m (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k))).
% 13.65/13.63 all V_w V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z)).
% 13.65/13.63 all V_z3 V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3))).
% 13.65/13.63 all V_n V_k V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 13.65/13.63 all V_n V_m V_k (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 13.65/13.63 all V_k V_j V_i (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))).
% 13.65/13.63 all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n)=V_m).
% 13.65/13.63 all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n)=V_m).
% 13.65/13.63 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)).
% 13.65/13.63 all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.63 all V_n V_m (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m).
% 13.65/13.63 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)).
% 13.65/13.63 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j)).
% 13.65/13.63 all V_i_2 V_k_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2))).
% 13.65/13.63 all V_m V_n V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k))).
% 13.65/13.63 all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m).
% 13.65/13.63 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)).
% 13.65/13.63 all V_i_2 V_j_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2))).
% 13.65/13.63 all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)=V_m).
% 13.65/13.63 all V_k_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_k_2<->V_j_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2))).
% 13.65/13.63 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))).
% 13.65/13.63 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)).
% 13.65/13.63 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)).
% 13.65/13.63 all V_n V_m (c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 13.65/13.63 all V_b_2 V_a_2 V_Pa_2 (hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,B_d))))).
% 13.65/13.63 all V_b_2 V_a_2 V_Pa_2 (hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,B_d)))))).
% 13.65/13.63 all V_n V_z (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 13.65/13.63 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 13.65/13.63 all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)).
% 13.65/13.63 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 13.65/13.63 all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)).
% 13.65/13.63 all V_x V_n (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))->c_RComplete_Onatceiling(V_x)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 13.65/13.63 all V_y_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_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(T_a)<->V_xa_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))).
% 13.65/13.63 all V_y V_x T_a (class_Rings_Olinordered__ring(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))).
% 13.65/13.63 all V_n_2 V_m_2 V_u_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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)))).
% 13.65/13.63 all V_n_2 V_m_2 V_u_2 V_i_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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))).
% 13.65/13.63 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)).
% 13.65/13.63 all V_z V_y V_x (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z))).
% 13.65/13.63 all V_k V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))).
% 13.65/13.63 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).
% 13.65/13.63 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).
% 13.65/13.63 all V_k V_j V_u V_i (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k)).
% 13.65/13.63 all V_n_2 V_m_2 V_k_2 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)<->V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=V_n_2).
% 13.65/13.63 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))).
% 13.65/13.63 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)).
% 13.65/13.63 all V_n_2 V_m_2 V_u_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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))).
% 13.65/13.63 all V_n V_m V_u V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u),V_n))).
% 13.65/13.63 all V_n_2 V_m_2 V_u_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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__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)))).
% 13.65/13.63 all V_n_2 V_m_2 V_u_2 V_i_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)-> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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)).
% 13.65/13.63 all V_n V_m V_u V_i V_j (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_i)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u),V_m),V_n)).
% 13.65/13.63 all V_n_2 V_m_2 V_u_2 V_i_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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__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))).
% 13.65/13.63 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__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__e_q(tc_Nat_Onat,V_m_2,V_n_2))).
% 13.65/13.63 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)).
% 13.65/13.63 all V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_m,V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_m)).
% 13.65/13.63 all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)).
% 13.65/13.63 all V_ry V_rx V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry))).
% 13.65/13.63 all V_ry V_rx V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry)).
% 13.65/13.63 all V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx))).
% 13.65/13.63 all V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly)).
% 13.65/13.63 all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)))).
% 13.65/13.63 all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry))).
% 13.65/13.63 all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry))).
% 13.65/13.63 all V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)).
% 13.65/13.63 all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d))).
% 13.65/13.63 all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d)).
% 13.65/13.63 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b)).
% 13.65/13.63 all V_d V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))).
% 13.65/13.63 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.63 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.63 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))).
% 13.65/13.63 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 13.65/13.63 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a).
% 13.65/13.63 all V_z V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z))).
% 13.65/13.63 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)))).
% 13.65/13.63 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))).
% 13.65/13.63 all V_b V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m)).
% 13.65/13.63 all V_z_2 V_xa_2 V_y_2 V_w_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_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_y_2))<->V_w_2=V_xa_2|V_y_2=V_z_2)).
% 13.65/13.63 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a).
% 13.65/13.63 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a).
% 13.65/13.63 all V_d V_c V_b V_a V_r T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_r!=c_Groups_Ozero__class_Ozero(T_a)-> (V_a=V_b&V_c!=V_d->c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c))!=c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d))))).
% 13.65/13.63 all V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m)).
% 13.65/13.63 all V_a V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m)).
% 13.65/13.63 all V_b V_a V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)))).
% 13.65/13.63 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)))).
% 13.65/13.63 all V_b T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)=c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.63 all V_y T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)=c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.63 all V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.63 all V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.63 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))).
% 13.65/13.63 all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),V_ya)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya))).
% 13.65/13.63 all V_b V_a_H V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H)),V_b)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b))).
% 13.65/13.63 all V_y V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y))).
% 13.65/13.63 all V_b_H V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H))).
% 13.65/13.63 all V_b_H V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H))=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H))).
% 13.65/13.63 all V_y V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y))).
% 13.65/13.63 all V_b V_a_H V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b)=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b))).
% 13.65/13.63 all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya)=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya))).
% 13.65/13.63 all V_r (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)-> (exists B_n (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_r)&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,B_n))))).
% 13.65/13.63 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)<-> (exists B_n (V_l_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n)))).
% 13.65/13.63 all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(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))))).
% 13.65/13.63 all V_n_2 V_Pa_2 (-hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))-> (hBOOL(hAPP(V_Pa_2,V_n_2))-> (exists B_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2)& (all B_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i,B_k)-> -hBOOL(hAPP(V_Pa_2,B_i))))&hBOOL(hAPP(V_Pa_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))).
% 13.65/13.63 all T_a (class_Rings_Oring__1(T_a)->c_member(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Oring__1__class_OInts(T_a))).
% 13.65/13.63 all V_b_2 V_a_2 T_a (class_Rings_Oring__1(T_a)-> (c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))-> (c_member(T_a,V_b_2,c_Int_Oring__1__class_OInts(T_a))->c_member(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Int_Oring__1__class_OInts(T_a))))).
% 13.65/13.63 all V_b_2 V_a_2 T_a (class_Rings_Oring__1(T_a)-> (c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))-> (c_member(T_a,V_b_2,c_Int_Oring__1__class_OInts(T_a))->c_member(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2),c_Int_Oring__1__class_OInts(T_a))))).
% 13.65/13.63 all V_b_2 V_a_2 T_a (class_Rings_Oring__1(T_a)-> (c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))-> (c_member(T_a,V_b_2,c_Int_Oring__1__class_OInts(T_a))->c_member(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Int_Oring__1__class_OInts(T_a))))).
% 13.65/13.63 all T_a (class_Rings_Oring__1(T_a)->c_member(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Oring__1__class_OInts(T_a))).
% 13.65/13.63 all V_n_2 c_member(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Int_Oring__1__class_OInts(tc_RealDef_Oreal)).
% 13.65/13.63 all V_a_2 T_a (class_Int_Oring__char__0(T_a)-> (c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(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)))).
% 13.65/13.63 all V_a_2 T_a (class_Int_Oring__char__0(T_a)-> (c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2),V_a_2)!=c_Groups_Ozero__class_Ozero(T_a))).
% 13.65/13.63 all V_n V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n))).
% 13.65/13.63 all V_a3_2 V_a2_2 V_a1_2 V_f_2 T_a (c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Set_Oinsert(T_a,V_a1_2,V_a2_2),V_a3_2)<-> (exists B_a B_A (c_Set_Oinsert(T_a,V_a1_2,V_a2_2)=c_Set_Oinsert(T_a,B_a,B_A)&c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A,V_a3_2)& -c_member(T_a,B_a,B_A)))).
% 13.65/13.63 all V_n_2 V_a_2 T_a (class_Rings_Oring__1(T_a)-> (c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))->c_member(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2),c_Int_Oring__1__class_OInts(T_a)))).
% 13.65/13.63 all V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a)).
% 13.65/13.63 all V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_x).
% 13.65/13.63 all V_q V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q))).
% 13.65/13.63 all V_q V_p V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q))).
% 13.65/13.63 all V_q V_p V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q))).
% 13.65/13.63 all V_x V_n T_a (class_Groups_Omonoid__mult(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))).
% 13.65/13.63 all V_m V_n T_a (class_Power_Opower(T_a)-> (V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=c_Groups_Oone__class_Oone(T_a))& (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))).
% 13.65/13.63 all V_n V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))))).
% 13.65/13.63 all V_z V_y V_x (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z))).
% 13.65/13.63 all V_z V_y V_x (hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z))).
% 13.65/13.63 all V_n V_m (c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n)).
% 13.65/13.63 all V_n V_m (hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n)=c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))).
% 13.65/13.63 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)).
% 13.65/13.63 all V_n V_m V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 13.65/13.63 all V_n V_x (V_x=c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))->c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n)).
% 13.65/13.63 all V_p V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=c_Groups_Oone__class_Oone(tc_Nat_Onat))& (V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))).
% 13.65/13.63 all V_n V_a T_a (class_Rings_Oring__1__no__zero__divisors(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)!=c_Groups_Ozero__class_Ozero(T_a))).
% 13.65/13.63 all V_n V_b V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))).
% 13.65/13.63 all V_n V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 13.65/13.63 all V_n T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a)).
% 13.65/13.63 all V_n V_m V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n)).
% 13.65/13.63 all V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_a).
% 13.65/13.63 all V_n V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))))).
% 13.65/13.63 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))).
% 13.65/13.63 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))).
% 13.65/13.63 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))).
% 13.65/13.63 all V_n_2 V_a_2 T_a (class_Power_Opower(T_a)&class_Rings_Omult__zero(T_a)&class_Rings_Ono__zero__divisors(T_a)&class_Rings_Ozero__ne_q__one(T_a)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a)&V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.65/13.63 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))).
% 13.65/13.63 all V_a T_a (class_Power_Opower(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a)).
% 13.65/13.63 all V_n V_m V_a T_a (class_Groups_Omonoid__mult(T_a)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 13.65/13.63 all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 13.65/13.63 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 13.65/13.63 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 13.65/13.63 all V_n T_a (class_Power_Opower(T_a)&class_Rings_Osemiring__0(T_a)-> (V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a))& (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Ozero__class_Ozero(T_a))).
% 13.65/13.63 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))))).
% 13.65/13.63 all V_n V_m V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)))).
% 13.65/13.63 all V_y_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_y_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_y_2)))).
% 13.65/13.63 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))))).
% 13.65/13.63 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 13.65/13.63 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))).
% 13.65/13.63 all V_b V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->V_a=V_b))))).
% 13.65/13.63 all V_a V_N V_n T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_N)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))))).
% 13.65/13.63 all V_y_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__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_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_xa_2,V_y_2)))).
% 13.65/13.63 all V_n V_m V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)))).
% 13.65/13.63 all V_n V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))).
% 13.65/13.63 all T_a (class_Power_Opower(T_a)->c_Power_Opower__class_Opower(T_a)=c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a))).
% 13.65/13.63 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)).
% 13.65/13.63 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)->c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)))).
% 13.65/13.63 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))).
% 13.65/13.63 all V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)=V_z).
% 13.65/13.63 all V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z).
% 13.65/13.63 all V_z3 V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3))).
% 13.65/13.63 all V_w V_z (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)).
% 13.65/13.63 all V_z2 V_z1 V_w (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))).
% 13.65/13.63 all V_w V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))).
% 13.65/13.63 all V_z2 V_z1 V_w (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2))).
% 13.65/13.63 all V_w V_z2 V_z1 (hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w))).
% 13.65/13.63 all V_a_2 V_times_2 V_one_2 T_a (hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_one_2).
% 13.65/13.63 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)))))).
% 13.65/13.63 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)))).
% 13.65/13.63 all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 13.65/13.63 all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)=V_z).
% 13.65/13.63 all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z).
% 13.65/13.63 all V_z (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z))).
% 13.65/13.63 all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.65/13.63 all V_z V_w (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)).
% 13.65/13.63 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)).
% 13.65/13.63 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).
% 13.65/13.63 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,V_z_2)).
% 13.65/13.63 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k))).
% 13.65/13.63 all V_z V_z_H V_w V_w_H (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_H,V_z)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)))).
% 13.65/13.63 all V_z3 V_z2 V_z1 (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3))).
% 13.65/13.63 all V_z V_y V_x (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z))).
% 13.65/13.63 all V_w V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)).
% 13.65/13.63 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j))).
% 13.65/13.63 all V_y V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x)).
% 13.65/13.63 all V_w_2 V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_w_2)&V_z_2!=V_w_2).
% 13.65/13.63 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))).
% 13.65/13.63 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)).
% 13.65/13.63 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 13.65/13.63 all V_z_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)).
% 13.65/13.63 c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.65/13.63 all V_q V_r V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)-> (V_a=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint))))).
% 13.65/13.63 all V_q V_r V_a (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)-> (V_a=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q)))).
% 13.65/13.63 all V_w c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_w).
% 13.65/13.63 all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z)).
% 13.65/13.63 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_j,V_k)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_k))).
% 13.65/13.63 all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z)->V_z=V_w)).
% 13.65/13.63 all V_r_H V_q_H V_b_H V_r V_q V_b (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H,V_b)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,V_q))))))).
% 13.65/13.63 all V_r V_q V_r_H V_q_H V_b (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,V_q_H))))).
% 13.65/13.63 all V_r_H V_q_H V_b_H V_r V_q V_b (c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H,V_b)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,V_q_H))))))).
% 13.65/13.63 all V_r V_q V_r_H V_q_H V_b (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,V_q))))).
% 13.65/13.63 all V_r_H V_q_H V_b_H (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint))))).
% 13.65/13.63 all V_r_H V_q_H V_b_H (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)-> (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H)))).
% 13.65/13.63 all V_n V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))).
% 13.65/13.63 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)))).
% 13.65/13.63 c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 13.65/13.63 c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 13.65/13.63 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)))).
% 13.65/13.63 all V_x V_y ((c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)->c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y))& (-c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)->c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 13.65/13.63 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),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Transcendental_Oln(V_x))).
% 13.65/13.63 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)).
% 13.65/13.63 all V_y_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_y_2)-> (c_Transcendental_Oln(V_xa_2)=c_Transcendental_Oln(V_y_2)<->V_xa_2=V_y_2))).
% 13.65/13.63 all V_y_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_y_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_xa_2),c_Transcendental_Oln(V_y_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2)))).
% 13.65/13.63 c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.65/13.63 all V_y_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_y_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(V_xa_2),c_Transcendental_Oln(V_y_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2)))).
% 13.65/13.63 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x))).
% 13.65/13.63 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))).
% 13.65/13.63 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))).
% 13.65/13.63 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))).
% 13.65/13.63 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)))).
% 13.65/13.63 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)))).
% 13.65/13.63 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))).
% 13.65/13.63 all V_x (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)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x))).
% 13.65/13.63 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__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_xa_2))<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_xa_2))).
% 13.65/13.63 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)))).
% 13.65/13.63 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)),V_x)).
% 13.65/13.63 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y)))).
% 13.65/13.63 all V_x V_y (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)->c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y)).
% 13.65/13.63 all V_xa_2 V_X_2 V_a_2 V_f_2 T_a (c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Set_Oinsert(T_a,V_a_2,V_X_2),V_xa_2)-> -(all B_a B_A (c_Set_Oinsert(T_a,V_a_2,V_X_2)=c_Set_Oinsert(T_a,B_a,B_A)-> (c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A,V_xa_2)->c_member(T_a,B_a,B_A))))).
% 13.65/13.63 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),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_x)))).
% 13.65/13.63 all T_1 class_Lattices_Obounded__lattice(tc_Limits_Onet(T_1)).
% 13.65/13.63 class_Lattices_Obounded__lattice(tc_HOL_Obool).
% 13.65/13.63 all T_2 T_1 (class_Lattices_Obounded__lattice(T_1)->class_Lattices_Obounded__lattice(tc_fun(T_2,T_1))).
% 13.65/13.63 all T_2 T_1 (class_Complete__Lattice_Ocomplete__lattice(T_1)->class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1))).
% 13.65/13.63 all T_2 T_1 (class_Lattices_Obounded__lattice(T_1)->class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1))).
% 13.65/13.63 all T_2 T_1 (class_Lattices_Obounded__lattice(T_1)->class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1))).
% 13.65/13.63 all T_2 T_1 (class_Lattices_Olattice(T_1)->class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1))).
% 13.65/13.63 all T_2 T_1 (class_Lattices_Olattice(T_1)->class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1))).
% 13.65/13.63 all T_2 T_1 (class_Lattices_Odistrib__lattice(T_1)->class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1))).
% 13.65/13.63 all T_2 T_1 (class_Orderings_Opreorder(T_1)->class_Orderings_Opreorder(tc_fun(T_2,T_1))).
% 13.65/13.63 all T_2 T_1 (class_Lattices_Olattice(T_1)->class_Lattices_Olattice(tc_fun(T_2,T_1))).
% 13.65/13.63 all T_2 T_1 (class_Orderings_Oorder(T_1)->class_Orderings_Oorder(tc_fun(T_2,T_1))).
% 13.65/13.63 all T_2 T_1 (class_Orderings_Otop(T_1)->class_Orderings_Otop(tc_fun(T_2,T_1))).
% 13.65/13.63 all T_2 T_1 (class_Orderings_Oord(T_1)->class_Orderings_Oord(tc_fun(T_2,T_1))).
% 13.65/13.63 all T_2 T_1 (class_Orderings_Obot(T_1)->class_Orderings_Obot(tc_fun(T_2,T_1))).
% 13.65/13.63 all T_2 T_1 (class_Groups_Ominus(T_1)->class_Groups_Ominus(tc_fun(T_2,T_1))).
% 13.65/13.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 13.65/13.63 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 13.65/13.63 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 13.65/13.63 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 13.65/13.63 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint).
% 13.65/13.63 class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 13.65/13.63 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint).
% 13.65/13.63 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 13.65/13.63 class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 13.65/13.63 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 13.65/13.63 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 13.65/13.63 class_Rings_Oordered__cancel__semiring(tc_Int_Oint).
% 13.65/13.63 class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 13.65/13.63 class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 13.65/13.63 class_Rings_Oordered__comm__semiring(tc_Int_Oint).
% 13.65/13.63 class_Rings_Olinordered__semiring__1(tc_Int_Oint).
% 13.65/13.63 class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 13.65/13.63 class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 13.65/13.63 class_Rings_Olinordered__semiring(tc_Int_Oint).
% 13.65/13.63 class_Rings_Olinordered__semidom(tc_Int_Oint).
% 13.65/13.63 class_Lattices_Osemilattice__sup(tc_Int_Oint).
% 13.65/13.63 class_Lattices_Osemilattice__inf(tc_Int_Oint).
% 13.65/13.63 class_Lattices_Odistrib__lattice(tc_Int_Oint).
% 13.65/13.63 class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 13.65/13.63 class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 13.65/13.63 class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 13.65/13.63 class_Rings_Oordered__semiring(tc_Int_Oint).
% 13.65/13.63 class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 13.65/13.63 class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 13.65/13.63 class_Rings_Olinordered__ring(tc_Int_Oint).
% 13.65/13.63 class_Rings_Olinordered__idom(tc_Int_Oint).
% 13.65/13.63 class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 13.65/13.63 class_Rings_Ocomm__semiring(tc_Int_Oint).
% 13.65/13.63 class_Groups_Oab__group__add(tc_Int_Oint).
% 13.65/13.63 class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 13.65/13.63 class_Rings_Oordered__ring(tc_Int_Oint).
% 13.65/13.63 class_Orderings_Opreorder(tc_Int_Oint).
% 13.65/13.63 class_Orderings_Olinorder(tc_Int_Oint).
% 13.65/13.63 class_Groups_Omonoid__mult(tc_Int_Oint).
% 13.65/13.63 class_Groups_Omonoid__add(tc_Int_Oint).
% 13.65/13.63 class_Rings_Osemiring__1(tc_Int_Oint).
% 13.65/13.63 class_Rings_Osemiring__0(tc_Int_Oint).
% 13.65/13.63 class_Lattices_Olattice(tc_Int_Oint).
% 13.65/13.63 class_Groups_Ogroup__add(tc_Int_Oint).
% 13.65/13.63 class_Rings_Omult__zero(tc_Int_Oint).
% 13.65/13.63 class_Orderings_Oorder(tc_Int_Oint).
% 13.65/13.63 class_Int_Oring__char__0(tc_Int_Oint).
% 13.65/13.63 class_Rings_Osemiring(tc_Int_Oint).
% 13.65/13.63 class_Orderings_Oord(tc_Int_Oint).
% 13.65/13.63 class_Rings_Oring__1(tc_Int_Oint).
% 13.65/13.63 class_Groups_Ominus(tc_Int_Oint).
% 13.65/13.63 class_Power_Opower(tc_Int_Oint).
% 13.65/13.63 class_Groups_Ozero(tc_Int_Oint).
% 13.65/13.63 class_Rings_Oring(tc_Int_Oint).
% 13.65/13.63 class_Groups_Oone(tc_Int_Oint).
% 13.65/13.63 class_GCD_Ogcd(tc_Int_Oint).
% 13.65/13.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 13.65/13.63 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 13.65/13.63 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 13.65/13.63 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 13.65/13.63 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 13.65/13.63 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 13.65/13.63 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 13.65/13.63 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 13.65/13.63 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 13.65/13.63 class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 13.65/13.63 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 13.65/13.63 class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 13.65/13.63 class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 13.65/13.63 class_Lattices_Osemilattice__sup(tc_Nat_Onat).
% 13.65/13.63 class_Lattices_Osemilattice__inf(tc_Nat_Onat).
% 13.65/13.63 class_Lattices_Odistrib__lattice(tc_Nat_Onat).
% 13.65/13.63 class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 13.65/13.63 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 13.65/13.63 class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 13.65/13.63 class_Rings_Oordered__semiring(tc_Nat_Onat).
% 13.65/13.63 class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 13.65/13.63 class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 13.65/13.63 class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 13.65/13.63 class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 13.65/13.63 class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 13.65/13.63 class_Orderings_Opreorder(tc_Nat_Onat).
% 13.65/13.63 class_Orderings_Olinorder(tc_Nat_Onat).
% 13.65/13.63 class_Groups_Omonoid__mult(tc_Nat_Onat).
% 13.65/13.63 class_Groups_Omonoid__add(tc_Nat_Onat).
% 13.65/13.63 class_Rings_Osemiring__1(tc_Nat_Onat).
% 13.65/13.63 class_Rings_Osemiring__0(tc_Nat_Onat).
% 13.65/13.63 class_Lattices_Olattice(tc_Nat_Onat).
% 13.65/13.63 class_Rings_Omult__zero(tc_Nat_Onat).
% 13.65/13.63 class_Orderings_Oorder(tc_Nat_Onat).
% 13.65/13.63 class_Rings_Osemiring(tc_Nat_Onat).
% 13.65/13.63 class_Orderings_Oord(tc_Nat_Onat).
% 13.65/13.63 class_Orderings_Obot(tc_Nat_Onat).
% 13.65/13.63 class_Groups_Ominus(tc_Nat_Onat).
% 13.65/13.63 class_Power_Opower(tc_Nat_Onat).
% 13.65/13.63 class_Groups_Ozero(tc_Nat_Onat).
% 13.65/13.63 class_Groups_Oone(tc_Nat_Onat).
% 13.65/13.63 class_GCD_Ogcd(tc_Nat_Onat).
% 13.65/13.63 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool).
% 13.65/13.63 class_Lattices_Obounded__lattice__top(tc_HOL_Obool).
% 13.65/13.63 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool).
% 13.65/13.63 class_Lattices_Osemilattice__sup(tc_HOL_Obool).
% 13.65/13.63 class_Lattices_Osemilattice__inf(tc_HOL_Obool).
% 13.65/13.63 class_Lattices_Odistrib__lattice(tc_HOL_Obool).
% 13.65/13.63 class_Orderings_Opreorder(tc_HOL_Obool).
% 13.65/13.63 class_Lattices_Olattice(tc_HOL_Obool).
% 13.65/13.63 class_Orderings_Oorder(tc_HOL_Obool).
% 13.65/13.63 class_Orderings_Otop(tc_HOL_Obool).
% 13.65/13.63 class_Orderings_Oord(tc_HOL_Obool).
% 13.65/13.63 class_Orderings_Obot(tc_HOL_Obool).
% 13.65/13.63 class_Groups_Ominus(tc_HOL_Obool).
% 13.65/13.63 all T_1 class_Complete__Lattice_Ocomplete__lattice(tc_Limits_Onet(T_1)).
% 13.65/13.63 all T_1 class_Lattices_Obounded__lattice__top(tc_Limits_Onet(T_1)).
% 13.65/13.63 all T_1 class_Lattices_Obounded__lattice__bot(tc_Limits_Onet(T_1)).
% 13.65/13.63 all T_1 class_Lattices_Osemilattice__sup(tc_Limits_Onet(T_1)).
% 13.65/13.63 all T_1 class_Lattices_Osemilattice__inf(tc_Limits_Onet(T_1)).
% 13.65/13.63 all T_1 class_Orderings_Opreorder(tc_Limits_Onet(T_1)).
% 13.65/13.63 all T_1 class_Lattices_Olattice(tc_Limits_Onet(T_1)).
% 13.65/13.63 all T_1 class_Orderings_Oorder(tc_Limits_Onet(T_1)).
% 13.65/13.63 all T_1 class_Orderings_Otop(tc_Limits_Onet(T_1)).
% 13.65/13.63 all T_1 class_Orderings_Oord(tc_Limits_Onet(T_1)).
% 13.65/13.63 all T_1 class_Orderings_Obot(tc_Limits_Onet(T_1)).
% 13.65/13.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal).
% 13.65/13.63 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Olinordered__semiring(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Olinordered__semidom(tc_RealDef_Oreal).
% 13.65/13.63 class_Lattices_Osemilattice__sup(tc_RealDef_Oreal).
% 13.65/13.63 class_Lattices_Osemilattice__inf(tc_RealDef_Oreal).
% 13.65/13.63 class_Lattices_Odistrib__lattice(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Oordered__semiring(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Olinordered__ring(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Olinordered__idom(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Ocomm__semiring(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Oab__group__add(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Oordered__ring(tc_RealDef_Oreal).
% 13.65/13.63 class_Orderings_Opreorder(tc_RealDef_Oreal).
% 13.65/13.63 class_Orderings_Olinorder(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Omonoid__mult(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Omonoid__add(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Osemiring__1(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Osemiring__0(tc_RealDef_Oreal).
% 13.65/13.63 class_Lattices_Olattice(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Ogroup__add(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Omult__zero(tc_RealDef_Oreal).
% 13.65/13.63 class_Orderings_Oorder(tc_RealDef_Oreal).
% 13.65/13.63 class_Int_Oring__char__0(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Osemiring(tc_RealDef_Oreal).
% 13.65/13.63 class_Orderings_Oord(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Oring__1(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Ominus(tc_RealDef_Oreal).
% 13.65/13.63 class_Power_Opower(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Ozero(tc_RealDef_Oreal).
% 13.65/13.63 class_Rings_Oring(tc_RealDef_Oreal).
% 13.65/13.63 class_Groups_Oone(tc_RealDef_Oreal).
% 13.65/13.63 all V_y_2 V_x_2 (-hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2))|V_x_2=V_y_2).
% 13.65/13.63 all V_y_2 V_x_2 (V_x_2!=V_y_2|hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2))).
% 13.65/13.63 -(exists B_x1 hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),c_Set_OCollect(tc_RealDef_Oreal,v_P)),B_x1))).
% 13.65/13.63 end_of_list.
% 13.65/13.63
% 13.65/13.63 -------> usable clausifies to:
% 13.65/13.63
% 13.65/13.63 list(usable).
% 13.65/13.63 0 [] A=A.
% 13.65/13.63 0 [] hAPP(V_f_2,$f1(V_g_2,V_f_2))!=hAPP(V_g_2,$f1(V_g_2,V_f_2))|V_f_2=V_g_2.
% 13.65/13.63 0 [] hBOOL(hAPP(v_P,v_x____)).
% 13.65/13.63 0 [] hBOOL(hAPP(v_P,$c1)).
% 13.65/13.63 0 [] -hBOOL(hAPP(v_P,B_x))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,$c2).
% 13.65/13.63 0 [] hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_xa_2)).
% 13.65/13.63 0 [] -class_Orderings_Otop(T_a)|hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_xa_2)=c_Orderings_Otop__class_Otop(T_a).
% 13.65/13.63 0 [] -hBOOL(hAPP(v_P,V_x))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,v_Y____).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)|c_Lubs_Oubs(T_a,V_R_2,V_S_2)=c_Set_OCollect(T_a,c_Lubs_OisUb(T_a,V_R_2,V_S_2)).
% 13.65/13.63 0 [] c_Set_OCollect(T_a,V_Pa_2)=V_Pa_2.
% 13.65/13.63 0 [] c_member(tc_RealDef_Oreal,$c3,c_Set_OCollect(tc_RealDef_Oreal,v_P)).
% 13.65/13.63 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)|c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(T_a).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2))| -c_Lubs_Osetge(T_a,V_xa_2,c_Set_OCollect(T_a,c_Lubs_OisUb(T_a,V_R_2,V_S_2)))|c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2))|c_Lubs_Osetle(T_a,V_S_2,V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)|hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2)).
% 13.65/13.63 0 [] c_Limits_Owithin(T_a,V_net_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))=V_net_2.
% 13.65/13.63 0 [] -c_member(tc_fun(T_a,tc_HOL_Obool),V_X_2,V_C_2)| -c_member(T_a,V_A_2,V_X_2)|c_member(T_a,V_A_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2)).
% 13.65/13.63 0 [] V_A_2!=V_B_2|c_member(T_a,V_c_2,V_A_2)| -c_member(T_a,V_c_2,V_B_2).
% 13.65/13.63 0 [] V_A_2!=V_B_2|c_member(T_a,V_c_2,V_B_2)| -c_member(T_a,V_c_2,V_A_2).
% 13.65/13.63 0 [] c_member(T_a,V_xa_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_x).
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|V_xa_2=V_y_2|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|V_xa_2!=V_y_2| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2).
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|V_xa_2!=V_y_2| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_xa_2)|V_xa_2=V_y_2.
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|V_xa_2!=V_y_2.
% 13.65/13.63 0 [] -c_member(T_a,V_xa_2,V_A_2)|hBOOL(hAPP(V_A_2,V_xa_2)).
% 13.65/13.63 0 [] c_member(T_a,V_xa_2,V_A_2)| -hBOOL(hAPP(V_A_2,V_xa_2)).
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 13.65/13.63 0 [] -c_member(T_a,V_xa_2,c_fe_qual(V_y_2))|V_xa_2=V_y_2.
% 13.65/13.63 0 [] c_member(T_a,V_xa_2,c_fe_qual(V_y_2))|V_xa_2!=V_y_2.
% 13.65/13.63 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2))|c_member(T_a,$f2(V_S_2,V_a_2,T_a),V_S_2).
% 13.65/13.63 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2))|c_Orderings_Oord__class_Oless(T_a,V_a_2,$f2(V_S_2,V_a_2,T_a)).
% 13.65/13.63 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)| -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2))| -c_member(T_a,B_x,V_S_2)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,B_x).
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_xa_2)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|V_xa_2=V_y_2.
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_xa_2)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|V_xa_2!=V_y_2.
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 13.65/13.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 13.65/13.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_y!=V_x.
% 13.65/13.63 0 [] V_A_2!=V_B_2| -c_member(T_a,V_xa_2,V_A_2)|c_member(T_a,V_xa_2,V_B_2).
% 13.65/13.63 0 [] V_A_2!=V_B_2|c_member(T_a,V_xa_2,V_A_2)| -c_member(T_a,V_xa_2,V_B_2).
% 13.65/13.63 0 [] V_xa_2!=V_y_2| -c_member(T_a,V_xa_2,V_A_2)|c_member(T_a,V_y_2,V_A_2).
% 13.65/13.63 0 [] V_xa_2!=V_y_2|c_member(T_a,V_xa_2,V_A_2)| -c_member(T_a,V_y_2,V_A_2).
% 13.65/13.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.65/13.63 0 [] V_a_2!=V_b_2| -c_member(T_a,V_b_2,V_A_2)|c_member(T_a,V_a_2,V_A_2).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_c).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_c,V_b)|c_Orderings_Oord__class_Oless(T_a,V_c,V_a).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_a,V_c).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_c,V_a).
% 13.65/13.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 13.65/13.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)|c_Lubs_Osetle(T_a,V_S_2,V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)|c_member(T_a,V_xa_2,V_R_2).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)|c_Lubs_Osetge(T_a,V_xa_2,c_Lubs_Oubs(T_a,V_R_2,V_S_2)).
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_Osetle(T_a,V_S_2,V_xa_2)| -c_member(T_a,V_xa_2,V_R_2)|hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2)).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2))|c_Lubs_Osetle(T_a,V_S_2,V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2))|c_member(T_a,V_xa_2,V_R_2).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)|hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2))| -c_Lubs_Osetle(T_a,V_S_2,V_xa_2)| -c_member(T_a,V_xa_2,V_R_2).
% 13.65/13.63 0 [] c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2))|c_member(T_a,V_xa_2,V_R_2).
% 13.65/13.63 0 [] c_member(T_a,V_xa_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)|c_Lubs_OleastP(T_a,c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_OleastP(T_a,c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2)|c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)|c_Lubs_OleastP(T_a,c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)|c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)| -c_Lubs_OleastP(T_a,c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_OleastP(T_a,V_Pa_2,V_xa_2)|c_Lubs_Osetge(T_a,V_xa_2,c_Set_OCollect(T_a,V_Pa_2)).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_OleastP(T_a,V_Pa_2,V_xa_2)|hBOOL(hAPP(V_Pa_2,V_xa_2)).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_OleastP(T_a,V_Pa_2,V_xa_2)|c_Lubs_Osetge(T_a,V_xa_2,c_Set_OCollect(T_a,V_Pa_2)).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)|c_Lubs_OleastP(T_a,V_Pa_2,V_xa_2)| -hBOOL(hAPP(V_Pa_2,V_xa_2))| -c_Lubs_Osetge(T_a,V_xa_2,c_Set_OCollect(T_a,V_Pa_2)).
% 13.65/13.63 0 [] -c_member(tc_RealDef_Oreal,B_X,V_S_2)| -hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),V_S_2),B_x1))|c_Lubs_OisLub(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),V_S_2,$f3(V_S_2)).
% 13.65/13.63 0 [] -c_member(tc_RealDef_Oreal,B_x,V_S_2)| -hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),V_S_2),B_x1))|c_Lubs_OisLub(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),V_S_2,$f4(V_S_2)).
% 13.65/13.63 0 [] -class_Rings_Olinordered__idom(T_a)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 13.65/13.63 0 [] hBOOL(hAPP(v_P,$c4)).
% 13.65/13.63 0 [] -hBOOL(hAPP(v_P,B_x))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,$c5).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)| -hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_y_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2).
% 13.65/13.63 0 [] c_member(T_a,$f5(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.63 0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x).
% 13.65/13.63 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_member(T_a,V_c_2,V_A_2)|c_member(T_a,V_c_2,V_B_2).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_b)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,$f6(V_g_2,V_f_2,T_a,T_b)),hAPP(V_g_2,$f6(V_g_2,V_f_2,T_a,T_b))).
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)|V_xa_2!=V_y_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)|V_xa_2!=V_y_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)|V_xa_2=V_y_2| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Opreorder(T_a)|V_x!=V_y|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 13.65/13.63 0 [] -c_member(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2)).
% 13.65/13.63 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),V_A_2,V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_2)).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)|V_xa_2=V_y_2.
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)|V_xa_2!=V_y_2.
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|V_b!=V_c|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|V_b!=V_c|c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)|V_x=V_y.
% 13.65/13.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_z).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|V_x=V_y.
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_2)).
% 13.65/13.63 0 [] -c_Lubs_OisLub(tc_RealDef_Oreal,V_R_2,V_S_2,V_xa_2)| -c_Lubs_OisLub(tc_RealDef_Oreal,V_R_2,V_S_2,V_y_2)|V_xa_2=V_y_2.
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_OleastP(T_a,V_Pa_2,V_xa_2)|hBOOL(hAPP(V_Pa_2,V_xa_2)).
% 13.65/13.63 0 [] -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_member(T_a,V_c_2,V_A_2)|c_member(T_a,V_c_2,V_B_2).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 13.65/13.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 13.65/13.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|V_a=V_b|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|V_a=V_b|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y.
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|V_xa_2=V_y_2.
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|V_xa_2!=V_y_2.
% 13.65/13.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)|V_xa_2=V_y_2.
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)|V_xa_2!=V_y_2.
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y).
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|V_xa_2=V_y_2.
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)|V_xa_2!=V_y_2.
% 13.65/13.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2).
% 13.65/13.63 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2).
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|V_xa_2!=V_y_2.
% 13.65/13.63 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)|V_xa_2=V_y_2.
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2).
% 13.65/13.63 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_member(T_a,V_xa_2,V_A_2)|c_member(T_a,V_xa_2,V_B_2).
% 13.65/13.63 0 [] -c_member(T_a,V_xa_2,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_member(T_a,V_xa_2,V_B_2).
% 13.65/13.63 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_member(T_a,V_xa_2,V_A_2)|c_member(T_a,V_xa_2,V_B_2).
% 13.65/13.63 0 [] -class_Orderings_Otop(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Orderings_Otop__class_Otop(T_a)).
% 13.65/13.63 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.63 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2),V_b_2)| -c_member(T_a,B_x,V_A_2)|c_Orderings_Oord__class_Oless__e_q(T_a,B_x,V_b_2).
% 13.65/13.63 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2),V_b_2)|c_member(T_a,$f7(V_b_2,V_A_2,T_a),V_A_2).
% 13.65/13.63 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,$f7(V_b_2,V_A_2,T_a),V_b_2).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_OleastP(T_a,V_Pa_2,V_xa_2)| -c_member(T_a,V_y_2,c_Set_OCollect(T_a,V_Pa_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_Osetle(T_a,V_S_2,V_xa_2)| -c_member(T_a,B_x,V_S_2)|c_Orderings_Oord__class_Oless__e_q(T_a,B_x,V_xa_2).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)|c_Lubs_Osetle(T_a,V_S_2,V_xa_2)|c_member(T_a,$f8(V_xa_2,V_S_2,T_a),V_S_2).
% 13.65/13.63 0 [] -class_Orderings_Oord(T_a)|c_Lubs_Osetle(T_a,V_S_2,V_xa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,$f8(V_xa_2,V_S_2,T_a),V_xa_2).
% 13.65/13.64 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_Osetge(T_a,V_xa_2,V_S_2)| -c_member(T_a,B_x,V_S_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,B_x).
% 13.65/13.64 0 [] -class_Orderings_Oord(T_a)|c_Lubs_Osetge(T_a,V_xa_2,V_S_2)|c_member(T_a,$f9(V_S_2,V_xa_2,T_a),V_S_2).
% 13.65/13.64 0 [] -class_Orderings_Oord(T_a)|c_Lubs_Osetge(T_a,V_xa_2,V_S_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,$f9(V_S_2,V_xa_2,T_a)).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)| -c_member(T_a,V_xa_2,V_A_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)).
% 13.65/13.64 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)| -c_member(T_a,V_y_2,V_S_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2).
% 13.65/13.64 0 [] -class_Orderings_Oord(T_a)| -hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2))| -c_member(T_a,V_y_2,V_S_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2).
% 13.65/13.64 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_Osetle(T_a,V_S_2,V_xa_2)| -c_member(T_a,V_y_2,V_S_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_xa_2).
% 13.65/13.64 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_Osetge(T_a,V_xa_2,V_S_2)| -c_member(T_a,V_y_2,V_S_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2).
% 13.65/13.64 0 [] -c_member(T_a,V_A_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))|c_member(T_a,V_A_2,$f10(V_C_2,V_A_2,T_a)).
% 13.65/13.64 0 [] -c_member(T_a,V_A_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))|c_member(tc_fun(T_a,tc_HOL_Obool),$f10(V_C_2,V_A_2,T_a),V_C_2).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)|c_member(T_a,$f11(V_z_2,V_A_2,T_a),V_A_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2),V_z_2).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,$f11(V_z_2,V_A_2,T_a),V_z_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2),V_z_2).
% 13.65/13.64 0 [] -class_Orderings_Oord(T_a)|c_member(T_a,$f12(V_u_2,V_S_2,T_a),V_S_2)|hBOOL(hAPP(c_Lubs_OisUb(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_u_2)).
% 13.65/13.64 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,$f12(V_u_2,V_S_2,T_a),V_u_2)|hBOOL(hAPP(c_Lubs_OisUb(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_u_2)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2)|V_xa_2=V_y_2.
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2)|V_xa_2!=V_y_2.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2)|V_xa_2!=V_y_2.
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2)|V_xa_2=V_y_2.
% 13.65/13.64 0 [] c_Set_OPow(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)).
% 13.65/13.64 0 [] -class_Orderings_Oord(T_a)|c_member(T_a,$f13(V_xa_2,V_S_2,T_a),V_S_2)|c_Lubs_Osetle(T_a,V_S_2,V_xa_2).
% 13.65/13.64 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,$f13(V_xa_2,V_S_2,T_a),V_xa_2)|c_Lubs_Osetle(T_a,V_S_2,V_xa_2).
% 13.65/13.64 0 [] -class_Orderings_Oord(T_a)|c_member(T_a,$f14(V_xa_2,V_S_2,T_a),V_S_2)|c_Lubs_Osetge(T_a,V_xa_2,V_S_2).
% 13.65/13.64 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,$f14(V_xa_2,V_S_2,T_a))|c_Lubs_Osetge(T_a,V_xa_2,V_S_2).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)| -c_member(T_a,V_xa_2,V_A_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2),V_xa_2).
% 13.65/13.64 0 [] c_member(tc_fun(T_a,tc_HOL_Obool),$f15(V_C_2,V_A_2,T_a),V_A_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),$f15(V_C_2,V_A_2,T_a),V_C_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)|V_A_2=V_B_2.
% 13.65/13.64 0 [] -c_member(T_a,V_A_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))| -c_member(tc_fun(T_a,tc_HOL_Obool),V_X_2,V_C_2)|c_member(T_a,V_A_2,V_X_2).
% 13.65/13.64 0 [] -c_member(T_a,V_A_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2))| -c_member(tc_fun(T_a,tc_HOL_Obool),V_X_2,V_C_2)|c_member(T_a,V_A_2,V_X_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_member(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OPow(T_a,V_B_2)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|V_A_2!=V_B_2.
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|V_A_2=V_B_2.
% 13.65/13.64 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2).
% 13.65/13.64 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2).
% 13.65/13.64 0 [] -class_Orderings_Oord(T_b)|c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2).
% 13.65/13.64 0 [] V_A_2!=V_B_2|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] V_A_2!=V_B_2|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2).
% 13.65/13.64 0 [] V_A_2=V_B_2| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|V_A_2=V_B_2.
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|V_A_2!=V_B_2.
% 13.65/13.64 0 [] -hBOOL(hAPP(V_Pa_2,V_xa_2))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_Pa_2,V_Q_2)|hBOOL(hAPP(V_Q_2,V_xa_2)).
% 13.65/13.64 0 [] V_A_2!=V_B_2|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] V_A_2!=V_B_2|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Set_OPow(T_a,V_A_2),c_Set_OPow(T_a,V_B_2)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),V_B_2,V_A_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_Pa_2,V_Q_2)| -hBOOL(hAPP(V_Pa_2,V_xa_2))|hBOOL(hAPP(V_Q_2,V_xa_2)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)|c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)|c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)|c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2).
% 13.65/13.64 0 [] V_A_2!=V_B_2|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] V_A_2!=V_B_2|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z)|V_z=V_w.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_j,V_k)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_k).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_w).
% 13.65/13.64 0 [] -c_member(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2).
% 13.65/13.64 0 [] -c_member(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OPow(T_a,V_B_2))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] -c_member(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OPow(T_a,V_B_2))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] c_member(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OPow(T_a,V_B_2))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] c_member(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OPow(T_a,V_A_2)).
% 13.65/13.64 0 [] c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Set_OPow(T_a,V_A_2))=V_A_2.
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),V_A_2,c_Set_OPow(T_a,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2))| -c_member(T_a,B_x,V_A_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,B_x).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2))|c_member(T_a,$f16(V_A_2,V_b_2,T_a),V_A_2).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,$f16(V_A_2,V_b_2,T_a)).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2),V_a_2)|c_member(T_a,$f17(V_a_2,V_S_2,T_a),V_S_2).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2),V_a_2)|c_Orderings_Oord__class_Oless(T_a,$f17(V_a_2,V_S_2,T_a),V_a_2).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)| -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2),V_a_2)| -c_member(T_a,B_x,V_S_2)| -c_Orderings_Oord__class_Oless(T_a,B_x,V_a_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Predicate_OPowp(T_a,V_A_2),c_Predicate_OPowp(T_a,V_B_2)).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)|c_member(T_a,$f18(V_z_2,V_A_2,T_a),V_A_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_z_2,c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_z_2,$f18(V_z_2,V_A_2,T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_z_2,c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)).
% 13.65/13.64 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Odecse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)).
% 13.65/13.64 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Odecse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f20(V_X_2,T_a),$f19(V_X_2,T_a)).
% 13.65/13.64 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Odecse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f19(V_X_2,T_a)),hAPP(V_X_2,$f20(V_X_2,T_a))).
% 13.65/13.64 0 [] c_member(tc_fun(T_a,tc_HOL_Obool),$f21(V_A_2,V_C_2,T_a),V_C_2)|c_member(T_a,V_A_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2)).
% 13.65/13.64 0 [] -c_member(T_a,V_A_2,$f21(V_A_2,V_C_2,T_a))|c_member(T_a,V_A_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_C_2)).
% 13.65/13.64 0 [] c_member(T_a,$f22(V_B_2,V_A_2,T_a),V_A_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] -c_member(T_a,$f22(V_B_2,V_A_2,T_a),V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)|c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(T_a).
% 13.65/13.64 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Oincse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)).
% 13.65/13.64 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Oincse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f24(V_X_2,T_a),$f23(V_X_2,T_a)).
% 13.65/13.64 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Oincse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f24(V_X_2,T_a)),hAPP(V_X_2,$f23(V_X_2,T_a))).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Orderings_Oord__class_Oless__e_q(T_b,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b,V_A_2,V_f_2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,T_b,V_B_2,V_f_2)).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Orderings_Oord__class_Oless__e_q(T_b,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b,V_B_2,V_f_2),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,T_b,V_A_2,V_f_2)).
% 13.65/13.64 0 [] -c_member(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_A_2).
% 13.65/13.64 0 [] c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] -class_Orderings_Obot(T_a)|hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_xa_2)=c_Orderings_Obot__class_Obot(T_a).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)|c_Complete__Lattice_OSup__class_OSup(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(T_a).
% 13.65/13.64 0 [] V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))| -c_member(T_a,V_a_2,V_A_2).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.64 0 [] -c_member(T_a,B_x,V_A_2)|V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_member(T_a,$f25(V_A_2,T_a),V_A_2)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_member(T_a,$f26(V_A_2,T_a),V_A_2)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] -c_member(T_a,B_x,V_A_2)|V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))!=c_Set_OCollect(T_a,V_Pa_2)| -hBOOL(hAPP(V_Pa_2,B_x)).
% 13.65/13.64 0 [] c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))=c_Set_OCollect(T_a,V_Pa_2)|hBOOL(hAPP(V_Pa_2,$f27(V_Pa_2,T_a))).
% 13.65/13.64 0 [] c_Set_OCollect(T_a,V_Pa_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))| -hBOOL(hAPP(V_Pa_2,B_x)).
% 13.65/13.64 0 [] c_Set_OCollect(T_a,V_Pa_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|hBOOL(hAPP(V_Pa_2,$f28(V_Pa_2,T_a))).
% 13.65/13.64 0 [] c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))|V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Set_OPow(T_a,V_A_2)!=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.64 0 [] -class_Orderings_Obot(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Orderings_Obot__class_Obot(T_a),V_x).
% 13.65/13.64 0 [] c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)|c_Complete__Lattice_OInf__class_OInf(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(T_a).
% 13.65/13.64 0 [] c_member(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Set_OPow(T_a,V_B_2)).
% 13.65/13.64 0 [] c_member(tc_fun(T_a,tc_HOL_Obool),$f29(V_B_2,V_A_2,T_a),V_A_2)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),$f29(V_B_2,V_A_2,T_a),V_B_2)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2),V_B_2).
% 13.65/13.64 0 [] c_member(tc_fun(T_a,tc_HOL_Obool),$f30(V_C_2,V_A_2,T_a),V_A_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,$f30(V_C_2,V_A_2,T_a))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)).
% 13.65/13.64 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Omonose_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,X1,X2)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,X2),hAPP(V_X_2,X1)).
% 13.65/13.64 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f32(V_X_2,T_a),$f31(V_X_2,T_a)).
% 13.65/13.64 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f32(V_X_2,T_a)),hAPP(V_X_2,$f31(V_X_2,T_a))).
% 13.65/13.64 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f34(V_X_2,T_a),$f33(V_X_2,T_a)).
% 13.65/13.64 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f33(V_X_2,T_a)),hAPP(V_X_2,$f34(V_X_2,T_a))).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=V_n_2.
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2.
% 13.65/13.64 0 [] -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.
% 13.65/13.64 0 [] 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).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=V_n_2.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|V_m=V_n|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 13.65/13.64 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).
% 13.65/13.64 0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 13.65/13.64 0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 13.65/13.64 0 [] V_x=V_y|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)|V_m!=V_n.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)|V_s!=V_t.
% 13.65/13.64 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_Pa_2,V_n_2),V_m_2)).
% 13.65/13.64 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Oincse_q(T_a,V_X_2)|c_SEQ_Omonose_q(T_a,V_X_2).
% 13.65/13.64 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Odecse_q(T_a,V_X_2)|c_SEQ_Omonose_q(T_a,V_X_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m).
% 13.65/13.64 0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_k).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|V_m=V_n.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 13.65/13.64 0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 13.65/13.64 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f36(V_X_2,T_a),$f35(V_X_2,T_a))|c_SEQ_Omonose_q(T_a,V_X_2).
% 13.65/13.64 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f36(V_X_2,T_a)),hAPP(V_X_2,$f35(V_X_2,T_a)))|c_SEQ_Omonose_q(T_a,V_X_2).
% 13.65/13.64 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f38(V_X_2,T_a),$f37(V_X_2,T_a))|c_SEQ_Omonose_q(T_a,V_X_2).
% 13.65/13.64 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f37(V_X_2,T_a)),hAPP(V_X_2,$f38(V_X_2,T_a)))|c_SEQ_Omonose_q(T_a,V_X_2).
% 13.65/13.64 0 [] c_Set_OPow(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)).
% 13.65/13.64 0 [] hBOOL(hAPP(V_Pa_2,$f39(T_a,V_Q_2,V_Pa_2)))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_OCollect(T_a,V_Pa_2),c_Set_OCollect(T_a,V_Q_2)).
% 13.65/13.64 0 [] -hBOOL(hAPP(V_Q_2,$f39(T_a,V_Q_2,V_Pa_2)))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_OCollect(T_a,V_Pa_2),c_Set_OCollect(T_a,V_Q_2)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f41(V_j_2,V_i_2,V_f_2),$f40(V_j_2,V_i_2,V_f_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(V_f_2,V_i_2),hAPP(V_f_2,V_j_2)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,$f41(V_j_2,V_i_2,V_f_2)),hAPP(V_f_2,$f40(V_j_2,V_i_2,V_f_2)))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(V_f_2,V_i_2),hAPP(V_f_2,V_j_2)).
% 13.65/13.64 0 [] -c_member(T_a,$f42(V_A_2,T_a),V_A_2)|c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))=V_A_2.
% 13.65/13.64 0 [] -c_member(T_a,V_a_2,V_B_2)|c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_B_2)).
% 13.65/13.64 0 [] V_a_2!=V_b_2|c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_B_2)).
% 13.65/13.64 0 [] -c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2))|V_a_2=V_b_2|c_member(T_a,V_a_2,V_A_2).
% 13.65/13.64 0 [] c_Set_Oinsert(T_a,V_xa_2,c_Set_Oinsert(T_a,V_xa_2,V_A_2))=c_Set_Oinsert(T_a,V_xa_2,V_A_2).
% 13.65/13.64 0 [] c_Set_Oinsert(T_a,V_xa_2,c_Set_Oinsert(T_a,V_y_2,V_A_2))=c_Set_Oinsert(T_a,V_y_2,c_Set_Oinsert(T_a,V_xa_2,V_A_2)).
% 13.65/13.64 0 [] -hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_xa_2))|V_y_2=V_xa_2|hBOOL(hAPP(V_A_2,V_xa_2)).
% 13.65/13.64 0 [] hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_xa_2))|V_y_2!=V_xa_2.
% 13.65/13.64 0 [] hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_xa_2))| -hBOOL(hAPP(V_A_2,V_xa_2)).
% 13.65/13.64 0 [] -c_member(T_a,V_a_2,V_A_2)|c_Set_Oinsert(T_a,V_a_2,V_A_2)=V_A_2.
% 13.65/13.64 0 [] -c_member(T_a,V_a_2,V_B_2)|c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_B_2)).
% 13.65/13.64 0 [] c_member(T_a,V_xa_2,V_A_2)|c_member(T_a,V_xa_2,V_B_2)|c_Set_Oinsert(T_a,V_xa_2,V_A_2)!=c_Set_Oinsert(T_a,V_xa_2,V_B_2)|V_A_2=V_B_2.
% 13.65/13.64 0 [] c_member(T_a,V_xa_2,V_A_2)|c_member(T_a,V_xa_2,V_B_2)|c_Set_Oinsert(T_a,V_xa_2,V_A_2)=c_Set_Oinsert(T_a,V_xa_2,V_B_2)|V_A_2!=V_B_2.
% 13.65/13.64 0 [] -c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2))|V_a_2=V_b_2|c_member(T_a,V_a_2,V_A_2).
% 13.65/13.64 0 [] c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2))|V_a_2!=V_b_2.
% 13.65/13.64 0 [] c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2))| -c_member(T_a,V_a_2,V_A_2).
% 13.65/13.64 0 [] c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)).
% 13.65/13.64 0 [] c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))!=c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))|V_a_2=V_b_2.
% 13.65/13.64 0 [] c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))!=c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_a_2=V_c_2|V_a_2=V_d_2.
% 13.65/13.64 0 [] c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))!=c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_a_2=V_c_2|V_b_2=V_c_2.
% 13.65/13.64 0 [] c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))!=c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_b_2=V_d_2|V_a_2=V_d_2.
% 13.65/13.64 0 [] c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))!=c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_b_2=V_d_2|V_b_2=V_c_2.
% 13.65/13.64 0 [] c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_a_2!=V_c_2|V_b_2!=V_d_2.
% 13.65/13.64 0 [] c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_a_2!=V_d_2|V_b_2!=V_c_2.
% 13.65/13.64 0 [] c_Set_Oinsert(T_a,V_a_2,V_A_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))!=c_Set_Oinsert(T_a,V_a_2,V_A_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_C_2),c_Set_Oinsert(T_a,V_a_2,V_D_2)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_b_2,V_B_2)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)).
% 13.65/13.64 0 [] -c_member(T_a,V_b_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_b_2=V_a_2.
% 13.65/13.64 0 [] c_member(T_a,V_b_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_b_2!=V_a_2.
% 13.65/13.64 0 [] -c_member(T_a,V_b_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_b_2=V_a_2.
% 13.65/13.64 0 [] c_member(T_a,V_xa_2,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] c_member(T_a,V_xa_2,V_A_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_xa_2,V_A_2),V_B_2)|c_member(T_a,V_xa_2,V_B_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_xa_2,V_A_2),V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_xa_2,V_A_2),V_B_2)| -c_member(T_a,V_xa_2,V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|V_A_2=c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)|c_Complete__Lattice_OSup__class_OSup(T_a,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=V_a_2.
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)|c_Complete__Lattice_OInf__class_OInf(T_a,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=V_a_2.
% 13.65/13.64 0 [] c_Set_Othe__elem(T_a,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=V_xa_2.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))| -c_member(T_a,V_xa_2,V_B_2)|c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))|c_member(T_a,V_xa_2,V_B_2)| -c_member(T_a,V_xa_2,V_A_2)|c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))|c_member(T_a,V_xa_2,V_B_2)|c_member(T_a,V_xa_2,V_A_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))|c_member(T_a,V_xa_2,V_B_2)|c_member(T_a,V_xa_2,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))|c_member(T_a,V_xa_2,V_B_2)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2)| -c_member(T_a,V_xa_2,V_A_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))|c_member(T_a,V_xa_2,V_B_2)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_member(T_a,V_xa_2,V_B_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_member(T_a,V_xa_2,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2)| -c_member(T_a,V_xa_2,V_A_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))| -c_member(T_a,V_xa_2,V_A_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))|c_member(T_a,V_xa_2,V_A_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))|c_member(T_a,V_xa_2,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2)| -c_member(T_a,V_xa_2,V_A_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2)| -c_member(T_a,V_xa_2,V_A_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,V_B_2)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a).
% 13.65/13.64 0 [] -hBOOL(hAPP(V_B_2,V_xa_2))|hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2)).
% 13.65/13.64 0 [] -hBOOL(hAPP(V_A_2,V_xa_2))|hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2)).
% 13.65/13.64 0 [] -hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2))|hBOOL(hAPP(V_A_2,V_xa_2))|hBOOL(hAPP(V_B_2,V_xa_2)).
% 13.65/13.64 0 [] -hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2))|hBOOL(hAPP(V_A_2,V_xa_2)).
% 13.65/13.64 0 [] -hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2))|hBOOL(hAPP(V_B_2,V_xa_2)).
% 13.65/13.64 0 [] -hBOOL(hAPP(V_A_2,V_xa_2))| -hBOOL(hAPP(V_B_2,V_xa_2))|hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2)).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|c_member(T_a,V_c_2,V_A_2)|c_member(T_a,V_c_2,V_B_2).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,V_B_2)|c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,V_A_2)|c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,V_A_2)| -c_member(T_a,V_c_2,V_B_2)|c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|c_member(T_a,V_c_2,V_A_2).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|c_member(T_a,V_c_2,V_B_2).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,V_A_2)|c_member(T_a,V_c_2,V_B_2)|c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|c_member(T_a,V_c_2,V_A_2).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,V_c_2,V_B_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)!=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2))=V_B_2.
% 13.65/13.64 0 [] c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),V_A_2,V_B_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)).
% 13.65/13.64 0 [] -hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2))|hBOOL(hAPP(V_B_2,V_xa_2)).
% 13.65/13.64 0 [] -hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2))|hBOOL(hAPP(V_A_2,V_xa_2)).
% 13.65/13.64 0 [] -hBOOL(hAPP(V_B_2,V_xa_2))|hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2)).
% 13.65/13.64 0 [] -hBOOL(hAPP(V_A_2,V_xa_2))|hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_xa_2)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2)).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))=c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),V_B_2).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))=V_A_2.
% 13.65/13.64 0 [] c_member(T_a,$f43(V_Pa_2,V_B_2,V_A_2,T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,B_x,V_A_2)|hBOOL(hAPP(V_Pa_2,B_x)).
% 13.65/13.64 0 [] c_member(T_a,$f43(V_Pa_2,V_B_2,V_A_2,T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,X3,V_B_2)|hBOOL(hAPP(V_Pa_2,X3)).
% 13.65/13.64 0 [] -hBOOL(hAPP(V_Pa_2,$f43(V_Pa_2,V_B_2,V_A_2,T_a)))| -c_member(T_a,B_x,V_A_2)|hBOOL(hAPP(V_Pa_2,B_x)).
% 13.65/13.64 0 [] -hBOOL(hAPP(V_Pa_2,$f43(V_Pa_2,V_B_2,V_A_2,T_a)))| -c_member(T_a,X3,V_B_2)|hBOOL(hAPP(V_Pa_2,X3)).
% 13.65/13.64 0 [] -c_member(T_a,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|hBOOL(hAPP(V_Pa_2,X4))|c_member(T_a,$f44(V_Pa_2,V_B_2,V_A_2,T_a),V_A_2)|c_member(T_a,$f45(V_Pa_2,V_B_2,V_A_2,T_a),V_B_2).
% 13.65/13.64 0 [] -c_member(T_a,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|hBOOL(hAPP(V_Pa_2,X4))|c_member(T_a,$f44(V_Pa_2,V_B_2,V_A_2,T_a),V_A_2)| -hBOOL(hAPP(V_Pa_2,$f45(V_Pa_2,V_B_2,V_A_2,T_a))).
% 13.65/13.64 0 [] -c_member(T_a,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|hBOOL(hAPP(V_Pa_2,X4))| -hBOOL(hAPP(V_Pa_2,$f44(V_Pa_2,V_B_2,V_A_2,T_a)))|c_member(T_a,$f45(V_Pa_2,V_B_2,V_A_2,T_a),V_B_2).
% 13.65/13.64 0 [] -c_member(T_a,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|hBOOL(hAPP(V_Pa_2,X4))| -hBOOL(hAPP(V_Pa_2,$f44(V_Pa_2,V_B_2,V_A_2,T_a)))| -hBOOL(hAPP(V_Pa_2,$f45(V_Pa_2,V_B_2,V_A_2,T_a))).
% 13.65/13.64 0 [] -c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -hBOOL(hAPP(V_Pa_2,B_x))|c_member(T_a,$f46(V_Pa_2,V_B_2,V_A_2,T_a),V_A_2)|c_member(T_a,$f47(V_Pa_2,V_B_2,V_A_2,T_a),V_B_2).
% 13.65/13.64 0 [] -c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -hBOOL(hAPP(V_Pa_2,B_x))|c_member(T_a,$f46(V_Pa_2,V_B_2,V_A_2,T_a),V_A_2)|hBOOL(hAPP(V_Pa_2,$f47(V_Pa_2,V_B_2,V_A_2,T_a))).
% 13.65/13.64 0 [] -c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -hBOOL(hAPP(V_Pa_2,B_x))|hBOOL(hAPP(V_Pa_2,$f46(V_Pa_2,V_B_2,V_A_2,T_a)))|c_member(T_a,$f47(V_Pa_2,V_B_2,V_A_2,T_a),V_B_2).
% 13.65/13.64 0 [] -c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -hBOOL(hAPP(V_Pa_2,B_x))|hBOOL(hAPP(V_Pa_2,$f46(V_Pa_2,V_B_2,V_A_2,T_a)))|hBOOL(hAPP(V_Pa_2,$f47(V_Pa_2,V_B_2,V_A_2,T_a))).
% 13.65/13.64 0 [] c_member(T_a,$f48(V_Pa_2,V_B_2,V_A_2,T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,X5,V_A_2)| -hBOOL(hAPP(V_Pa_2,X5)).
% 13.65/13.64 0 [] c_member(T_a,$f48(V_Pa_2,V_B_2,V_A_2,T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,X6,V_B_2)| -hBOOL(hAPP(V_Pa_2,X6)).
% 13.65/13.64 0 [] hBOOL(hAPP(V_Pa_2,$f48(V_Pa_2,V_B_2,V_A_2,T_a)))| -c_member(T_a,X5,V_A_2)| -hBOOL(hAPP(V_Pa_2,X5)).
% 13.65/13.64 0 [] hBOOL(hAPP(V_Pa_2,$f48(V_Pa_2,V_B_2,V_A_2,T_a)))| -c_member(T_a,X6,V_B_2)| -hBOOL(hAPP(V_Pa_2,X6)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2),V_A_2)=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2),V_A_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)=c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2)=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2),V_A_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_B_2)=c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))=c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_B_2)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)=V_A_2.
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)=V_A_2.
% 13.65/13.64 0 [] c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),V_A_2,V_B_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)).
% 13.65/13.64 0 [] c_Set_OPow(T_a,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Set_OPow(T_a,V_A_2),c_Set_OPow(T_a,V_B_2)).
% 13.65/13.64 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)!=c_RealDef_Oreal(tc_Nat_Onat,V_m_2)|V_n_2=V_m_2.
% 13.65/13.64 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_RealDef_Oreal(tc_Nat_Onat,V_m_2)|V_n_2!=V_m_2.
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_A_2.
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),V_A_2,V_B_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2))).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),V_A_2,V_B_2))).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|c_member(T_a,V_c_2,V_A_2)|c_member(T_a,V_c_2,V_B_2).
% 13.65/13.64 0 [] c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,V_c_2,V_A_2).
% 13.65/13.64 0 [] c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,V_c_2,V_B_2).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,V_A_2)|c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,V_B_2)|c_member(T_a,V_c_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|c_member(T_a,V_c_2,V_A_2).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|c_member(T_a,V_c_2,V_B_2).
% 13.65/13.64 0 [] c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,V_c_2,V_A_2)| -c_member(T_a,V_c_2,V_B_2).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|c_member(T_a,V_c_2,V_A_2).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|c_member(T_a,V_c_2,V_B_2).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|c_member(T_a,V_c_2,V_A_2).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,V_c_2,V_B_2).
% 13.65/13.64 0 [] c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,V_c_2,V_A_2)|c_member(T_a,V_c_2,V_B_2).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|c_member(T_a,V_c_2,V_A_2).
% 13.65/13.64 0 [] -c_member(T_a,V_c_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,V_c_2,V_B_2).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_B_2)=V_B_2.
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=V_A_2.
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|V_B_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|V_B_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_B_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))| -c_member(T_a,B_x,V_A_2)| -c_member(T_a,B_xa,V_B_2)|B_x!=B_xa.
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|c_member(T_a,$f50(V_B_2,V_A_2,T_a),V_A_2).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|c_member(T_a,$f49(V_B_2,V_A_2,T_a),V_B_2).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|$f50(V_B_2,V_A_2,T_a)=$f49(V_B_2,V_A_2,T_a).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_A_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=V_A_2.
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2)=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_A_2),c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_B_2)=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_B_2.
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)!=V_B_2.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_B_2.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_A_2.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_C_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_D_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))=V_A_2.
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_B_2)=V_B_2.
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_A_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_B_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_A_2.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=V_B_2.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_C_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_D_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),V_A_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_D_2,V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)|c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_A_2))=V_A_2.
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Set_OPow(T_a,V_A_2),c_Set_OPow(T_a,V_B_2)),c_Set_OPow(T_a,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 13.65/13.64 0 [] c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2).
% 13.65/13.64 0 [] -c_member(T_a,V_a_2,V_C_2)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2)=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)).
% 13.65/13.64 0 [] -c_member(T_a,V_a_2,V_A_2)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.64 0 [] c_member(T_a,V_a_2,V_C_2)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2)=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2).
% 13.65/13.64 0 [] c_member(T_a,V_a_2,V_A_2)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] -c_member(T_a,V_a_2,V_C_2)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2)=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)).
% 13.65/13.64 0 [] c_member(T_a,V_a_2,V_C_2)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_B_2),V_C_2)=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2).
% 13.65/13.64 0 [] -c_member(T_a,V_a_2,V_A_2)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Set_Oinsert(T_a,V_a_2,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.64 0 [] c_member(T_a,V_a_2,V_A_2)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] -c_member(T_a,V_xa_2,V_B_2)|c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_xa_2,V_A_2),V_B_2)=c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] -c_member(T_a,V_xa_2,V_B_2)|c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_xa_2,V_A_2),V_B_2)=c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 13.65/13.64 0 [] c_member(T_a,V_xa_2,V_B_2)|c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_xa_2,V_A_2),V_B_2)=c_Set_Oinsert(T_a,V_xa_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)|c_Complete__Lattice_OSup__class_OSup(T_a,c_Set_Oinsert(T_a,V_a_2,V_A_2))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a_2,c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2)).
% 13.65/13.64 0 [] c_Set_Oinsert(T_a,V_a_2,V_A_2)=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_A_2).
% 13.65/13.64 0 [] c_Set_Oinsert(T_a,V_a_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))=c_Set_Oinsert(T_a,V_a_2,V_A_2).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_B_2).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,V_B_2))=c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2),c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)|c_Complete__Lattice_OInf__class_OInf(T_a,c_Set_Oinsert(T_a,V_a_2,V_A_2))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a_2,c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2),V_A_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))| -c_member(tc_fun(T_a,tc_HOL_Obool),B_x,V_C_2)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),B_x,V_A_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2),V_A_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|c_member(tc_fun(T_a,tc_HOL_Obool),$f51(V_A_2,V_C_2,T_a),V_C_2).
% 13.65/13.64 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2),V_A_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),$f51(V_A_2,V_C_2,T_a),V_A_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))).
% 13.65/13.64 0 [] c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),V_a_2,V_B_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_a_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_B_2)).
% 13.65/13.64 0 [] c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),V_a_2,V_B_2))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_a_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)|c_Complete__Lattice_OSup__class_OSup(T_a,c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a_2,V_b_2).
% 13.65/13.64 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)|c_Complete__Lattice_OInf__class_OInf(T_a,c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a_2,V_b_2).
% 13.65/13.64 0 [] -c_member(T_a,V_a_2,V_A_2)|c_Set_Oinsert(T_a,V_a_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))=V_A_2.
% 13.65/13.64 0 [] c_member(T_a,V_xa_2,V_A_2)|c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_xa_2,V_A_2),c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=V_A_2.
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))).
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)),c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z))).
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,T_a),V_f_2,V_g_2),V_xa_2)=c_Lattices_Osemilattice__inf__class_Oinf(T_a,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_2)).
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a),V_f_2,V_g_2),V_xa_2)=c_Lattices_Osemilattice__sup__class_Osup(T_a,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_2)).
% 13.65/13.64 0 [] -class_Lattices_Obounded__lattice__top(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Orderings_Otop__class_Otop(T_a),V_x)=V_x.
% 13.65/13.64 0 [] -class_Lattices_Obounded__lattice__top(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Orderings_Otop__class_Otop(T_a))=V_x.
% 13.65/13.64 0 [] -class_Lattices_Obounded__lattice__top(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_xa_2,V_y_2)!=c_Orderings_Otop__class_Otop(T_a)|V_xa_2=c_Orderings_Otop__class_Otop(T_a).
% 13.65/13.64 0 [] -class_Lattices_Obounded__lattice__top(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_xa_2,V_y_2)!=c_Orderings_Otop__class_Otop(T_a)|V_y_2=c_Orderings_Otop__class_Otop(T_a).
% 13.65/13.64 0 [] -class_Lattices_Obounded__lattice__top(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_xa_2,V_y_2)=c_Orderings_Otop__class_Otop(T_a)|V_xa_2!=c_Orderings_Otop__class_Otop(T_a)|V_y_2!=c_Orderings_Otop__class_Otop(T_a).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),V_z)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)).
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),V_z)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_c)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_c)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z)).
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_c))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_c)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y).
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b))=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x).
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)=c_Lattices_Osemilattice__sup__class_Osup(T_a,V_b,V_a).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_x)=V_x.
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_a)=V_a.
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_z)=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)).
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_z)=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_c)=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_c)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)).
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_c))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_c)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y).
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_x).
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_x).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)=c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_b,V_a).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_x)=V_x.
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_a)=V_a.
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_x)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_x).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_x)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_x).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_d)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_c,V_d)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z),V_x).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_x)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b),V_x).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)=V_x.
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)=V_y.
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_y_2),V_z_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_z_2).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_y_2),V_z_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_z_2).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_y_2),V_z_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_z_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_z_2).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_y_2)=V_y_2.
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_y_2)!=V_y_2.
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)).
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)).
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b))|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b))|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_b).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_d)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_c,V_d)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_z)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)=V_y.
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y)=V_x.
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_x)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_x)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y_2,V_z_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y_2,V_z_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_z_2).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y_2,V_z_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_z_2).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_xa_2,V_y_2)=V_xa_2.
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_y_2)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_xa_2,V_y_2)!=V_xa_2.
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_y).
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_y).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_x).
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),V_x).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_a)|c_Orderings_Oord__class_Oless(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_b)|c_Orderings_Oord__class_Oless(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_b)).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_x)|c_Orderings_Oord__class_Oless(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x).
% 13.65/13.64 0 [] -class_Lattices_Osemilattice__inf(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_x)|c_Orderings_Oord__class_Oless(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_b),V_x).
% 13.65/13.64 0 [] -class_Lattices_Obounded__lattice__bot(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_y_2)!=c_Orderings_Obot__class_Obot(T_a)|V_xa_2=c_Orderings_Obot__class_Obot(T_a).
% 13.65/13.64 0 [] -class_Lattices_Obounded__lattice__bot(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_y_2)!=c_Orderings_Obot__class_Obot(T_a)|V_y_2=c_Orderings_Obot__class_Obot(T_a).
% 13.65/13.64 0 [] -class_Lattices_Obounded__lattice__bot(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_y_2)=c_Orderings_Obot__class_Obot(T_a)|V_xa_2!=c_Orderings_Obot__class_Obot(T_a)|V_y_2!=c_Orderings_Obot__class_Obot(T_a).
% 13.65/13.64 0 [] -class_Lattices_Obounded__lattice__bot(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Orderings_Obot__class_Obot(T_a))=V_x.
% 13.65/13.64 0 [] -class_Lattices_Obounded__lattice__bot(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Orderings_Obot__class_Obot(T_a),V_x)=V_x.
% 13.65/13.64 0 [] -class_Lattices_Obounded__lattice__bot(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Orderings_Obot__class_Obot(T_a))=c_Orderings_Obot__class_Obot(T_a).
% 13.65/13.64 0 [] -class_Lattices_Obounded__lattice__bot(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Orderings_Obot__class_Obot(T_a),V_x)=c_Orderings_Obot__class_Obot(T_a).
% 13.65/13.64 0 [] -class_Lattices_Odistrib__lattice(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z),V_x)=c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_x),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_z,V_x)).
% 13.65/13.64 0 [] -class_Lattices_Odistrib__lattice(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z),V_x)=c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_x),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_z,V_x)).
% 13.65/13.64 0 [] -class_Lattices_Odistrib__lattice(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_y,V_z))=c_Lattices_Osemilattice__inf__class_Oinf(T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y),c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_z)).
% 13.65/13.64 0 [] -class_Lattices_Odistrib__lattice(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_y,V_z))=c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y),c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_z)).
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_y))=V_x.
% 13.65/13.64 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_y))=V_x.
% 13.65/13.64 0 [] -class_Lattices_Obounded__lattice__top(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Orderings_Otop__class_Otop(T_a))=c_Orderings_Otop__class_Otop(T_a).
% 13.65/13.64 0 [] -class_Lattices_Obounded__lattice__top(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Orderings_Otop__class_Otop(T_a),V_x)=c_Orderings_Otop__class_Otop(T_a).
% 13.65/13.64 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)).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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__e_q(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_d_2).
% 13.65/13.64 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__e_q(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_d_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_member(T_a,$f52(V_Q_2,V_Pa_2,V_B_2,V_A_2,T_a),V_A_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OCollect(T_a,V_Pa_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_OCollect(T_a,V_Q_2))).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|hBOOL(hAPP(V_Pa_2,$f52(V_Q_2,V_Pa_2,V_B_2,V_A_2,T_a)))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OCollect(T_a,V_Pa_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_OCollect(T_a,V_Q_2))).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -hBOOL(hAPP(V_Q_2,$f52(V_Q_2,V_Pa_2,V_B_2,V_A_2,T_a)))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OCollect(T_a,V_Pa_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_OCollect(T_a,V_Q_2))).
% 13.65/13.64 0 [] -c_member(T_a,V_xa_2,V_A_2)| -c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_y_2)|c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_xa_2),V_y_2)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),V_a_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 13.65/13.64 0 [] c_Nitpick_Ofold__graph_H(T_a,T_b,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_a2_2).
% 13.65/13.64 0 [] c_Nitpick_Ofold__graph_H(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i))=V_i.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)|V_m_2=V_n_2.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)|V_m_2!=V_n_2.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_m)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=V_b_2.
% 13.65/13.64 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=V_b_2.
% 13.65/13.64 0 [] -class_Groups_Oab__group__add(T_a)|V_a_2!=V_b_2|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Groups_Oab__group__add(T_a)|V_a_2=V_b_2|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_xa_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_xa_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.65/13.64 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 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)).
% 13.65/13.64 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)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)|c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_c,V_a)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_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).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_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).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.65/13.64 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|V_a_2!=V_b_2|V_c_2=V_d_2.
% 13.65/13.64 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|V_a_2=V_b_2|V_c_2!=V_d_2.
% 13.65/13.64 0 [] -c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))|V_a2_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)=hAPP(hAPP(V_a3_2,$f54(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a)),$f53(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a)).
% 13.65/13.64 0 [] -c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))|V_a2_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|c_member(T_a,$f54(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a),V_a2_2).
% 13.65/13.64 0 [] -c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))|V_a2_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_a2_2,c_Set_Oinsert(T_a,$f54(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),$f53(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a)).
% 13.65/13.64 0 [] -c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))|hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)=V_a4_2|hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)=hAPP(hAPP(V_a3_2,$f54(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a)),$f53(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a)).
% 13.65/13.64 0 [] -c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))|hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)=V_a4_2|c_member(T_a,$f54(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a),V_a2_2).
% 13.65/13.64 0 [] -c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))|hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)=V_a4_2|c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_a2_2,c_Set_Oinsert(T_a,$f54(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),$f53(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a)).
% 13.65/13.64 0 [] c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))|V_a2_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)!=V_a4_2.
% 13.65/13.64 0 [] c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))|hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)!=hAPP(hAPP(V_a3_2,B_x),B_y)| -c_member(T_a,B_x,V_a2_2)| -c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_a2_2,c_Set_Oinsert(T_a,B_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),B_y).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_xa_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_xa_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_xa_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_xa_2).
% 13.65/13.64 0 [] c_member(tc_fun(T_a,tc_HOL_Obool),V_xa_2,V_F_2)|c_member(tc_fun(T_a,tc_HOL_Obool),$f56(V_F_2,V_xa_2,T_a),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),V_xa_2,V_F_2))|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_xa_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_F_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_member(tc_fun(T_a,tc_HOL_Obool),V_xa_2,V_F_2)|c_member(tc_fun(T_a,tc_HOL_Obool),$f55(V_F_2,V_xa_2,T_a),c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool),V_xa_2,V_F_2))|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_xa_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_F_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_member(tc_fun(T_a,tc_HOL_Obool),V_xa_2,V_F_2)|$f56(V_F_2,V_xa_2,T_a)!=$f55(V_F_2,V_xa_2,T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_xa_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_F_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] c_member(tc_fun(T_a,tc_HOL_Obool),V_xa_2,V_F_2)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),$f56(V_F_2,V_xa_2,T_a),$f55(V_F_2,V_xa_2,T_a))!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_xa_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_F_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatfloor(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)).
% 13.65/13.64 0 [] c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m=V_n.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.64 0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 13.65/13.64 0 [] V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 13.65/13.64 0 [] c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n.
% 13.65/13.64 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)).
% 13.65/13.64 0 [] c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)|c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatceiling(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 13.65/13.64 0 [] -c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_xa_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),V_y_2)| -c_member(T_a,V_xa_2,V_A_2)|c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_xa_2),V_y_2)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))).
% 13.65/13.64 0 [] c_member(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Nat_Osemiring__1__class_ONats(tc_RealDef_Oreal)).
% 13.65/13.64 0 [] -class_GCD_Ogcd(T_a)|c_GCD_Ogcd__class_OGcd(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a).
% 13.65/13.64 0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.65/13.64 0 [] c_Orderings_Obot__class_Obot(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] -c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_xa_2)|V_xa_2=V_z_2.
% 13.65/13.64 0 [] c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2).
% 13.65/13.64 0 [] c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_z_2).
% 13.65/13.64 0 [] -class_Rings_Osemiring__1(T_a)|c_member(T_a,c_Groups_Oone__class_Oone(T_a),c_Nat_Osemiring__1__class_ONats(T_a)).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)).
% 13.65/13.64 0 [] c_member(T_a,V_xa_2,V_A_2)| -c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2,V_y_2)|c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,c_Set_Oinsert(T_a,V_xa_2,V_A_2),hAPP(hAPP(V_f_2,V_xa_2),V_y_2)).
% 13.65/13.64 0 [] -class_Rings_Osemiring__1(T_a)|c_member(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_ONats(T_a)).
% 13.65/13.64 0 [] -class_GCD_Ogcd(T_a)|c_GCD_Ogcd__class_OLcm(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(T_a).
% 13.65/13.64 0 [] -c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2,V_xa_2)|c_member(T_a,V_a_2,V_A_2)|c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Set_Oinsert(T_a,V_a_2,V_A_2),V_xa_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatfloor(V_x)=V_n.
% 13.65/13.64 0 [] -class_Groups_Oab__semigroup__mult(T_a)| -c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2,V_xa_2)| -c_member(T_a,V_a_2,V_A_2)|c_member(T_a,V_b_2,V_A_2)|c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),V_xa_2).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__1(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)|c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)!=c_Groups_Oone__class_Oone(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a).
% 13.65/13.64 0 [] -class_Rings_Ono__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Rings_Ono__zero__divisors(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)!=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Rings_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_b_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Rings_Omult__zero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Rings_Omult__zero(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Groups_Omonoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a.
% 13.65/13.64 0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a.
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] -class_Groups_Omonoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 13.65/13.64 0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 13.65/13.64 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2)|V_a_2=V_b_2.
% 13.65/13.64 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2)|V_a_2!=V_b_2.
% 13.65/13.64 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2)|V_a_2=V_b_2.
% 13.65/13.64 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2)|V_a_2!=V_b_2.
% 13.65/13.64 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_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.65/13.64 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_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.65/13.64 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_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_y_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.65/13.64 0 [] V_m!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)|V_n=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)|V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)|V_m_2!=V_n_2.
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2!=V_n_2.
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] -class_Rings_Oring__1(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z)=V_z.
% 13.65/13.64 0 [] -class_Groups_Ocomm__monoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a.
% 13.65/13.64 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a.
% 13.65/13.64 0 [] -class_Groups_Ocomm__monoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a.
% 13.65/13.64 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a.
% 13.65/13.64 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 13.65/13.64 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 13.65/13.64 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 13.65/13.64 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 13.65/13.64 0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 13.65/13.64 0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)).
% 13.65/13.64 0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 13.65/13.64 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b).
% 13.65/13.64 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b).
% 13.65/13.64 0 [] -class_Groups_Oab__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 13.65/13.64 0 [] -class_Groups_Oab__semigroup__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 13.65/13.64 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.
% 13.65/13.64 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.
% 13.65/13.64 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.
% 13.65/13.64 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.
% 13.65/13.64 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)!=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)|V_b=V_c.
% 13.65/13.64 0 [] -class_Groups_Ocancel__ab__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)!=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)|V_b=V_c.
% 13.65/13.64 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_b,V_a)!=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)|V_b=V_c.
% 13.65/13.64 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.65/13.64 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.65/13.64 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 13.65/13.64 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)).
% 13.65/13.64 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)).
% 13.65/13.64 0 [] c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2)),V_w)=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 13.65/13.64 0 [] -class_Rings_Osemiring(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)).
% 13.65/13.64 0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)=V_a.
% 13.65/13.64 0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)=V_x.
% 13.65/13.64 0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b).
% 13.65/13.64 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.
% 13.65/13.64 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.
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b)=V_a.
% 13.65/13.64 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=V_a.
% 13.65/13.64 0 [] -class_Rings_Oring(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)).
% 13.65/13.64 0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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)).
% 13.65/13.64 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)).
% 13.65/13.64 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_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__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).
% 13.65/13.64 0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_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__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).
% 13.65/13.64 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_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__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)).
% 13.65/13.64 0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_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__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)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__1__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)|c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)!=c_Groups_Oone__class_Oone(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a).
% 13.65/13.64 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 13.65/13.64 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 13.65/13.64 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 13.65/13.64 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_xa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_xa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_xa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 13.65/13.64 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 13.65/13.64 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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)).
% 13.65/13.64 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)).
% 13.65/13.64 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 13.65/13.64 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 13.65/13.64 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))).
% 13.65/13.64 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 13.65/13.64 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 13.65/13.64 0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 13.65/13.64 0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 13.65/13.64 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 13.65/13.64 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 13.65/13.64 0 [] -class_Rings_Oordered__comm__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 13.65/13.64 0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 13.65/13.64 0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 13.65/13.64 0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 13.65/13.64 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__comm__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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)).
% 13.65/13.64 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).
% 13.65/13.64 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)).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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)).
% 13.65/13.64 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).
% 13.65/13.64 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)).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b))).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)).
% 13.65/13.64 0 [] -c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2,V_xa_2)|V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 13.65/13.64 0 [] -c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_xa_2).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)).
% 13.65/13.64 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_y_2),V_z_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2).
% 13.65/13.64 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_y_2),V_z_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y)).
% 13.65/13.64 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.65/13.64 0 [] -class_Rings_Osemiring__1(T_a)| -c_member(T_a,V_a_2,c_Nat_Osemiring__1__class_ONats(T_a))| -c_member(T_a,V_b_2,c_Nat_Osemiring__1__class_ONats(T_a))|c_member(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)).
% 13.65/13.64 0 [] -class_Rings_Osemiring__1(T_a)| -c_member(T_a,V_a_2,c_Nat_Osemiring__1__class_ONats(T_a))| -c_member(T_a,V_b_2,c_Nat_Osemiring__1__class_ONats(T_a))|c_member(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)).
% 13.65/13.64 0 [] c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.65/13.64 0 [] c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.65/13.64 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 13.65/13.64 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 13.65/13.64 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 13.65/13.64 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 13.65/13.64 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)).
% 13.65/13.64 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__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))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2).
% 13.65/13.64 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__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))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2).
% 13.65/13.64 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__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))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 13.65/13.64 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__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))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 13.65/13.64 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x).
% 13.65/13.64 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2).
% 13.65/13.64 0 [] -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)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 13.65/13.64 0 [] 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).
% 13.65/13.64 0 [] 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__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_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__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_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).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 13.65/13.64 0 [] -class_Groups_Oab__semigroup__mult(T_a)| -c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_b_2,V_A_2,V_y_2)|c_member(T_a,V_b_2,V_A_2)|c_Finite__Set_Ofold__graph(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a),V_z_2,c_Set_Oinsert(T_a,V_b_2,V_A_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z_2),V_y_2)).
% 13.65/13.64 0 [] -c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_b_2)|V_a_2=V_b_2.
% 13.65/13.64 0 [] c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),V_b_2)|V_a_2!=V_b_2.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_xa_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_xa_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_xa_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_xa_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_xa_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 13.65/13.64 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_y_2),V_y_2)))|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 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_y_2),V_y_2)))|V_xa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 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_y_2),V_y_2)))|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))|V_xa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)!=V_m|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 13.65/13.64 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n.
% 13.65/13.64 0 [] V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 13.65/13.64 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.65/13.64 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.65/13.64 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)=V_n.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_z)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)).
% 13.65/13.64 0 [] -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))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 13.65/13.64 0 [] 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))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 13.65/13.64 0 [] -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,$f57(V_n_2,V_m_2)).
% 13.65/13.64 0 [] 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).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3)).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n)=V_m.
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n)=V_m.
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m.
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)=V_m.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)!=V_k_2|V_j_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_k_2|V_j_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i).
% 13.65/13.64 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 13.65/13.64 0 [] -hBOOL(hAPP(V_Pa_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_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.65/13.64 0 [] -hBOOL(hAPP(V_Pa_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_Pa_2,B_d)).
% 13.65/13.64 0 [] hBOOL(hAPP(V_Pa_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,$f58(V_b_2,V_a_2,V_Pa_2)).
% 13.65/13.64 0 [] hBOOL(hAPP(V_Pa_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_Pa_2,$f58(V_b_2,V_a_2,V_Pa_2))).
% 13.65/13.64 0 [] hBOOL(hAPP(V_Pa_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f58(V_b_2,V_a_2,V_Pa_2)).
% 13.65/13.64 0 [] hBOOL(hAPP(V_Pa_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_Pa_2,$f58(V_b_2,V_a_2,V_Pa_2))).
% 13.65/13.64 0 [] -hBOOL(hAPP(V_Pa_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 13.65/13.64 0 [] -hBOOL(hAPP(V_Pa_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|V_a_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)|hBOOL(hAPP(V_Pa_2,B_d)).
% 13.65/13.64 0 [] hBOOL(hAPP(V_Pa_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f59(V_b_2,V_a_2,V_Pa_2)).
% 13.65/13.64 0 [] hBOOL(hAPP(V_Pa_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_Pa_2,$f59(V_b_2,V_a_2,V_Pa_2))).
% 13.65/13.64 0 [] hBOOL(hAPP(V_Pa_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f59(V_b_2,V_a_2,V_Pa_2)).
% 13.65/13.64 0 [] hBOOL(hAPP(V_Pa_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_Pa_2,$f59(V_b_2,V_a_2,V_Pa_2))).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatceiling(V_x)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 13.65/13.64 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_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 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_y_2),V_y_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 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_y_2),V_y_2))=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Rings_Olinordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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).
% 13.65/13.64 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m).
% 13.65/13.64 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)).
% 13.65/13.64 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)).
% 13.65/13.64 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.
% 13.65/13.64 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.
% 13.65/13.64 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.
% 13.65/13.64 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.
% 13.65/13.64 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=V_n_2.
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2!=V_n_2.
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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.
% 13.65/13.64 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.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u),V_n)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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__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)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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__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)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_i)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u),V_m),V_n).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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__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).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_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__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).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_m,V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_m).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a.
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)).
% 13.65/13.64 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)).
% 13.65/13.64 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)).
% 13.65/13.64 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)).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m).
% 13.65/13.64 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_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_y_2))|V_w_2=V_xa_2|V_y_2=V_z_2.
% 13.65/13.64 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_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_y_2))|V_w_2!=V_xa_2.
% 13.65/13.64 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_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_y_2))|V_y_2!=V_z_2.
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a))=V_a.
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)=V_a.
% 13.65/13.64 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_r=c_Groups_Ozero__class_Ozero(T_a)|V_a!=V_b|V_c=V_d|c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c))!=c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m).
% 13.65/13.64 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))).
% 13.65/13.64 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)).
% 13.65/13.64 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)).
% 13.65/13.64 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),V_ya)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)).
% 13.65/13.64 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H)),V_b)=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)).
% 13.65/13.64 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)).
% 13.65/13.64 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H))=c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)).
% 13.65/13.64 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H))=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)).
% 13.65/13.64 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)).
% 13.65/13.64 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b)=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)).
% 13.65/13.64 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya)=c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,$f60(V_r),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_r).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,$f60(V_r))).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)|V_l_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,$f61(V_l_2,V_k_2)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)|V_l_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n).
% 13.65/13.64 0 [] -class_Rings_Olinordered__idom(T_a)| -c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(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)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__idom(T_a)| -c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(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)).
% 13.65/13.64 0 [] hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_Pa_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f62(V_n_2,V_Pa_2),V_n_2).
% 13.65/13.64 0 [] hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_Pa_2,V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i,$f62(V_n_2,V_Pa_2))| -hBOOL(hAPP(V_Pa_2,B_i)).
% 13.65/13.64 0 [] hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_Pa_2,V_n_2))|hBOOL(hAPP(V_Pa_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,$f62(V_n_2,V_Pa_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 13.65/13.64 0 [] -class_Rings_Oring__1(T_a)|c_member(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Oring__1__class_OInts(T_a)).
% 13.65/13.64 0 [] -class_Rings_Oring__1(T_a)| -c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))| -c_member(T_a,V_b_2,c_Int_Oring__1__class_OInts(T_a))|c_member(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Int_Oring__1__class_OInts(T_a)).
% 13.65/13.64 0 [] -class_Rings_Oring__1(T_a)| -c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))| -c_member(T_a,V_b_2,c_Int_Oring__1__class_OInts(T_a))|c_member(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2),c_Int_Oring__1__class_OInts(T_a)).
% 13.65/13.64 0 [] -class_Rings_Oring__1(T_a)| -c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))| -c_member(T_a,V_b_2,c_Int_Oring__1__class_OInts(T_a))|c_member(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Int_Oring__1__class_OInts(T_a)).
% 13.65/13.64 0 [] -class_Rings_Oring__1(T_a)|c_member(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Oring__1__class_OInts(T_a)).
% 13.65/13.64 0 [] c_member(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Int_Oring__1__class_OInts(tc_RealDef_Oreal)).
% 13.65/13.64 0 [] -class_Int_Oring__char__0(T_a)| -c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(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).
% 13.65/13.64 0 [] -class_Int_Oring__char__0(T_a)| -c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(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).
% 13.65/13.64 0 [] -class_Int_Oring__char__0(T_a)| -c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2),V_a_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n)).
% 13.65/13.64 0 [] -c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Set_Oinsert(T_a,V_a1_2,V_a2_2),V_a3_2)|c_Set_Oinsert(T_a,V_a1_2,V_a2_2)=c_Set_Oinsert(T_a,$f64(V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a),$f63(V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a)).
% 13.65/13.64 0 [] -c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Set_Oinsert(T_a,V_a1_2,V_a2_2),V_a3_2)|c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,$f64(V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a),$f63(V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a),V_a3_2).
% 13.65/13.64 0 [] -c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Set_Oinsert(T_a,V_a1_2,V_a2_2),V_a3_2)| -c_member(T_a,$f64(V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a),$f63(V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a)).
% 13.65/13.64 0 [] c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Set_Oinsert(T_a,V_a1_2,V_a2_2),V_a3_2)|c_Set_Oinsert(T_a,V_a1_2,V_a2_2)!=c_Set_Oinsert(T_a,B_a,B_A)| -c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A,V_a3_2)|c_member(T_a,B_a,B_A).
% 13.65/13.64 0 [] -class_Rings_Oring__1(T_a)| -c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))|c_member(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2),c_Int_Oring__1__class_OInts(T_a)).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_x.
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)).
% 13.65/13.64 0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)).
% 13.65/13.64 0 [] -class_Groups_Omonoid__mult(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x)=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n).
% 13.65/13.64 0 [] -class_Power_Opower(T_a)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=c_Groups_Oone__class_Oone(T_a).
% 13.65/13.64 0 [] -class_Power_Opower(T_a)|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)).
% 13.65/13.64 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z)=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)).
% 13.65/13.64 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)).
% 13.65/13.64 0 [] c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n).
% 13.65/13.64 0 [] hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n)=c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 13.65/13.64 0 [] V_x!=c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))|c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n).
% 13.65/13.64 0 [] V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 13.65/13.64 0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 13.65/13.64 0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)!=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Groups_Ocomm__monoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)).
% 13.65/13.64 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.65/13.64 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a).
% 13.65/13.64 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n).
% 13.65/13.64 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_a.
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.65/13.64 0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 0 [] -class_Power_Opower(T_a)| -class_Rings_Omult__zero(T_a)| -class_Rings_Ono__zero__divisors(T_a)| -class_Rings_Ozero__ne_q__one(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.65/13.64 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.
% 13.65/13.64 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.
% 13.65/13.64 0 [] -class_Power_Opower(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a).
% 13.65/13.64 0 [] -class_Groups_Omonoid__mult(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))).
% 13.65/13.64 0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Oone__class_Oone(T_a).
% 13.65/13.64 0 [] -class_Power_Opower(T_a)| -class_Rings_Osemiring__0(T_a)|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n)=c_Groups_Ozero__class_Ozero(T_a).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 13.65/13.64 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_y_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_y_2).
% 13.65/13.64 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_y_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_y_2).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)|hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)!=hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|V_a=V_b.
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_N)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_xa_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_xa_2,V_y_2).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_xa_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_xa_2,V_y_2).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 13.65/13.64 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)).
% 13.65/13.64 0 [] -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(T_a)=c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)|c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 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).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)=V_z.
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint))=V_z.
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)).
% 13.65/13.64 0 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)).
% 13.65/13.64 0 [] hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_one_2.
% 13.65/13.64 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),$f65(V_a,V_n)).
% 13.65/13.64 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),$f65(V_a,V_n)),V_n)=V_a.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n)!=V_a|B_y=$f65(V_a,V_n).
% 13.65/13.64 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),$f66(V_a,V_n)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)|hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),$f66(V_a,V_n)),V_n)=V_a.
% 13.65/13.64 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 13.65/13.64 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)=V_z.
% 13.65/13.64 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 13.65/13.64 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.
% 13.65/13.64 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).
% 13.65/13.64 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.
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,V_z_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,V_z_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_H,V_z)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)).
% 13.65/13.64 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)).
% 13.65/13.64 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)).
% 13.65/13.64 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j)).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_w_2).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)|V_z_2!=V_w_2.
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_w_2)|V_z_2=V_w_2.
% 13.65/13.64 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)).
% 13.65/13.64 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)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2).
% 13.65/13.64 0 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)|V_a!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)|V_a!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_w).
% 13.65/13.64 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_j,V_k)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_k).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z)|V_z=V_w.
% 13.65/13.64 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H,V_b)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,V_q).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,V_q_H).
% 13.65/13.64 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)!=c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_b_H,V_b)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q,V_q_H).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,V_q).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 13.65/13.64 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H).
% 13.65/13.65 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)).
% 13.65/13.65 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)).
% 13.65/13.65 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 13.65/13.65 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 13.65/13.65 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)).
% 13.65/13.65 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)|c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y).
% 13.65/13.65 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)|c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 13.65/13.65 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),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Transcendental_Oln(V_x)).
% 13.65/13.65 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).
% 13.65/13.65 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_y_2)|c_Transcendental_Oln(V_xa_2)!=c_Transcendental_Oln(V_y_2)|V_xa_2=V_y_2.
% 13.65/13.65 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_y_2)|c_Transcendental_Oln(V_xa_2)=c_Transcendental_Oln(V_y_2)|V_xa_2!=V_y_2.
% 13.65/13.65 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_y_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_xa_2),c_Transcendental_Oln(V_y_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2).
% 13.65/13.65 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_y_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_xa_2),c_Transcendental_Oln(V_y_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_y_2).
% 13.65/13.65 0 [] c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.65/13.65 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_y_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(V_xa_2),c_Transcendental_Oln(V_y_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2).
% 13.65/13.65 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_y_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(V_xa_2),c_Transcendental_Oln(V_y_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_y_2).
% 13.65/13.65 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)).
% 13.65/13.65 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)).
% 13.65/13.65 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).
% 13.65/13.65 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).
% 13.65/13.65 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).
% 13.65/13.65 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).
% 13.65/13.65 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)).
% 13.65/13.65 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)).
% 13.65/13.65 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)).
% 13.65/13.65 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).
% 13.65/13.65 0 [] -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)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x).
% 13.65/13.65 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__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_xa_2))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_xa_2).
% 13.65/13.65 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__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_xa_2))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_xa_2).
% 13.65/13.65 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)).
% 13.65/13.65 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Transcendental_Oln(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)),V_x).
% 13.65/13.65 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y)).
% 13.65/13.65 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_y,V_x)|c_Nat__Transfer_Otsub(V_x,V_y)=c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y).
% 13.65/13.65 0 [] -c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Set_Oinsert(T_a,V_a_2,V_X_2),V_xa_2)|c_Set_Oinsert(T_a,V_a_2,V_X_2)=c_Set_Oinsert(T_a,$f68(V_xa_2,V_X_2,V_a_2,V_f_2,T_a),$f67(V_xa_2,V_X_2,V_a_2,V_f_2,T_a)).
% 13.65/13.65 0 [] -c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Set_Oinsert(T_a,V_a_2,V_X_2),V_xa_2)|c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,$f68(V_xa_2,V_X_2,V_a_2,V_f_2,T_a),$f67(V_xa_2,V_X_2,V_a_2,V_f_2,T_a),V_xa_2).
% 13.65/13.65 0 [] -c_Finite__Set_Ofold1Set(T_a,V_f_2,c_Set_Oinsert(T_a,V_a_2,V_X_2),V_xa_2)| -c_member(T_a,$f68(V_xa_2,V_X_2,V_a_2,V_f_2,T_a),$f67(V_xa_2,V_X_2,V_a_2,V_f_2,T_a)).
% 13.65/13.65 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),c_RealDef_Oreal(tc_Nat_Onat,$f69(V_x,B_y))),V_x)).
% 13.65/13.65 0 [] class_Lattices_Obounded__lattice(tc_Limits_Onet(T_1)).
% 13.65/13.65 0 [] class_Lattices_Obounded__lattice(tc_HOL_Obool).
% 13.65/13.65 0 [] -class_Lattices_Obounded__lattice(T_1)|class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)).
% 13.65/13.65 0 [] -class_Complete__Lattice_Ocomplete__lattice(T_1)|class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)).
% 13.65/13.65 0 [] -class_Lattices_Obounded__lattice(T_1)|class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)).
% 13.65/13.65 0 [] -class_Lattices_Obounded__lattice(T_1)|class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)).
% 13.65/13.65 0 [] -class_Lattices_Olattice(T_1)|class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)).
% 13.65/13.65 0 [] -class_Lattices_Olattice(T_1)|class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)).
% 13.65/13.65 0 [] -class_Lattices_Odistrib__lattice(T_1)|class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)).
% 13.65/13.65 0 [] -class_Orderings_Opreorder(T_1)|class_Orderings_Opreorder(tc_fun(T_2,T_1)).
% 13.65/13.65 0 [] -class_Lattices_Olattice(T_1)|class_Lattices_Olattice(tc_fun(T_2,T_1)).
% 13.65/13.65 0 [] -class_Orderings_Oorder(T_1)|class_Orderings_Oorder(tc_fun(T_2,T_1)).
% 13.65/13.65 0 [] -class_Orderings_Otop(T_1)|class_Orderings_Otop(tc_fun(T_2,T_1)).
% 13.65/13.65 0 [] -class_Orderings_Oord(T_1)|class_Orderings_Oord(tc_fun(T_2,T_1)).
% 13.65/13.65 0 [] -class_Orderings_Obot(T_1)|class_Orderings_Obot(tc_fun(T_2,T_1)).
% 13.65/13.65 0 [] -class_Groups_Ominus(T_1)|class_Groups_Ominus(tc_fun(T_2,T_1)).
% 13.65/13.65 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Oordered__cancel__semiring(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Oordered__comm__semiring(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Olinordered__semiring__1(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Olinordered__semiring(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Olinordered__semidom(tc_Int_Oint).
% 13.65/13.65 0 [] class_Lattices_Osemilattice__sup(tc_Int_Oint).
% 13.65/13.65 0 [] class_Lattices_Osemilattice__inf(tc_Int_Oint).
% 13.65/13.65 0 [] class_Lattices_Odistrib__lattice(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Oordered__semiring(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Olinordered__ring(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Olinordered__idom(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Ocomm__semiring(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Oab__group__add(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Oordered__ring(tc_Int_Oint).
% 13.65/13.65 0 [] class_Orderings_Opreorder(tc_Int_Oint).
% 13.65/13.65 0 [] class_Orderings_Olinorder(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Omonoid__mult(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Omonoid__add(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Osemiring__1(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Osemiring__0(tc_Int_Oint).
% 13.65/13.65 0 [] class_Lattices_Olattice(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Ogroup__add(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Omult__zero(tc_Int_Oint).
% 13.65/13.65 0 [] class_Orderings_Oorder(tc_Int_Oint).
% 13.65/13.65 0 [] class_Int_Oring__char__0(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Osemiring(tc_Int_Oint).
% 13.65/13.65 0 [] class_Orderings_Oord(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Oring__1(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Ominus(tc_Int_Oint).
% 13.65/13.65 0 [] class_Power_Opower(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Ozero(tc_Int_Oint).
% 13.65/13.65 0 [] class_Rings_Oring(tc_Int_Oint).
% 13.65/13.65 0 [] class_Groups_Oone(tc_Int_Oint).
% 13.65/13.65 0 [] class_GCD_Ogcd(tc_Int_Oint).
% 13.65/13.65 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Lattices_Osemilattice__sup(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Lattices_Osemilattice__inf(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Lattices_Odistrib__lattice(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Rings_Oordered__semiring(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Orderings_Opreorder(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Orderings_Olinorder(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Groups_Omonoid__mult(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Groups_Omonoid__add(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Rings_Osemiring__1(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Rings_Osemiring__0(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Lattices_Olattice(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Rings_Omult__zero(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Orderings_Oorder(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Rings_Osemiring(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Orderings_Oord(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Orderings_Obot(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Groups_Ominus(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Power_Opower(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Groups_Ozero(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Groups_Oone(tc_Nat_Onat).
% 13.65/13.65 0 [] class_GCD_Ogcd(tc_Nat_Onat).
% 13.65/13.65 0 [] class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool).
% 13.65/13.65 0 [] class_Lattices_Obounded__lattice__top(tc_HOL_Obool).
% 13.65/13.65 0 [] class_Lattices_Obounded__lattice__bot(tc_HOL_Obool).
% 13.65/13.65 0 [] class_Lattices_Osemilattice__sup(tc_HOL_Obool).
% 13.65/13.65 0 [] class_Lattices_Osemilattice__inf(tc_HOL_Obool).
% 13.65/13.65 0 [] class_Lattices_Odistrib__lattice(tc_HOL_Obool).
% 13.65/13.65 0 [] class_Orderings_Opreorder(tc_HOL_Obool).
% 13.65/13.65 0 [] class_Lattices_Olattice(tc_HOL_Obool).
% 13.65/13.65 0 [] class_Orderings_Oorder(tc_HOL_Obool).
% 13.65/13.65 0 [] class_Orderings_Otop(tc_HOL_Obool).
% 13.65/13.65 0 [] class_Orderings_Oord(tc_HOL_Obool).
% 13.65/13.65 0 [] class_Orderings_Obot(tc_HOL_Obool).
% 13.65/13.65 0 [] class_Groups_Ominus(tc_HOL_Obool).
% 13.65/13.65 0 [] class_Complete__Lattice_Ocomplete__lattice(tc_Limits_Onet(T_1)).
% 13.65/13.65 0 [] class_Lattices_Obounded__lattice__top(tc_Limits_Onet(T_1)).
% 13.65/13.65 0 [] class_Lattices_Obounded__lattice__bot(tc_Limits_Onet(T_1)).
% 13.65/13.65 0 [] class_Lattices_Osemilattice__sup(tc_Limits_Onet(T_1)).
% 13.65/13.65 0 [] class_Lattices_Osemilattice__inf(tc_Limits_Onet(T_1)).
% 13.65/13.65 0 [] class_Orderings_Opreorder(tc_Limits_Onet(T_1)).
% 13.65/13.65 0 [] class_Lattices_Olattice(tc_Limits_Onet(T_1)).
% 13.65/13.65 0 [] class_Orderings_Oorder(tc_Limits_Onet(T_1)).
% 13.65/13.65 0 [] class_Orderings_Otop(tc_Limits_Onet(T_1)).
% 13.65/13.65 0 [] class_Orderings_Oord(tc_Limits_Onet(T_1)).
% 13.65/13.65 0 [] class_Orderings_Obot(tc_Limits_Onet(T_1)).
% 13.65/13.65 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Olinordered__semiring(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Olinordered__semidom(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Lattices_Osemilattice__sup(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Lattices_Osemilattice__inf(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Lattices_Odistrib__lattice(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Oab__semigroup__add(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Oordered__semiring(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Ono__zero__divisors(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Olinordered__ring(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Olinordered__idom(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Ocomm__semiring(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Oab__group__add(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Oordered__ring(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Orderings_Opreorder(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Orderings_Olinorder(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Omonoid__mult(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Omonoid__add(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Osemiring__1(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Osemiring__0(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Lattices_Olattice(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Ogroup__add(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Omult__zero(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Orderings_Oorder(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Int_Oring__char__0(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Osemiring(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Orderings_Oord(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Oring__1(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Ominus(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Power_Opower(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Ozero(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Rings_Oring(tc_RealDef_Oreal).
% 13.65/13.65 0 [] class_Groups_Oone(tc_RealDef_Oreal).
% 13.65/13.65 0 [] -hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2))|V_x_2=V_y_2.
% 13.65/13.65 0 [] V_x_2!=V_y_2|hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2)).
% 13.65/13.65 0 [] -hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),c_Set_OCollect(tc_RealDef_Oreal,v_P)),B_x1)).
% 13.65/13.65 end_of_list.
% 13.65/13.65
% 13.65/13.65 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 13.65/13.65
% 13.65/13.65 This ia a non-Horn set with equality. The strategy will be
% 13.65/13.65 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 13.65/13.65 deletion, with positive clauses in sos and nonpositive
% 13.65/13.65 clauses in usable.
% 13.65/13.65
% 13.65/13.65 dependent: set(knuth_bendix).
% 13.65/13.65 dependent: set(anl_eq).
% 13.65/13.65 dependent: set(para_from).
% 13.65/13.65 dependent: set(para_into).
% 13.65/13.65 dependent: clear(para_from_right).
% 13.65/13.65 dependent: clear(para_into_right).
% 13.65/13.65 dependent: set(para_from_vars).
% 13.65/13.65 dependent: set(eq_units_both_ways).
% 13.65/13.65 dependent: set(dynamic_demod_all).
% 13.65/13.65 dependent: set(dynamic_demod).
% 13.65/13.65 dependent: set(order_eq).
% 13.65/13.65 dependent: set(back_demod).
% 13.65/13.65 dependent: set(lrpo).
% 13.65/13.65 dependent: set(hyper_res).
% 13.65/13.65 dependent: set(unit_deletion).
% 13.65/13.65 dependent: set(factor).
% 13.65/13.65
% 13.65/13.65 ------------> process usable:
% 13.65/13.65 ** KEPT (pick-wt=14): 1 [] hAPP(A,$f1(B,A))!=hAPP(B,$f1(B,A))|A=B.
% 13.65/13.65 ** KEPT (pick-wt=8): 2 [] -hBOOL(hAPP(v_P,A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,$c2).
% 13.65/13.65 ** KEPT (pick-wt=11): 3 [] -class_Orderings_Otop(A)|hAPP(c_Orderings_Otop__class_Otop(tc_fun(B,A)),C)=c_Orderings_Otop__class_Otop(A).
% 13.65/13.65 ** KEPT (pick-wt=8): 4 [] -hBOOL(hAPP(v_P,A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,v_Y____).
% 13.65/13.65 ** KEPT (pick-wt=13): 6 [copy,5,flip.2] -class_Orderings_Oord(A)|c_Set_OCollect(A,c_Lubs_OisUb(A,B,C))=c_Lubs_Oubs(A,B,C).
% 13.65/13.65 ** KEPT (pick-wt=11): 7 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_Complete__Lattice_OSup__class_OSup(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(A).
% 13.65/13.65 ** KEPT (pick-wt=23): 8 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Lubs_OisUb(A,B,C),D))| -c_Lubs_Osetge(A,D,c_Set_OCollect(A,c_Lubs_OisUb(A,B,C)))|c_Lubs_OisLub(A,B,C,D).
% 13.65/13.65 ** KEPT (pick-wt=13): 9 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Lubs_OisUb(A,B,C),D))|c_Lubs_Osetle(A,C,D).
% 13.65/13.65 ** KEPT (pick-wt=14): 10 [] -class_Orderings_Oord(A)| -c_Lubs_OisLub(A,B,C,D)|hBOOL(hAPP(c_Lubs_OisUb(A,B,C),D)).
% 13.65/13.65 ** KEPT (pick-wt=18): 11 [] -c_member(tc_fun(A,tc_HOL_Obool),B,C)| -c_member(A,D,B)|c_member(A,D,c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),C)).
% 13.65/13.65 ** KEPT (pick-wt=11): 12 [] A!=B|c_member(C,D,A)| -c_member(C,D,B).
% 13.65/13.65 ** KEPT (pick-wt=11): 13 [] A!=B|c_member(C,D,B)| -c_member(C,D,A).
% 13.65/13.65 ** KEPT (pick-wt=6): 14 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,B).
% 13.65/13.65 ** KEPT (pick-wt=13): 15 [] -class_Orderings_Olinorder(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 13.65/13.65 ** KEPT (pick-wt=9): 16 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,B,C).
% 13.65/13.65 ** KEPT (pick-wt=9): 17 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,B).
% 13.65/13.65 Following clause subsumed by 15 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.
% 13.65/13.65 ** KEPT (pick-wt=10): 18 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 13.65/13.65 Following clause subsumed by 16 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 13.65/13.65 ** KEPT (pick-wt=8): 19 [] -c_member(A,B,C)|hBOOL(hAPP(C,B)).
% 13.65/13.65 ** KEPT (pick-wt=8): 20 [] c_member(A,B,C)| -hBOOL(hAPP(C,B)).
% 13.65/13.65 Following clause subsumed by 15 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).
% 13.65/13.65 ** KEPT (pick-wt=8): 21 [] -c_member(A,B,c_fe_qual(C))|B=C.
% 13.65/13.65 ** KEPT (pick-wt=8): 22 [] c_member(A,B,c_fe_qual(C))|B!=C.
% 13.65/13.65 ** KEPT (pick-wt=17): 23 [] -class_Complete__Lattice_Ocomplete__lattice(A)| -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,c_Complete__Lattice_OSup__class_OSup(A,C))|c_member(A,$f2(C,B,A),C).
% 13.65/13.65 ** KEPT (pick-wt=17): 24 [] -class_Complete__Lattice_Ocomplete__lattice(A)| -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,c_Complete__Lattice_OSup__class_OSup(A,C))|c_Orderings_Oord__class_Oless(A,B,$f2(C,B,A)).
% 13.65/13.65 ** KEPT (pick-wt=18): 25 [] -class_Complete__Lattice_Ocomplete__lattice(A)| -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,c_Complete__Lattice_OSup__class_OSup(A,C))| -c_member(A,D,C)| -c_Orderings_Oord__class_Oless(A,B,D).
% 13.65/13.65 Following clause subsumed by 15 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.
% 13.65/13.65 Following clause subsumed by 16 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.
% 13.65/13.65 Following clause subsumed by 15 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).
% 13.65/13.65 ** KEPT (pick-wt=9): 26 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 13.65/13.65 ** KEPT (pick-wt=10): 27 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 13.65/13.65 Following clause subsumed by 27 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 13.65/13.65 Following clause subsumed by 26 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 13.65/13.65 ** KEPT (pick-wt=9): 28 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=B.
% 13.65/13.65 Following clause subsumed by 13 during input processing: 0 [] A!=B| -c_member(C,D,A)|c_member(C,D,B).
% 13.65/13.65 Following clause subsumed by 12 during input processing: 0 [] A!=B|c_member(C,D,A)| -c_member(C,D,B).
% 13.65/13.65 ** KEPT (pick-wt=11): 29 [] A!=B| -c_member(C,A,D)|c_member(C,B,D).
% 13.65/13.65 ** KEPT (pick-wt=11): 30 [] A!=B|c_member(C,A,D)| -c_member(C,B,D).
% 13.65/13.65 Following clause subsumed by 27 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 13.65/13.65 ** KEPT (pick-wt=10): 31 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 13.65/13.65 Following clause subsumed by 30 during input processing: 0 [] A!=B| -c_member(C,B,D)|c_member(C,A,D).
% 13.65/13.65 ** KEPT (pick-wt=13): 32 [] -class_Orderings_Oord(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 13.65/13.65 ** KEPT (pick-wt=13): 33 [] -class_Orderings_Oorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,D,C)|c_Orderings_Oord__class_Oless(A,D,B).
% 13.65/13.65 ** KEPT (pick-wt=13): 34 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=D|c_Orderings_Oord__class_Oless(A,B,D).
% 13.65/13.65 ** KEPT (pick-wt=13): 35 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=D|c_Orderings_Oord__class_Oless(A,D,C).
% 13.65/13.65 ** KEPT (pick-wt=14): 36 [] -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).
% 13.65/13.65 ** KEPT (pick-wt=14): 37 [] -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).
% 13.65/13.65 Following clause subsumed by 27 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 13.65/13.65 ** KEPT (pick-wt=11): 38 [] -class_Orderings_Oord(A)| -c_Lubs_OisLub(A,B,C,D)|c_Lubs_Osetle(A,C,D).
% 13.65/13.65 ** KEPT (pick-wt=11): 39 [] -class_Orderings_Oord(A)| -c_Lubs_OisLub(A,B,C,D)|c_member(A,D,B).
% 13.65/13.65 ** KEPT (pick-wt=14): 40 [] -class_Orderings_Oord(A)| -c_Lubs_OisLub(A,B,C,D)|c_Lubs_Osetge(A,D,c_Lubs_Oubs(A,B,C)).
% 13.65/13.65 Following clause subsumed by 15 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).
% 13.65/13.65 ** KEPT (pick-wt=17): 41 [] -class_Orderings_Oord(A)| -c_Lubs_Osetle(A,B,C)| -c_member(A,C,D)|hBOOL(hAPP(c_Lubs_OisUb(A,D,B),C)).
% 13.65/13.65 Following clause subsumed by 9 during input processing: 0 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Lubs_OisUb(A,B,C),D))|c_Lubs_Osetle(A,C,D).
% 13.65/13.65 ** KEPT (pick-wt=13): 42 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Lubs_OisUb(A,B,C),D))|c_member(A,D,B).
% 13.65/13.65 Following clause subsumed by 41 during input processing: 0 [] -class_Orderings_Oord(A)|hBOOL(hAPP(c_Lubs_OisUb(A,B,C),D))| -c_Lubs_Osetle(A,C,D)| -c_member(A,D,B).
% 13.65/13.65 Following clause subsumed by 42 during input processing: 0 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Lubs_OisUb(A,B,C),D))|c_member(A,D,B).
% 13.65/13.65 ** KEPT (pick-wt=14): 43 [] -class_Orderings_Oord(A)| -c_Lubs_OisLub(A,B,C,D)|c_Lubs_OleastP(A,c_Lubs_OisUb(A,B,C),D).
% 13.65/13.65 ** KEPT (pick-wt=14): 44 [] -class_Orderings_Oord(A)| -c_Lubs_OleastP(A,c_Lubs_OisUb(A,B,C),D)|c_Lubs_OisLub(A,B,C,D).
% 13.65/13.65 Following clause subsumed by 43 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Lubs_OisLub(A,B,C,D)|c_Lubs_OleastP(A,c_Lubs_OisUb(A,B,C),D).
% 13.65/13.65 Following clause subsumed by 44 during input processing: 0 [] -class_Orderings_Oord(A)|c_Lubs_OisLub(A,B,C,D)| -c_Lubs_OleastP(A,c_Lubs_OisUb(A,B,C),D).
% 13.65/13.65 ** KEPT (pick-wt=12): 45 [] -class_Orderings_Oord(A)| -c_Lubs_OleastP(A,B,C)|c_Lubs_Osetge(A,C,c_Set_OCollect(A,B)).
% 13.65/13.65 ** KEPT (pick-wt=10): 46 [] -class_Orderings_Oord(A)| -c_Lubs_OleastP(A,B,C)|hBOOL(hAPP(B,C)).
% 13.65/13.65 Following clause subsumed by 45 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Lubs_OleastP(A,B,C)|c_Lubs_Osetge(A,C,c_Set_OCollect(A,B)).
% 13.65/13.65 ** KEPT (pick-wt=16): 47 [] -class_Orderings_Oord(A)|c_Lubs_OleastP(A,B,C)| -hBOOL(hAPP(B,C))| -c_Lubs_Osetge(A,C,c_Set_OCollect(A,B)).
% 13.65/13.65 ** KEPT (pick-wt=23): 48 [] -c_member(tc_RealDef_Oreal,A,B)| -hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),B),C))|c_Lubs_OisLub(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),B,$f3(B)).
% 13.65/13.65 ** KEPT (pick-wt=23): 49 [] -c_member(tc_RealDef_Oreal,A,B)| -hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),B),C))|c_Lubs_OisLub(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),B,$f4(B)).
% 13.65/13.65 ** KEPT (pick-wt=13): 50 [] -class_Rings_Olinordered__idom(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 13.65/13.65 ** KEPT (pick-wt=8): 51 [] -hBOOL(hAPP(v_P,A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,$c5).
% 13.65/13.65 ** KEPT (pick-wt=18): 52 [] -class_Orderings_Oord(A)| -c_Lubs_OisLub(A,B,C,D)| -hBOOL(hAPP(c_Lubs_OisUb(A,B,C),E))|c_Orderings_Oord__class_Oless__e_q(A,D,E).
% 13.65/13.65 ** KEPT (pick-wt=6): 53 [] -class_Orderings_Opreorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,B).
% 13.65/13.65 ** KEPT (pick-wt=14): 54 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_member(A,D,B)|c_member(A,D,C).
% 13.65/13.65 ** KEPT (pick-wt=16): 55 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 13.65/13.65 ** KEPT (pick-wt=24): 56 [] -class_Orderings_Oord(A)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,$f6(D,C,B,A)),hAPP(D,$f6(D,C,B,A))).
% 13.65/13.65 ** KEPT (pick-wt=10): 57 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 13.65/13.65 ** KEPT (pick-wt=9): 58 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 13.65/13.65 ** KEPT (pick-wt=9): 59 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 13.65/13.65 ** KEPT (pick-wt=13): 60 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 13.65/13.65 ** KEPT (pick-wt=9): 61 [] -class_Orderings_Opreorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 13.65/13.65 ** KEPT (pick-wt=16): 62 [] -c_member(tc_fun(A,tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),C)).
% 13.65/13.65 ** KEPT (pick-wt=22): 63 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),C)).
% 13.65/13.65 Following clause subsumed by 55 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 13.65/13.65 Following clause subsumed by 60 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|C=B.
% 13.65/13.65 Following clause subsumed by 58 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B)|C!=B.
% 13.65/13.65 ** KEPT (pick-wt=13): 64 [] -class_Orderings_Oord(A)|B!=C| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.65/13.65 ** KEPT (pick-wt=13): 65 [] -class_Orderings_Oorder(A)|B!=C| -c_Orderings_Oord__class_Oless__e_q(A,D,C)|c_Orderings_Oord__class_Oless__e_q(A,D,B).
% 13.65/13.65 ** KEPT (pick-wt=13): 66 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|C!=D|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.65/13.65 ** KEPT (pick-wt=13): 67 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=D|c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 13.65/13.65 Following clause subsumed by 60 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|B=C.
% 13.65/13.65 ** KEPT (pick-wt=14): 68 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.65/13.65 Following clause subsumed by 60 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|C=B.
% 13.65/13.65 ** KEPT (pick-wt=14): 69 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,B)|c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 13.65/13.65 Following clause subsumed by 55 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 13.65/13.65 ** KEPT (pick-wt=13): 70 [] -c_Lubs_OisLub(tc_RealDef_Oreal,A,B,C)| -c_Lubs_OisLub(tc_RealDef_Oreal,A,B,D)|C=D.
% 13.65/13.65 Following clause subsumed by 57 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 13.65/13.65 Following clause subsumed by 46 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Lubs_OleastP(A,B,C)|hBOOL(hAPP(B,C)).
% 13.65/13.65 ** KEPT (pick-wt=14): 71 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)| -c_member(A,D,B)|c_member(A,D,C).
% 13.65/13.65 ** KEPT (pick-wt=14): 72 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C).
% 13.65/13.65 ** KEPT (pick-wt=14): 73 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 13.65/13.65 ** KEPT (pick-wt=14): 74 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C).
% 13.65/13.65 ** KEPT (pick-wt=14): 75 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 13.65/13.65 ** KEPT (pick-wt=13): 76 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|C=B|c_Orderings_Oord__class_Oless(A,B,C).
% 13.65/13.65 ** KEPT (pick-wt=13): 77 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,B,C).
% 13.65/13.65 Following clause subsumed by 77 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 13.65/13.65 ** KEPT (pick-wt=13): 78 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 13.65/13.65 Following clause subsumed by 16 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 13.65/13.65 ** KEPT (pick-wt=10): 79 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 13.65/13.65 ** KEPT (pick-wt=10): 80 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 13.65/13.65 Following clause subsumed by 76 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|c_Orderings_Oord__class_Oless(A,C,B).
% 13.65/13.65 Following clause subsumed by 77 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C).
% 13.65/13.65 Following clause subsumed by 78 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C.
% 13.65/13.65 ** KEPT (pick-wt=13): 81 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C.
% 13.65/13.65 ** KEPT (pick-wt=10): 82 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 13.65/13.65 Following clause subsumed by 82 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 13.65/13.65 Following clause subsumed by 77 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 13.65/13.65 ** KEPT (pick-wt=10): 83 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,B,C).
% 13.65/13.65 Following clause subsumed by 58 during input processing: 0 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C.
% 13.65/13.65 Following clause subsumed by 79 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 13.65/13.65 ** KEPT (pick-wt=10): 84 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 13.65/13.65 ** KEPT (pick-wt=14): 85 [] -class_Orderings_Opreorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 13.65/13.65 Following clause subsumed by 83 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 13.65/13.65 Following clause subsumed by 26 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 13.65/13.65 Following clause subsumed by 77 during input processing: 0 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C.
% 13.65/13.65 Following clause subsumed by 82 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 13.65/13.65 Following clause subsumed by 82 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 13.65/13.65 Following clause subsumed by 80 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 13.65/13.65 Following clause subsumed by 82 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 13.65/13.65 Following clause subsumed by 80 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 13.65/13.65 Following clause subsumed by 54 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_member(A,D,B)|c_member(A,D,C).
% 13.65/13.65 Following clause subsumed by 54 during input processing: 0 [] -c_member(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,D)|c_member(A,B,D).
% 13.65/13.65 Following clause subsumed by 54 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_member(A,D,B)|c_member(A,D,C).
% 13.65/13.65 ** KEPT (pick-wt=7): 86 [] -class_Orderings_Otop(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Orderings_Otop__class_Otop(A)).
% 13.65/13.65 ** KEPT (pick-wt=16): 87 [] -class_Complete__Lattice_Ocomplete__lattice(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Complete__Lattice_OSup__class_OSup(A,B),C)| -c_member(A,D,B)|c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 13.65/13.65 ** KEPT (pick-wt=15): 88 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Complete__Lattice_OSup__class_OSup(A,B),C)|c_member(A,$f7(C,B,A),B).
% 13.65/13.65 ** KEPT (pick-wt=15): 89 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Complete__Lattice_OSup__class_OSup(A,B),C)| -c_Orderings_Oord__class_Oless__e_q(A,$f7(C,B,A),C).
% 13.65/13.65 ** KEPT (pick-wt=16): 90 [] -class_Orderings_Oord(A)| -c_Lubs_OleastP(A,B,C)| -c_member(A,D,c_Set_OCollect(A,B))|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 13.65/13.65 ** KEPT (pick-wt=14): 91 [] -class_Orderings_Oord(A)| -c_Lubs_Osetle(A,B,C)| -c_member(A,D,B)|c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 13.65/13.65 ** KEPT (pick-wt=13): 92 [] -class_Orderings_Oord(A)|c_Lubs_Osetle(A,B,C)|c_member(A,$f8(C,B,A),B).
% 13.65/13.65 ** KEPT (pick-wt=13): 93 [] -class_Orderings_Oord(A)|c_Lubs_Osetle(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,$f8(C,B,A),C).
% 13.65/13.65 ** KEPT (pick-wt=14): 94 [] -class_Orderings_Oord(A)| -c_Lubs_Osetge(A,B,C)| -c_member(A,D,C)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.65/13.65 ** KEPT (pick-wt=13): 95 [] -class_Orderings_Oord(A)|c_Lubs_Osetge(A,B,C)|c_member(A,$f9(C,B,A),C).
% 13.65/13.65 ** KEPT (pick-wt=13): 96 [] -class_Orderings_Oord(A)|c_Lubs_Osetge(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,$f9(C,B,A)).
% 13.65/13.65 ** KEPT (pick-wt=12): 97 [] -class_Complete__Lattice_Ocomplete__lattice(A)| -c_member(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Complete__Lattice_OSup__class_OSup(A,C)).
% 13.65/13.65 ** KEPT (pick-wt=15): 98 [] -class_Orderings_Oord(A)| -c_Lubs_OisLub(A,B,C,D)| -c_member(A,E,C)|c_Orderings_Oord__class_Oless__e_q(A,E,D).
% 13.65/13.65 ** KEPT (pick-wt=17): 99 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Lubs_OisUb(A,B,C),D))| -c_member(A,E,C)|c_Orderings_Oord__class_Oless__e_q(A,E,D).
% 13.65/13.65 Following clause subsumed by 91 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Lubs_Osetle(A,B,C)| -c_member(A,D,B)|c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 13.65/13.65 Following clause subsumed by 94 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Lubs_Osetge(A,B,C)| -c_member(A,D,C)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.65/13.65 ** KEPT (pick-wt=15): 100 [] -c_member(A,B,c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),C))|c_member(A,B,$f10(C,B,A)).
% 13.65/13.65 ** KEPT (pick-wt=17): 101 [] -c_member(A,B,c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),C))|c_member(tc_fun(A,tc_HOL_Obool),$f10(C,B,A),C).
% 13.65/13.65 ** KEPT (pick-wt=15): 102 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_member(A,$f11(B,C,A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Complete__Lattice_OSup__class_OSup(A,C),B).
% 13.65/13.65 ** KEPT (pick-wt=15): 103 [] -class_Complete__Lattice_Ocomplete__lattice(A)| -c_Orderings_Oord__class_Oless__e_q(A,$f11(B,C,A),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Complete__Lattice_OSup__class_OSup(A,C),B).
% 13.65/13.65 ** KEPT (pick-wt=19): 104 [] -class_Orderings_Oord(A)|c_member(A,$f12(B,C,A),C)|hBOOL(hAPP(c_Lubs_OisUb(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),C),B)).
% 13.65/13.65 ** KEPT (pick-wt=19): 105 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(A,$f12(B,C,A),B)|hBOOL(hAPP(c_Lubs_OisUb(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),C),B)).
% 13.65/13.65 ** KEPT (pick-wt=11): 106 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|A=B.
% 13.65/13.65 ** KEPT (pick-wt=8): 107 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B).
% 13.65/13.65 ** KEPT (pick-wt=7): 108 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|A!=B.
% 13.65/13.65 Following clause subsumed by 107 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B).
% 13.65/13.65 ** KEPT (pick-wt=7): 109 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|A!=B.
% 13.65/13.65 Following clause subsumed by 106 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|A=B.
% 13.65/13.65 ** KEPT (pick-wt=13): 110 [] -class_Orderings_Oord(A)|c_member(A,$f13(B,C,A),C)|c_Lubs_Osetle(A,C,B).
% 13.65/13.65 ** KEPT (pick-wt=13): 111 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(A,$f13(B,C,A),B)|c_Lubs_Osetle(A,C,B).
% 13.65/13.65 ** KEPT (pick-wt=13): 112 [] -class_Orderings_Oord(A)|c_member(A,$f14(B,C,A),C)|c_Lubs_Osetge(A,B,C).
% 13.65/13.65 ** KEPT (pick-wt=13): 113 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,$f14(B,C,A))|c_Lubs_Osetge(A,B,C).
% 13.65/13.65 ** KEPT (pick-wt=12): 114 [] -class_Complete__Lattice_Ocomplete__lattice(A)| -c_member(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Complete__Lattice_OInf__class_OInf(A,C),B).
% 13.65/13.65 ** KEPT (pick-wt=19): 115 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),$f15(B,C,A),B)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),C),B).
% 13.65/13.65 ** KEPT (pick-wt=15): 116 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,B)|B=C.
% 13.65/13.65 ** KEPT (pick-wt=18): 117 [] -c_member(A,B,c_Complete__Lattice_OInf__class_OInf(tc_fun(A,tc_HOL_Obool),C))| -c_member(tc_fun(A,tc_HOL_Obool),D,C)|c_member(A,B,D).
% 13.65/13.65 Following clause subsumed by 117 during input processing: 0 [] -c_member(A,B,c_Complete__Lattice_OInf__class_OInf(tc_fun(A,tc_HOL_Obool),C))| -c_member(tc_fun(A,tc_HOL_Obool),D,C)|c_member(A,B,D).
% 13.65/13.65 ** KEPT (pick-wt=14): 118 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_member(tc_fun(A,tc_HOL_Obool),B,c_Set_OPow(A,C)).
% 13.65/13.65 ** KEPT (pick-wt=12): 119 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C).
% 13.65/13.65 ** KEPT (pick-wt=9): 120 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)|B!=C.
% 13.65/13.65 ** KEPT (pick-wt=15): 121 [] c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|B=C.
% 13.65/13.65 ** KEPT (pick-wt=14): 122 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D).
% 13.65/13.65 ** KEPT (pick-wt=14): 123 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D,C).
% 13.65/13.65 ** KEPT (pick-wt=20): 124 [] -class_Orderings_Oord(A)|c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D,C).
% 13.65/13.65 ** KEPT (pick-wt=9): 125 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,B).
% 13.65/13.65 ** KEPT (pick-wt=9): 126 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),B,A).
% 13.65/13.65 Following clause subsumed by 116 during input processing: 0 [] A=B| -c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),B,A).
% 13.65/13.65 Following clause subsumed by 121 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)|B=C.
% 13.65/13.65 Following clause subsumed by 119 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C).
% 13.65/13.65 Following clause subsumed by 125 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|B!=C.
% 13.65/13.65 ** KEPT (pick-wt=14): 127 [] -hBOOL(hAPP(A,B))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,D)|hBOOL(hAPP(D,B)).
% 13.65/13.65 Following clause subsumed by 125 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,B).
% 13.65/13.65 Following clause subsumed by 126 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),B,A).
% 13.65/13.65 Following clause subsumed by 119 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C).
% 13.65/13.65 ** KEPT (pick-wt=18): 128 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_Set_OPow(A,B),c_Set_OPow(A,C)).
% 13.65/13.65 ** KEPT (pick-wt=22): 129 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Complete__Lattice_OInf__class_OInf(tc_fun(A,tc_HOL_Obool),C),c_Complete__Lattice_OInf__class_OInf(tc_fun(A,tc_HOL_Obool),B)).
% 13.65/13.65 Following clause subsumed by 127 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -hBOOL(hAPP(B,D))|hBOOL(hAPP(C,D)).
% 13.65/13.65 ** KEPT (pick-wt=18): 130 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),C,D)|c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,D).
% 13.65/13.65 ** KEPT (pick-wt=18): 131 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,D)|c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,D).
% 13.65/13.65 ** KEPT (pick-wt=18): 132 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),C,D)|c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,D).
% 13.65/13.65 ** KEPT (pick-wt=18): 133 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,D).
% 13.65/13.65 Following clause subsumed by 125 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,B).
% 13.65/13.65 Following clause subsumed by 126 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),B,A).
% 13.65/13.65 ** KEPT (pick-wt=11): 134 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,A)|A=B.
% 13.65/13.65 ** KEPT (pick-wt=12): 135 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,C).
% 13.65/13.65 ** KEPT (pick-wt=16): 136 [] -c_member(tc_fun(A,tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Complete__Lattice_OInf__class_OInf(tc_fun(A,tc_HOL_Obool),C),B).
% 13.65/13.65 ** KEPT (pick-wt=14): 137 [] -c_member(tc_fun(A,tc_HOL_Obool),B,c_Set_OPow(A,C))|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C).
% 13.65/13.65 Following clause subsumed by 137 during input processing: 0 [] -c_member(tc_fun(A,tc_HOL_Obool),B,c_Set_OPow(A,C))|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C).
% 13.65/13.65 Following clause subsumed by 118 during input processing: 0 [] c_member(tc_fun(A,tc_HOL_Obool),B,c_Set_OPow(A,C))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C).
% 13.65/13.65 ** KEPT (pick-wt=16): 138 [] -class_Complete__Lattice_Ocomplete__lattice(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Complete__Lattice_OInf__class_OInf(A,C))| -c_member(A,D,C)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.65/13.65 ** KEPT (pick-wt=15): 139 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Complete__Lattice_OInf__class_OInf(A,C))|c_member(A,$f16(C,B,A),C).
% 13.65/13.65 ** KEPT (pick-wt=15): 140 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Complete__Lattice_OInf__class_OInf(A,C))| -c_Orderings_Oord__class_Oless__e_q(A,B,$f16(C,B,A)).
% 13.65/13.65 ** KEPT (pick-wt=17): 141 [] -class_Complete__Lattice_Ocomplete__lattice(A)| -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,c_Complete__Lattice_OInf__class_OInf(A,B),C)|c_member(A,$f17(C,B,A),B).
% 13.65/13.65 ** KEPT (pick-wt=17): 142 [] -class_Complete__Lattice_Ocomplete__lattice(A)| -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,c_Complete__Lattice_OInf__class_OInf(A,B),C)|c_Orderings_Oord__class_Oless(A,$f17(C,B,A),C).
% 13.65/13.65 ** KEPT (pick-wt=18): 143 [] -class_Complete__Lattice_Ocomplete__lattice(A)| -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,c_Complete__Lattice_OInf__class_OInf(A,B),C)| -c_member(A,D,B)| -c_Orderings_Oord__class_Oless(A,D,C).
% 13.65/13.65 ** KEPT (pick-wt=18): 144 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool),c_Predicate_OPowp(A,B),c_Predicate_OPowp(A,C)).
% 13.65/13.65 ** KEPT (pick-wt=15): 145 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_member(A,$f18(B,C,A),C)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Complete__Lattice_OInf__class_OInf(A,C)).
% 13.65/13.65 ** KEPT (pick-wt=15): 146 [] -class_Complete__Lattice_Ocomplete__lattice(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,$f18(B,C,A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Complete__Lattice_OInf__class_OInf(A,C)).
% 13.65/13.65 ** KEPT (pick-wt=17): 147 [] -class_Orderings_Oorder(A)| -c_SEQ_Odecse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,D),hAPP(B,C)).
% 13.65/13.65 ** KEPT (pick-wt=13): 148 [] -class_Orderings_Oorder(A)|c_SEQ_Odecse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f20(B,A),$f19(B,A)).
% 13.65/13.65 ** KEPT (pick-wt=17): 149 [] -class_Orderings_Oorder(A)|c_SEQ_Odecse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f19(B,A)),hAPP(B,$f20(B,A))).
% 13.65/13.65 ** KEPT (pick-wt=15): 150 [] -c_member(A,B,$f21(B,C,A))|c_member(A,B,c_Complete__Lattice_OInf__class_OInf(tc_fun(A,tc_HOL_Obool),C)).
% 13.65/13.65 ** KEPT (pick-wt=13): 151 [] -c_member(A,$f22(B,C,A),B)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,B).
% 13.65/13.65 ** KEPT (pick-wt=11): 152 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_Complete__Lattice_OInf__class_OInf(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(A).
% 13.65/13.65 ** KEPT (pick-wt=17): 153 [] -class_Orderings_Oorder(A)| -c_SEQ_Oincse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,C),hAPP(B,D)).
% 13.65/13.65 ** KEPT (pick-wt=13): 154 [] -class_Orderings_Oorder(A)|c_SEQ_Oincse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f24(B,A),$f23(B,A)).
% 13.65/13.65 ** KEPT (pick-wt=17): 155 [] -class_Orderings_Oorder(A)|c_SEQ_Oincse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f24(B,A)),hAPP(B,$f23(B,A))).
% 13.65/13.65 ** KEPT (pick-wt=20): 156 [] -class_Complete__Lattice_Ocomplete__lattice(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,tc_HOL_Obool),C,D)|c_Orderings_Oord__class_Oless__e_q(A,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(B,A,C,E),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(B,A,D,E)).
% 13.65/13.65 ** KEPT (pick-wt=20): 157 [] -class_Complete__Lattice_Ocomplete__lattice(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,tc_HOL_Obool),C,D)|c_Orderings_Oord__class_Oless__e_q(A,c_Complete__Lattice_Ocomplete__lattice__class_OINFI(B,A,D,E),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(B,A,C,E)).
% 13.65/13.65 ** KEPT (pick-wt=7): 158 [] -c_member(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 13.65/13.65 ** KEPT (pick-wt=11): 159 [] -class_Orderings_Obot(A)|hAPP(c_Orderings_Obot__class_Obot(tc_fun(B,A)),C)=c_Orderings_Obot__class_Obot(A).
% 13.65/13.65 ** KEPT (pick-wt=11): 160 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_Complete__Lattice_OSup__class_OSup(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(A).
% 13.65/13.65 ** KEPT (pick-wt=10): 161 [] A!=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))| -c_member(B,C,A).
% 13.65/13.65 Following clause subsumed by 158 during input processing: 0 [] -c_member(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 13.65/13.65 Following clause subsumed by 161 during input processing: 0 [] -c_member(A,B,C)|C!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 13.65/13.65 Following clause subsumed by 161 during input processing: 0 [] -c_member(A,B,C)|C!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 13.74/13.65 ** KEPT (pick-wt=12): 162 [] c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))!=c_Set_OCollect(A,B)| -hBOOL(hAPP(B,C)).
% 13.74/13.65 ** KEPT (pick-wt=12): 163 [] c_Set_OCollect(A,B)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))| -hBOOL(hAPP(B,C)).
% 13.74/13.65 ** KEPT (pick-wt=9): 164 [] c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 13.74/13.65 ** KEPT (pick-wt=15): 165 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))|B=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 13.74/13.65 Following clause subsumed by 125 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))|B!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 13.74/13.65 ** KEPT (pick-wt=10): 166 [] c_Set_OPow(A,B)!=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool)).
% 13.74/13.65 ** KEPT (pick-wt=9): 167 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 13.74/13.65 ** KEPT (pick-wt=7): 168 [] -class_Orderings_Obot(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Orderings_Obot__class_Obot(A),B).
% 13.74/13.65 ** KEPT (pick-wt=11): 170 [copy,169,flip.2] -class_Complete__Lattice_Ocomplete__lattice(A)|c_Orderings_Otop__class_Otop(A)=c_Complete__Lattice_OInf__class_OInf(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 13.74/13.65 ** KEPT (pick-wt=27): 171 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),$f29(B,C,A),B)|C=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool))|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Complete__Lattice_OInf__class_OInf(tc_fun(A,tc_HOL_Obool),C),B).
% 13.74/13.65 ** KEPT (pick-wt=19): 172 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,$f30(B,C,A))|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Complete__Lattice_OInf__class_OInf(tc_fun(A,tc_HOL_Obool),C)).
% 13.74/13.65 ** KEPT (pick-wt=29): 173 [] -class_Orderings_Oorder(A)| -c_SEQ_Omonose_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,C),hAPP(B,D))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,E,F)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,F),hAPP(B,E)).
% 13.74/13.65 ** KEPT (pick-wt=13): 174 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f32(B,A),$f31(B,A)).
% 13.74/13.65 ** KEPT (pick-wt=17): 175 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f32(B,A)),hAPP(B,$f31(B,A))).
% 13.74/13.65 ** KEPT (pick-wt=13): 176 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f34(B,A),$f33(B,A)).
% 13.74/13.65 ** KEPT (pick-wt=17): 177 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f33(B,A)),hAPP(B,$f34(B,A))).
% 13.74/13.65 ** KEPT (pick-wt=8): 178 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 13.74/13.65 ** KEPT (pick-wt=7): 179 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 13.74/13.65 ** KEPT (pick-wt=11): 180 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B.
% 13.74/13.65 Following clause subsumed by 180 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B.
% 13.74/13.65 Following clause subsumed by 178 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 13.74/13.65 ** KEPT (pick-wt=7): 181 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A!=B.
% 13.74/13.65 Following clause subsumed by 178 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 13.74/13.65 Following clause subsumed by 178 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 13.74/13.65 Following clause subsumed by 180 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 13.74/13.65 ** KEPT (pick-wt=4): 182 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 13.74/13.65 Following clause subsumed by 179 during input processing: 0 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 13.74/13.65 ** KEPT (pick-wt=7): 183 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 13.74/13.65 Following clause subsumed by 182 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 13.74/13.65 Following clause subsumed by 183 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=A.
% 13.74/13.65 Following clause subsumed by 179 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 13.74/13.65 ** KEPT (pick-wt=8): 184 [] -class_Orderings_Oorder(A)| -c_SEQ_Oincse_q(A,B)|c_SEQ_Omonose_q(A,B).
% 13.74/13.65 ** KEPT (pick-wt=8): 185 [] -class_Orderings_Oorder(A)| -c_SEQ_Odecse_q(A,B)|c_SEQ_Omonose_q(A,B).
% 13.74/13.65 Following clause subsumed by 181 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 13.74/13.65 ** KEPT (pick-wt=12): 186 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 13.74/13.65 ** KEPT (pick-wt=11): 187 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,A)|A=B.
% 13.74/13.65 Following clause subsumed by 178 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 13.74/13.65 Following clause subsumed by 181 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 13.74/13.65 ** KEPT (pick-wt=13): 188 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f36(B,A),$f35(B,A))|c_SEQ_Omonose_q(A,B).
% 13.74/13.65 ** KEPT (pick-wt=17): 189 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f36(B,A)),hAPP(B,$f35(B,A)))|c_SEQ_Omonose_q(A,B).
% 13.74/13.65 ** KEPT (pick-wt=13): 190 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f38(B,A),$f37(B,A))|c_SEQ_Omonose_q(A,B).
% 13.74/13.65 ** KEPT (pick-wt=17): 191 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f37(B,A)),hAPP(B,$f38(B,A)))|c_SEQ_Omonose_q(A,B).
% 13.74/13.65 ** KEPT (pick-wt=10): 192 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),c_RComplete_Onatceiling(B)).
% 13.74/13.65 ** KEPT (pick-wt=17): 193 [] -hBOOL(hAPP(A,$f39(B,A,C)))|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,tc_HOL_Obool),c_Set_OCollect(B,C),c_Set_OCollect(B,A)).
% 13.74/13.65 ** KEPT (pick-wt=22): 194 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f41(A,B,C),$f40(A,B,C))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(C,B),hAPP(C,A)).
% 13.74/13.65 ** KEPT (pick-wt=26): 195 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,$f41(B,C,A)),hAPP(A,$f40(B,C,A)))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(A,C),hAPP(A,B)).
% 13.74/13.65 ** KEPT (pick-wt=12): 196 [] -c_member(A,$f42(B,A),B)|c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))=B.
% 13.74/13.65 ** KEPT (pick-wt=11): 197 [] -c_member(A,B,C)|c_member(A,B,c_Set_Oinsert(A,D,C)).
% 13.74/13.65 ** KEPT (pick-wt=10): 198 [] A!=B|c_member(C,A,c_Set_Oinsert(C,B,D)).
% 13.74/13.65 ** KEPT (pick-wt=14): 199 [] -c_member(A,B,c_Set_Oinsert(A,C,D))|B=C|c_member(A,B,D).
% 13.74/13.65 ** KEPT (pick-wt=14): 200 [] -hBOOL(hAPP(c_Set_Oinsert(A,B,C),D))|B=D|hBOOL(hAPP(C,D)).
% 13.74/13.65 ** KEPT (pick-wt=10): 201 [] hBOOL(hAPP(c_Set_Oinsert(A,B,C),D))|B!=D.
% 13.74/13.65 ** KEPT (pick-wt=11): 202 [] hBOOL(hAPP(c_Set_Oinsert(A,B,C),D))| -hBOOL(hAPP(C,D)).
% 13.74/13.65 ** KEPT (pick-wt=10): 203 [] -c_member(A,B,C)|c_Set_Oinsert(A,B,C)=C.
% 13.74/13.65 Following clause subsumed by 197 during input processing: 0 [] -c_member(A,B,C)|c_member(A,B,c_Set_Oinsert(A,D,C)).
% 13.74/13.65 ** KEPT (pick-wt=20): 204 [] c_member(A,B,C)|c_member(A,B,D)|c_Set_Oinsert(A,B,C)!=c_Set_Oinsert(A,B,D)|C=D.
% 13.74/13.65 ** KEPT (pick-wt=20): 205 [] c_member(A,B,C)|c_member(A,B,D)|c_Set_Oinsert(A,B,C)=c_Set_Oinsert(A,B,D)|C!=D.
% 13.74/13.65 Following clause subsumed by 199 during input processing: 0 [] -c_member(A,B,c_Set_Oinsert(A,C,D))|B=C|c_member(A,B,D).
% 13.74/13.65 Following clause subsumed by 198 during input processing: 0 [] c_member(A,B,c_Set_Oinsert(A,C,D))|B!=C.
% 13.74/13.65 Following clause subsumed by 197 during input processing: 0 [] c_member(A,B,c_Set_Oinsert(A,C,D))| -c_member(A,B,D).
% 13.74/13.65 ** KEPT (pick-wt=18): 206 [] c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))!=c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))|B=C.
% 13.74/13.65 ** KEPT (pick-wt=27): 207 [] c_Set_Oinsert(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))!=c_Set_Oinsert(A,D,c_Set_Oinsert(A,E,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B=D|B=E.
% 13.74/13.65 ** KEPT (pick-wt=27): 208 [] c_Set_Oinsert(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))!=c_Set_Oinsert(A,D,c_Set_Oinsert(A,E,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B=D|C=D.
% 13.74/13.65 ** KEPT (pick-wt=27): 209 [] c_Set_Oinsert(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))!=c_Set_Oinsert(A,D,c_Set_Oinsert(A,E,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|C=E|B=E.
% 13.74/13.65 ** KEPT (pick-wt=27): 210 [] c_Set_Oinsert(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))!=c_Set_Oinsert(A,D,c_Set_Oinsert(A,E,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|C=E|C=D.
% 13.74/13.65 ** KEPT (pick-wt=27): 211 [] c_Set_Oinsert(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))=c_Set_Oinsert(A,D,c_Set_Oinsert(A,E,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B!=D|C!=E.
% 13.74/13.65 ** KEPT (pick-wt=27): 212 [] c_Set_Oinsert(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))=c_Set_Oinsert(A,D,c_Set_Oinsert(A,E,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B!=E|C!=D.
% 13.74/13.65 ** KEPT (pick-wt=9): 213 [] c_Set_Oinsert(A,B,C)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 13.74/13.65 ** KEPT (pick-wt=9): 214 [] c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))!=c_Set_Oinsert(A,B,C).
% 13.74/13.65 ** KEPT (pick-wt=18): 215 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,D,B),c_Set_Oinsert(A,D,C)).
% 13.74/13.65 ** KEPT (pick-wt=15): 216 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,D,C)).
% 13.74/13.65 ** KEPT (pick-wt=13): 217 [] -c_member(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B=C.
% 13.74/13.65 Following clause subsumed by 198 during input processing: 0 [] c_member(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B!=C.
% 13.74/13.65 Following clause subsumed by 217 during input processing: 0 [] -c_member(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B=C.
% 13.74/13.65 ** KEPT (pick-wt=19): 218 [] c_member(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,c_Set_Oinsert(A,B,D))|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,D).
% 13.74/13.65 Following clause subsumed by 216 during input processing: 0 [] c_member(A,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,c_Set_Oinsert(A,B,D))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,D).
% 13.74/13.65 ** KEPT (pick-wt=13): 219 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,B,C),D)|c_member(A,B,D).
% 13.74/13.65 ** KEPT (pick-wt=15): 220 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,B,C),D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,D).
% 13.74/13.65 ** KEPT (pick-wt=19): 221 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,B,C),D)| -c_member(A,B,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,D).
% 13.74/13.65 ** KEPT (pick-wt=27): 222 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|B=c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 13.74/13.65 ** KEPT (pick-wt=13): 223 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_Complete__Lattice_OSup__class_OSup(A,c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))=B.
% 13.74/13.65 ** KEPT (pick-wt=13): 224 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_Complete__Lattice_OInf__class_OInf(A,c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))=B.
% 13.74/13.65 ** KEPT (pick-wt=19): 225 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,D))| -c_member(A,C,D)|c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,D).
% 13.74/13.65 ** KEPT (pick-wt=34): 226 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,D))|c_member(A,C,D)| -c_member(A,C,B)|c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))),D).
% 13.74/13.65 ** KEPT (pick-wt=23): 227 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,D))|c_member(A,C,D)|c_member(A,C,B)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,D).
% 13.74/13.65 ** KEPT (pick-wt=23): 228 [] c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,D))|c_member(A,C,D)|c_member(A,C,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,D).
% 13.74/13.65 ** KEPT (pick-wt=34): 229 [] c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,D))|c_member(A,C,D)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))),D)| -c_member(A,C,B).
% 13.74/13.65 ** KEPT (pick-wt=36): 230 [] c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,D))|c_member(A,C,D)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))),D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,D).
% 13.74/13.65 ** KEPT (pick-wt=19): 231 [] c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,D))| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,D)| -c_member(A,C,D).
% 13.74/13.65 ** KEPT (pick-wt=25): 232 [] c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,D))| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,D)|c_member(A,C,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,D).
% 13.74/13.65 ** KEPT (pick-wt=36): 233 [] c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,D))| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,D)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))),D)| -c_member(A,C,B).
% 13.74/13.65 ** KEPT (pick-wt=38): 234 [] c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,D))| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,D)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))),D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,D).
% 13.74/13.65 ** KEPT (pick-wt=30): 235 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,D))| -c_member(A,C,B)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))),D).
% 13.74/13.65 Following clause subsumed by 218 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,D))|c_member(A,C,B)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,D).
% 13.74/13.65 Following clause subsumed by 216 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,D))|c_member(A,C,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,D).
% 13.74/13.65 ** KEPT (pick-wt=30): 236 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,D))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))),D)| -c_member(A,C,B).
% 13.74/13.66 Following clause subsumed by 216 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,D))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))),D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,D).
% 13.74/13.66 Following clause subsumed by 236 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))),D)| -c_member(A,C,B)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,D)).
% 13.74/13.66 ** KEPT (pick-wt=11): 237 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),B).
% 13.74/13.66 ** KEPT (pick-wt=13): 238 [] -hBOOL(hAPP(A,B))|hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(C,tc_HOL_Obool),D,A),B)).
% 13.74/13.66 ** KEPT (pick-wt=13): 239 [] -hBOOL(hAPP(A,B))|hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(C,tc_HOL_Obool),A,D),B)).
% 13.74/13.66 ** KEPT (pick-wt=17): 240 [] -hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),B,C),D))|hBOOL(hAPP(B,D))|hBOOL(hAPP(C,D)).
% 13.74/13.66 ** KEPT (pick-wt=13): 241 [] -hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,C),D))|hBOOL(hAPP(B,D)).
% 13.74/13.66 ** KEPT (pick-wt=13): 242 [] -hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,C),D))|hBOOL(hAPP(C,D)).
% 13.74/13.66 ** KEPT (pick-wt=17): 243 [] -hBOOL(hAPP(A,B))| -hBOOL(hAPP(C,B))|hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(D,tc_HOL_Obool),A,C),B)).
% 13.74/13.66 ** KEPT (pick-wt=17): 244 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))|c_member(A,B,C)|c_member(A,B,D).
% 13.74/13.66 ** KEPT (pick-wt=13): 245 [] -c_member(A,B,C)|c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),D,C)).
% 13.74/13.66 ** KEPT (pick-wt=13): 246 [] -c_member(A,B,C)|c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D)).
% 13.74/13.66 ** KEPT (pick-wt=17): 247 [] -c_member(A,B,C)| -c_member(A,B,D)|c_member(A,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,D)).
% 13.74/13.66 ** KEPT (pick-wt=13): 248 [] -c_member(A,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,D))|c_member(A,B,C).
% 13.74/13.66 ** KEPT (pick-wt=13): 249 [] -c_member(A,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,D))|c_member(A,B,D).
% 13.74/13.66 ** KEPT (pick-wt=17): 250 [] -c_member(A,B,C)|c_member(A,B,D)|c_member(A,B,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),C,D)).
% 13.74/13.66 ** KEPT (pick-wt=13): 251 [] -c_member(A,B,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),C,D))|c_member(A,B,C).
% 13.74/13.66 ** KEPT (pick-wt=13): 252 [] -c_member(A,B,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),C,D))| -c_member(A,B,D).
% 13.74/13.66 ** KEPT (pick-wt=22): 253 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),B,C),D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D)).
% 13.74/13.66 ** KEPT (pick-wt=22): 254 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),B,C),D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D)).
% 13.74/13.66 ** KEPT (pick-wt=29): 255 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,C),D)!=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),D,B).
% 13.74/13.66 ** KEPT (pick-wt=29): 256 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,C),D)=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),D,B).
% 13.74/13.66 ** KEPT (pick-wt=19): 257 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),B,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),C,B))=C.
% 13.74/13.66 Following clause subsumed by 242 during input processing: 0 [] -hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,C),D))|hBOOL(hAPP(C,D)).
% 13.74/13.66 Following clause subsumed by 241 during input processing: 0 [] -hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,C),D))|hBOOL(hAPP(B,D)).
% 13.74/13.66 Following clause subsumed by 238 during input processing: 0 [] -hBOOL(hAPP(A,B))|hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(C,tc_HOL_Obool),D,A),B)).
% 13.74/13.66 Following clause subsumed by 239 during input processing: 0 [] -hBOOL(hAPP(A,B))|hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(C,tc_HOL_Obool),A,D),B)).
% 13.74/13.66 ** KEPT (pick-wt=21): 258 [] c_member(A,$f43(B,C,D,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),D,C))| -c_member(A,E,D)|hBOOL(hAPP(B,E)).
% 13.74/13.66 ** KEPT (pick-wt=21): 259 [] c_member(A,$f43(B,C,D,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),D,C))| -c_member(A,E,C)|hBOOL(hAPP(B,E)).
% 13.74/13.66 ** KEPT (pick-wt=16): 260 [] -hBOOL(hAPP(A,$f43(A,B,C,D)))| -c_member(D,E,C)|hBOOL(hAPP(A,E)).
% 13.74/13.66 ** KEPT (pick-wt=16): 261 [] -hBOOL(hAPP(A,$f43(A,B,C,D)))| -c_member(D,E,B)|hBOOL(hAPP(A,E)).
% 13.74/13.66 ** KEPT (pick-wt=29): 262 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))|hBOOL(hAPP(E,B))|c_member(A,$f44(E,D,C,A),C)|c_member(A,$f45(E,D,C,A),D).
% 13.74/13.66 ** KEPT (pick-wt=29): 263 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))|hBOOL(hAPP(E,B))|c_member(A,$f44(E,D,C,A),C)| -hBOOL(hAPP(E,$f45(E,D,C,A))).
% 13.74/13.66 ** KEPT (pick-wt=29): 264 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))|hBOOL(hAPP(E,B))| -hBOOL(hAPP(E,$f44(E,D,C,A)))|c_member(A,$f45(E,D,C,A),D).
% 13.74/13.66 ** KEPT (pick-wt=29): 265 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))|hBOOL(hAPP(E,B))| -hBOOL(hAPP(E,$f44(E,D,C,A)))| -hBOOL(hAPP(E,$f45(E,D,C,A))).
% 13.74/13.66 ** KEPT (pick-wt=29): 266 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))| -hBOOL(hAPP(E,B))|c_member(A,$f46(E,D,C,A),C)|c_member(A,$f47(E,D,C,A),D).
% 13.74/13.66 ** KEPT (pick-wt=29): 267 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))| -hBOOL(hAPP(E,B))|c_member(A,$f46(E,D,C,A),C)|hBOOL(hAPP(E,$f47(E,D,C,A))).
% 13.74/13.66 ** KEPT (pick-wt=29): 268 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))| -hBOOL(hAPP(E,B))|hBOOL(hAPP(E,$f46(E,D,C,A)))|c_member(A,$f47(E,D,C,A),D).
% 13.74/13.66 ** KEPT (pick-wt=29): 269 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))| -hBOOL(hAPP(E,B))|hBOOL(hAPP(E,$f46(E,D,C,A)))|hBOOL(hAPP(E,$f47(E,D,C,A))).
% 13.74/13.66 ** KEPT (pick-wt=21): 270 [] c_member(A,$f48(B,C,D,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),D,C))| -c_member(A,E,D)| -hBOOL(hAPP(B,E)).
% 13.74/13.66 ** KEPT (pick-wt=21): 271 [] c_member(A,$f48(B,C,D,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),D,C))| -c_member(A,E,C)| -hBOOL(hAPP(B,E)).
% 13.74/13.66 ** KEPT (pick-wt=16): 272 [] hBOOL(hAPP(A,$f48(A,B,C,D)))| -c_member(D,E,C)| -hBOOL(hAPP(A,E)).
% 13.74/13.66 ** KEPT (pick-wt=16): 273 [] hBOOL(hAPP(A,$f48(A,B,C,D)))| -c_member(D,E,B)| -hBOOL(hAPP(A,E)).
% 13.74/13.66 ** KEPT (pick-wt=10): 274 [] c_RealDef_Oreal(tc_Nat_Onat,A)!=c_RealDef_Oreal(tc_Nat_Onat,B)|A=B.
% 13.74/13.66 ** KEPT (pick-wt=10): 275 [] c_RealDef_Oreal(tc_Nat_Onat,A)=c_RealDef_Oreal(tc_Nat_Onat,B)|A!=B.
% 13.74/13.66 ** KEPT (pick-wt=19): 276 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,C)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),B,C)=B.
% 13.74/13.66 Following clause subsumed by 244 during input processing: 0 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))|c_member(A,B,C)|c_member(A,B,D).
% 13.74/13.66 Following clause subsumed by 246 during input processing: 0 [] c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))| -c_member(A,B,C).
% 13.74/13.66 Following clause subsumed by 245 during input processing: 0 [] c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))| -c_member(A,B,D).
% 13.74/13.66 Following clause subsumed by 246 during input processing: 0 [] -c_member(A,B,C)|c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D)).
% 13.74/13.66 Following clause subsumed by 245 during input processing: 0 [] -c_member(A,B,C)|c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),D,C)).
% 13.74/13.66 Following clause subsumed by 248 during input processing: 0 [] -c_member(A,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,D))|c_member(A,B,C).
% 13.74/13.66 Following clause subsumed by 249 during input processing: 0 [] -c_member(A,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,D))|c_member(A,B,D).
% 13.74/13.66 Following clause subsumed by 247 during input processing: 0 [] c_member(A,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,D))| -c_member(A,B,C)| -c_member(A,B,D).
% 13.74/13.66 Following clause subsumed by 248 during input processing: 0 [] -c_member(A,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,D))|c_member(A,B,C).
% 13.74/13.66 Following clause subsumed by 249 during input processing: 0 [] -c_member(A,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,D))|c_member(A,B,D).
% 13.74/13.66 Following clause subsumed by 251 during input processing: 0 [] -c_member(A,B,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),C,D))|c_member(A,B,C).
% 13.74/13.66 Following clause subsumed by 252 during input processing: 0 [] -c_member(A,B,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),C,D))| -c_member(A,B,D).
% 13.74/13.66 Following clause subsumed by 250 during input processing: 0 [] c_member(A,B,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),C,D))| -c_member(A,B,C)|c_member(A,B,D).
% 13.74/13.66 Following clause subsumed by 251 during input processing: 0 [] -c_member(A,B,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),C,D))|c_member(A,B,C).
% 13.74/13.66 Following clause subsumed by 252 during input processing: 0 [] -c_member(A,B,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),C,D))| -c_member(A,B,D).
% 13.74/13.66 ** KEPT (pick-wt=17): 277 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),B,C)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|B=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 13.74/13.66 ** KEPT (pick-wt=17): 278 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),B,C)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|C=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 13.74/13.66 ** KEPT (pick-wt=23): 279 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),B,C)=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|B!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|C!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 13.74/13.66 ** KEPT (pick-wt=22): 280 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,C)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))| -c_member(A,D,B)| -c_member(A,E,C)|D!=E.
% 13.74/13.66 ** KEPT (pick-wt=14): 281 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),B,C)=C.
% 13.74/13.66 ** KEPT (pick-wt=14): 282 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),B,C)!=C.
% 13.74/13.66 Following clause subsumed by 281 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),B,C)=C.
% 13.74/13.66 ** KEPT (pick-wt=14): 283 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,B)=C.
% 13.74/13.66 ** KEPT (pick-wt=23): 284 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),D,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),B,D),C).
% 13.74/13.66 ** KEPT (pick-wt=28): 285 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),D,E)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),B,D),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,E)).
% 13.74/13.66 ** KEPT (pick-wt=14): 286 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,C)=B.
% 13.74/13.66 ** KEPT (pick-wt=14): 287 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,B)=B.
% 13.74/13.66 ** KEPT (pick-wt=23): 288 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,D)).
% 13.74/13.66 ** KEPT (pick-wt=28): 289 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),D,E)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,D),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,E)).
% 13.74/13.66 ** KEPT (pick-wt=28): 290 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),D,E)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),B,E),c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),C,D)).
% 13.74/13.66 ** KEPT (pick-wt=25): 291 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,D)|c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),C,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),D,B))=B.
% 13.74/13.66 ** KEPT (pick-wt=12): 292 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_RealDef_Oreal(tc_Nat_Onat,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 13.74/13.66 ** KEPT (pick-wt=12): 293 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_RealDef_Oreal(tc_Nat_Onat,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 13.74/13.66 ** KEPT (pick-wt=12): 294 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_RealDef_Oreal(tc_Nat_Onat,B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 13.74/13.66 ** KEPT (pick-wt=12): 295 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_RealDef_Oreal(tc_Nat_Onat,B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 13.74/13.66 ** KEPT (pick-wt=23): 297 [copy,296,flip.2] -c_member(A,B,C)|c_Set_Oinsert(A,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),D,C))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,B,D),C).
% 13.74/13.66 ** KEPT (pick-wt=23): 299 [copy,298,flip.2] -c_member(A,B,C)|c_Set_Oinsert(A,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,D))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,c_Set_Oinsert(A,B,D)).
% 13.74/13.66 Following clause subsumed by 297 during input processing: 0 [flip.2] -c_member(A,B,C)|c_Set_Oinsert(A,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),D,C))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,B,D),C).
% 13.74/13.66 Following clause subsumed by 299 during input processing: 0 [flip.2] -c_member(A,B,C)|c_Set_Oinsert(A,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,D))=c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,c_Set_Oinsert(A,B,D)).
% 13.74/13.66 ** KEPT (pick-wt=20): 300 [] -c_member(A,B,C)|c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,B,D),C)=c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),D,C).
% 13.74/13.66 Following clause subsumed by 300 during input processing: 0 [] -c_member(A,B,C)|c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,B,D),C)=c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),D,C).
% 13.74/13.66 ** KEPT (pick-wt=15): 301 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_Complete__Lattice_OSup__class_OSup(A,c_Set_Oinsert(A,B,C))=c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Complete__Lattice_OSup__class_OSup(A,C)).
% 13.74/13.66 ** KEPT (pick-wt=15): 302 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_Complete__Lattice_OInf__class_OInf(A,c_Set_Oinsert(A,B,C))=c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Complete__Lattice_OInf__class_OInf(A,C)).
% 13.74/13.66 ** KEPT (pick-wt=32): 303 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B),C)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))| -c_member(tc_fun(A,tc_HOL_Obool),D,B)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),D,C)=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 13.74/13.66 ** KEPT (pick-wt=29): 304 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),B),C)=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),$f51(C,B,A),C)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 13.74/13.66 ** KEPT (pick-wt=19): 305 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_Complete__Lattice_OSup__class_OSup(A,c_Set_Oinsert(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))=c_Lattices_Osemilattice__sup__class_Osup(A,B,C).
% 13.74/13.66 ** KEPT (pick-wt=19): 306 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_Complete__Lattice_OInf__class_OInf(A,c_Set_Oinsert(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))=c_Lattices_Osemilattice__inf__class_Oinf(A,B,C).
% 13.74/13.66 ** KEPT (pick-wt=21): 307 [] -c_member(A,B,C)|c_Set_Oinsert(A,B,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),C,c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))))=C.
% 13.74/13.66 ** KEPT (pick-wt=21): 308 [] -class_Lattices_Olattice(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__sup__class_Osup(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),c_Lattices_Osemilattice__inf__class_Oinf(A,B,D)),c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D))).
% 13.74/13.66 ** KEPT (pick-wt=21): 309 [] -class_Lattices_Olattice(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)),c_Lattices_Osemilattice__inf__class_Oinf(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),c_Lattices_Osemilattice__sup__class_Osup(A,B,D))).
% 13.74/13.66 ** KEPT (pick-wt=19): 310 [] -class_Lattices_Olattice(A)|hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(B,A),C,D),E)=c_Lattices_Osemilattice__inf__class_Oinf(A,hAPP(C,E),hAPP(D,E)).
% 13.74/13.66 ** KEPT (pick-wt=19): 311 [] -class_Lattices_Olattice(A)|hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D),E)=c_Lattices_Osemilattice__sup__class_Osup(A,hAPP(C,E),hAPP(D,E)).
% 13.74/13.66 ** KEPT (pick-wt=9): 312 [] -class_Lattices_Obounded__lattice__top(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,c_Orderings_Otop__class_Otop(A),B)=B.
% 13.74/13.66 ** KEPT (pick-wt=9): 313 [] -class_Lattices_Obounded__lattice__top(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Orderings_Otop__class_Otop(A))=B.
% 13.74/13.66 ** KEPT (pick-wt=13): 314 [] -class_Lattices_Obounded__lattice__top(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)!=c_Orderings_Otop__class_Otop(A)|B=c_Orderings_Otop__class_Otop(A).
% 13.74/13.66 ** KEPT (pick-wt=13): 315 [] -class_Lattices_Obounded__lattice__top(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)!=c_Orderings_Otop__class_Otop(A)|C=c_Orderings_Otop__class_Otop(A).
% 13.74/13.66 ** KEPT (pick-wt=17): 316 [] -class_Lattices_Obounded__lattice__top(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)=c_Orderings_Otop__class_Otop(A)|B!=c_Orderings_Otop__class_Otop(A)|C!=c_Orderings_Otop__class_Otop(A).
% 13.74/13.66 ** KEPT (pick-wt=17): 317 [] -class_Lattices_Osemilattice__sup(A)|c_Lattices_Osemilattice__sup__class_Osup(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D)=c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)).
% 13.74/13.66 ** KEPT (pick-wt=17): 318 [] -class_Lattices_Olattice(A)|c_Lattices_Osemilattice__sup__class_Osup(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D)=c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)).
% 13.74/13.66 Following clause subsumed by 317 during input processing: 0 [] -class_Lattices_Osemilattice__sup(A)|c_Lattices_Osemilattice__sup__class_Osup(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D)=c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)).
% 13.74/13.66 ** KEPT (pick-wt=17): 319 [] -class_Lattices_Osemilattice__sup(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D))=c_Lattices_Osemilattice__sup__class_Osup(A,C,c_Lattices_Osemilattice__sup__class_Osup(A,B,D)).
% 13.74/13.66 ** KEPT (pick-wt=17): 320 [] -class_Lattices_Olattice(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D))=c_Lattices_Osemilattice__sup__class_Osup(A,C,c_Lattices_Osemilattice__sup__class_Osup(A,B,D)).
% 13.74/13.66 Following clause subsumed by 319 during input processing: 0 [] -class_Lattices_Osemilattice__sup(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D))=c_Lattices_Osemilattice__sup__class_Osup(A,C,c_Lattices_Osemilattice__sup__class_Osup(A,B,D)).
% 13.74/13.66 ** KEPT (pick-wt=14): 321 [] -class_Lattices_Osemilattice__sup(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C))=c_Lattices_Osemilattice__sup__class_Osup(A,B,C).
% 13.74/13.66 ** KEPT (pick-wt=14): 322 [] -class_Lattices_Olattice(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C))=c_Lattices_Osemilattice__sup__class_Osup(A,B,C).
% 13.74/13.66 Following clause subsumed by 321 during input processing: 0 [] -class_Lattices_Osemilattice__sup(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C))=c_Lattices_Osemilattice__sup__class_Osup(A,B,C).
% 13.74/13.66 ** KEPT (pick-wt=11): 323 [] -class_Lattices_Osemilattice__sup(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,C)=c_Lattices_Osemilattice__sup__class_Osup(A,C,B).
% 13.74/13.66 ** KEPT (pick-wt=11): 324 [] -class_Lattices_Olattice(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,C)=c_Lattices_Osemilattice__sup__class_Osup(A,C,B).
% 13.74/13.66 Following clause subsumed by 323 during input processing: 0 [] -class_Lattices_Osemilattice__sup(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,C)=c_Lattices_Osemilattice__sup__class_Osup(A,C,B).
% 13.74/13.66 ** KEPT (pick-wt=8): 325 [] -class_Lattices_Osemilattice__sup(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,B)=B.
% 13.74/13.66 Following clause subsumed by 325 during input processing: 0 [] -class_Lattices_Osemilattice__sup(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,B)=B.
% 13.74/13.66 ** KEPT (pick-wt=17): 326 [] -class_Lattices_Osemilattice__inf(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),D)=c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)).
% 13.74/13.66 ** KEPT (pick-wt=17): 327 [] -class_Lattices_Olattice(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),D)=c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)).
% 13.74/13.66 Following clause subsumed by 326 during input processing: 0 [] -class_Lattices_Osemilattice__inf(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),D)=c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)).
% 13.74/13.66 ** KEPT (pick-wt=17): 328 [] -class_Lattices_Osemilattice__inf(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D))=c_Lattices_Osemilattice__inf__class_Oinf(A,C,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D)).
% 13.74/13.66 ** KEPT (pick-wt=17): 329 [] -class_Lattices_Olattice(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D))=c_Lattices_Osemilattice__inf__class_Oinf(A,C,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D)).
% 13.74/13.66 Following clause subsumed by 328 during input processing: 0 [] -class_Lattices_Osemilattice__inf(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D))=c_Lattices_Osemilattice__inf__class_Oinf(A,C,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D)).
% 13.74/13.66 ** KEPT (pick-wt=14): 330 [] -class_Lattices_Osemilattice__inf(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C))=c_Lattices_Osemilattice__inf__class_Oinf(A,B,C).
% 13.74/13.66 ** KEPT (pick-wt=14): 331 [] -class_Lattices_Olattice(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C))=c_Lattices_Osemilattice__inf__class_Oinf(A,B,C).
% 13.74/13.66 Following clause subsumed by 330 during input processing: 0 [] -class_Lattices_Osemilattice__inf(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C))=c_Lattices_Osemilattice__inf__class_Oinf(A,B,C).
% 13.74/13.66 ** KEPT (pick-wt=11): 332 [] -class_Lattices_Osemilattice__inf(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)=c_Lattices_Osemilattice__inf__class_Oinf(A,C,B).
% 13.74/13.66 ** KEPT (pick-wt=11): 333 [] -class_Lattices_Olattice(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)=c_Lattices_Osemilattice__inf__class_Oinf(A,C,B).
% 13.74/13.66 Following clause subsumed by 332 during input processing: 0 [] -class_Lattices_Osemilattice__inf(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)=c_Lattices_Osemilattice__inf__class_Oinf(A,C,B).
% 13.74/13.66 ** KEPT (pick-wt=8): 334 [] -class_Lattices_Osemilattice__inf(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,B)=B.
% 13.74/13.66 Following clause subsumed by 334 during input processing: 0 [] -class_Lattices_Osemilattice__inf(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,B)=B.
% 13.74/13.66 ** KEPT (pick-wt=13): 335 [] -class_Lattices_Osemilattice__sup(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.74/13.66 ** KEPT (pick-wt=13): 336 [] -class_Lattices_Osemilattice__sup(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D)|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 13.74/13.66 ** KEPT (pick-wt=20): 337 [] -class_Lattices_Osemilattice__sup(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)|c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,D),c_Lattices_Osemilattice__sup__class_Osup(A,C,E)).
% 13.74/13.66 ** KEPT (pick-wt=17): 338 [] -class_Lattices_Osemilattice__sup(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,D),C).
% 13.74/13.66 Following clause subsumed by 338 during input processing: 0 [] -class_Lattices_Osemilattice__sup(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,D),C).
% 13.74/13.66 ** KEPT (pick-wt=12): 339 [] -class_Lattices_Osemilattice__sup(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Lattices_Osemilattice__sup__class_Osup(A,C,B)=C.
% 13.74/13.66 ** KEPT (pick-wt=12): 340 [] -class_Lattices_Osemilattice__sup(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Lattices_Osemilattice__sup__class_Osup(A,B,C)=C.
% 13.74/13.66 ** KEPT (pick-wt=13): 341 [] -class_Lattices_Osemilattice__sup(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,D,C)).
% 13.74/13.66 ** KEPT (pick-wt=13): 342 [] -class_Lattices_Osemilattice__sup(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)).
% 13.74/13.66 Following clause subsumed by 335 during input processing: 0 [] -class_Lattices_Osemilattice__sup(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.74/13.66 Following clause subsumed by 336 during input processing: 0 [] -class_Lattices_Osemilattice__sup(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D)|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 13.74/13.66 Following clause subsumed by 338 during input processing: 0 [] -class_Lattices_Osemilattice__sup(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),D)| -c_Orderings_Oord__class_Oless__e_q(A,B,D)| -c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 13.74/13.66 Following clause subsumed by 340 during input processing: 0 [] -class_Lattices_Osemilattice__sup(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Lattices_Osemilattice__sup__class_Osup(A,B,C)=C.
% 13.74/13.66 ** KEPT (pick-wt=12): 343 [] -class_Lattices_Osemilattice__sup(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Lattices_Osemilattice__sup__class_Osup(A,B,C)!=C.
% 13.74/13.66 ** KEPT (pick-wt=9): 344 [] -class_Lattices_Osemilattice__sup(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,B)).
% 13.74/13.66 ** KEPT (pick-wt=9): 345 [] -class_Lattices_Olattice(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,B)).
% 13.74/13.66 ** KEPT (pick-wt=9): 346 [] -class_Lattices_Osemilattice__sup(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C)).
% 13.74/13.66 ** KEPT (pick-wt=9): 347 [] -class_Lattices_Olattice(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C)).
% 13.74/13.66 ** KEPT (pick-wt=13): 348 [] -class_Lattices_Osemilattice__inf(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D))|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 13.74/13.66 ** KEPT (pick-wt=13): 349 [] -class_Lattices_Osemilattice__inf(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D))|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.74/13.66 ** KEPT (pick-wt=20): 350 [] -class_Lattices_Osemilattice__inf(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)|c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D),c_Lattices_Osemilattice__inf__class_Oinf(A,C,E)).
% 13.74/13.66 ** KEPT (pick-wt=17): 351 [] -class_Lattices_Osemilattice__inf(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,D)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)).
% 13.74/13.66 Following clause subsumed by 351 during input processing: 0 [] -class_Lattices_Osemilattice__inf(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,D)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D)).
% 13.74/13.66 ** KEPT (pick-wt=12): 352 [] -class_Lattices_Osemilattice__inf(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Lattices_Osemilattice__inf__class_Oinf(A,C,B)=B.
% 13.74/13.66 ** KEPT (pick-wt=12): 353 [] -class_Lattices_Osemilattice__inf(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)=B.
% 13.74/13.66 ** KEPT (pick-wt=13): 354 [] -class_Lattices_Osemilattice__inf(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__inf__class_Oinf(A,D,B),C).
% 13.74/13.66 ** KEPT (pick-wt=13): 355 [] -class_Lattices_Osemilattice__inf(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D),C).
% 13.74/13.66 Following clause subsumed by 348 during input processing: 0 [] -class_Lattices_Osemilattice__inf(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D))|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 13.74/13.66 Following clause subsumed by 349 during input processing: 0 [] -class_Lattices_Osemilattice__inf(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D))|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.74/13.66 Following clause subsumed by 351 during input processing: 0 [] -class_Lattices_Osemilattice__inf(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D))| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.74/13.66 Following clause subsumed by 353 during input processing: 0 [] -class_Lattices_Osemilattice__inf(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)=B.
% 13.74/13.66 ** KEPT (pick-wt=12): 356 [] -class_Lattices_Osemilattice__inf(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)!=B.
% 13.74/13.66 ** KEPT (pick-wt=9): 357 [] -class_Lattices_Osemilattice__inf(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),C).
% 13.74/13.66 ** KEPT (pick-wt=9): 358 [] -class_Lattices_Olattice(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),C).
% 13.74/13.66 ** KEPT (pick-wt=9): 359 [] -class_Lattices_Osemilattice__inf(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),B).
% 13.74/13.66 ** KEPT (pick-wt=9): 360 [] -class_Lattices_Olattice(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),B).
% 13.74/13.66 ** KEPT (pick-wt=13): 361 [] -class_Lattices_Osemilattice__sup(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)).
% 13.74/13.66 ** KEPT (pick-wt=13): 362 [] -class_Lattices_Osemilattice__sup(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,D,C)).
% 13.74/13.66 ** KEPT (pick-wt=13): 363 [] -class_Lattices_Osemilattice__inf(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,D),C).
% 13.74/13.66 ** KEPT (pick-wt=13): 364 [] -class_Lattices_Osemilattice__inf(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Lattices_Osemilattice__inf__class_Oinf(A,D,B),C).
% 13.74/13.66 ** KEPT (pick-wt=13): 365 [] -class_Lattices_Obounded__lattice__bot(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,C)!=c_Orderings_Obot__class_Obot(A)|B=c_Orderings_Obot__class_Obot(A).
% 13.74/13.66 ** KEPT (pick-wt=13): 366 [] -class_Lattices_Obounded__lattice__bot(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,C)!=c_Orderings_Obot__class_Obot(A)|C=c_Orderings_Obot__class_Obot(A).
% 13.74/13.66 ** KEPT (pick-wt=17): 367 [] -class_Lattices_Obounded__lattice__bot(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,C)=c_Orderings_Obot__class_Obot(A)|B!=c_Orderings_Obot__class_Obot(A)|C!=c_Orderings_Obot__class_Obot(A).
% 13.74/13.66 ** KEPT (pick-wt=9): 368 [] -class_Lattices_Obounded__lattice__bot(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Orderings_Obot__class_Obot(A))=B.
% 13.74/13.66 ** KEPT (pick-wt=9): 369 [] -class_Lattices_Obounded__lattice__bot(A)|c_Lattices_Osemilattice__sup__class_Osup(A,c_Orderings_Obot__class_Obot(A),B)=B.
% 13.74/13.66 ** KEPT (pick-wt=10): 370 [] -class_Lattices_Obounded__lattice__bot(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Orderings_Obot__class_Obot(A))=c_Orderings_Obot__class_Obot(A).
% 13.74/13.66 ** KEPT (pick-wt=10): 371 [] -class_Lattices_Obounded__lattice__bot(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,c_Orderings_Obot__class_Obot(A),B)=c_Orderings_Obot__class_Obot(A).
% 13.74/13.66 ** KEPT (pick-wt=20): 372 [] -class_Lattices_Odistrib__lattice(A)|c_Lattices_Osemilattice__sup__class_Osup(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),D)=c_Lattices_Osemilattice__inf__class_Oinf(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,D),c_Lattices_Osemilattice__sup__class_Osup(A,C,D)).
% 13.74/13.66 ** KEPT (pick-wt=20): 374 [copy,373,flip.2] -class_Lattices_Odistrib__lattice(A)|c_Lattices_Osemilattice__sup__class_Osup(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),c_Lattices_Osemilattice__inf__class_Oinf(A,D,C))=c_Lattices_Osemilattice__inf__class_Oinf(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,D),C).
% 13.74/13.66 ** KEPT (pick-wt=20): 375 [] -class_Lattices_Odistrib__lattice(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,C,D))=c_Lattices_Osemilattice__inf__class_Oinf(A,c_Lattices_Osemilattice__sup__class_Osup(A,B,C),c_Lattices_Osemilattice__sup__class_Osup(A,B,D)).
% 13.74/13.66 ** KEPT (pick-wt=20): 377 [copy,376,flip.2] -class_Lattices_Odistrib__lattice(A)|c_Lattices_Osemilattice__sup__class_Osup(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),c_Lattices_Osemilattice__inf__class_Oinf(A,B,D))=c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,D)).
% 13.74/13.66 ** KEPT (pick-wt=11): 378 [] -class_Lattices_Olattice(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C))=B.
% 13.74/13.66 ** KEPT (pick-wt=11): 379 [] -class_Lattices_Olattice(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C))=B.
% 13.74/13.66 ** KEPT (pick-wt=10): 380 [] -class_Lattices_Obounded__lattice__top(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Orderings_Otop__class_Otop(A))=c_Orderings_Otop__class_Otop(A).
% 13.74/13.66 ** KEPT (pick-wt=10): 381 [] -class_Lattices_Obounded__lattice__top(A)|c_Lattices_Osemilattice__sup__class_Osup(A,c_Orderings_Otop__class_Otop(A),B)=c_Orderings_Otop__class_Otop(A).
% 13.74/13.66 ** KEPT (pick-wt=19): 382 [] -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)).
% 13.74/13.66 ** KEPT (pick-wt=19): 383 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,D,E).
% 13.74/13.66 ** KEPT (pick-wt=19): 384 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E).
% 13.74/13.66 ** KEPT (pick-wt=19): 385 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,D,E).
% 13.74/13.66 ** KEPT (pick-wt=19): 386 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E).
% 13.74/13.66 ** KEPT (pick-wt=35): 387 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_member(A,$f52(D,E,C,B,A),B)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,c_Set_OCollect(A,E)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,c_Set_OCollect(A,D))).
% 13.74/13.66 ** KEPT (pick-wt=35): 388 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|hBOOL(hAPP(D,$f52(E,D,C,B,A)))|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,c_Set_OCollect(A,D)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,c_Set_OCollect(A,E))).
% 13.74/13.66 ** KEPT (pick-wt=35): 389 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -hBOOL(hAPP(D,$f52(D,E,C,B,A)))|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,c_Set_OCollect(A,E)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,c_Set_OCollect(A,D))).
% 13.74/13.66 ** KEPT (pick-wt=33): 390 [] -c_member(A,B,C)| -c_Nitpick_Ofold__graph_H(A,D,E,F,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),C,c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))),G)|c_Nitpick_Ofold__graph_H(A,D,E,F,C,hAPP(hAPP(E,B),G)).
% 13.74/13.66 ** KEPT (pick-wt=16): 391 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,B)).
% 13.74/13.66 Following clause subsumed by 237 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,B)).
% 13.74/13.66 ** KEPT (pick-wt=19): 392 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B),c_RealDef_Oreal(tc_Nat_Onat,A)).
% 13.74/13.66 ** KEPT (pick-wt=18): 393 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)).
% 13.74/13.66 ** KEPT (pick-wt=11): 394 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),B).
% 13.74/13.66 ** KEPT (pick-wt=14): 395 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)).
% 13.74/13.66 ** KEPT (pick-wt=14): 396 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)).
% 13.74/13.66 ** KEPT (pick-wt=13): 397 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=A.
% 13.74/13.66 ** KEPT (pick-wt=20): 398 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)|B=C.
% 13.74/13.66 ** KEPT (pick-wt=20): 399 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)|B!=C.
% 13.74/13.66 ** KEPT (pick-wt=23): 400 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C).
% 13.74/13.66 ** KEPT (pick-wt=22): 401 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 13.74/13.66 Following clause subsumed by 396 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 13.74/13.66 ** KEPT (pick-wt=10): 402 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.66 ** KEPT (pick-wt=10): 403 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.66 ** KEPT (pick-wt=12): 404 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|B=C.
% 13.74/13.66 ** KEPT (pick-wt=12): 405 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)=c_Groups_Ozero__class_Ozero(A)|B!=C.
% 13.74/13.66 ** KEPT (pick-wt=12): 406 [] -class_Groups_Oab__group__add(A)|B!=C|c_Groups_Ominus__class_Ominus(A,B,C)=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.66 ** KEPT (pick-wt=12): 407 [] -class_Groups_Oab__group__add(A)|B=C|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.66 ** KEPT (pick-wt=9): 408 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,B)=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.66 ** KEPT (pick-wt=9): 409 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 13.74/13.66 ** KEPT (pick-wt=12): 410 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.74/13.66 ** KEPT (pick-wt=12): 411 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,A,B),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.74/13.66 ** KEPT (pick-wt=14): 412 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.66 ** KEPT (pick-wt=14): 413 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.66 ** KEPT (pick-wt=14): 414 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.66 ** KEPT (pick-wt=14): 415 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.66 ** KEPT (pick-wt=19): 416 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),B)|c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,c_RealDef_Oreal(tc_Nat_Onat,A)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(B),A).
% 13.74/13.66 ** KEPT (pick-wt=18): 417 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)).
% 13.74/13.66 ** KEPT (pick-wt=22): 418 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 13.74/13.66 Following clause subsumed by 417 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 13.74/13.66 ** KEPT (pick-wt=7): 419 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 13.74/13.66 ** KEPT (pick-wt=17): 420 [] -class_Groups_Oab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|B!=C|D=E.
% 13.74/13.66 ** KEPT (pick-wt=17): 421 [] -class_Groups_Oab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|B=C|D!=E.
% 13.74/13.66 ** KEPT (pick-wt=42): 423 [copy,422,flip.3] -c_Nitpick_Ofold__graph_H(A,B,C,D,E,hAPP(hAPP(C,F),G))|E=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|hAPP(hAPP(C,$f54(G,F,E,D,C,B,A)),$f53(G,F,E,D,C,B,A))=hAPP(hAPP(C,F),G).
% 13.74/13.66 ** KEPT (pick-wt=28): 424 [] -c_Nitpick_Ofold__graph_H(A,B,C,D,E,hAPP(hAPP(C,F),G))|E=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|c_member(A,$f54(G,F,E,D,C,B,A),E).
% 13.74/13.66 ** KEPT (pick-wt=49): 425 [] -c_Nitpick_Ofold__graph_H(A,B,C,D,E,hAPP(hAPP(C,F),G))|E=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|c_Nitpick_Ofold__graph_H(A,B,C,D,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),E,c_Set_Oinsert(A,$f54(G,F,E,D,C,B,A),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))),$f53(G,F,E,D,C,B,A)).
% 13.74/13.66 ** KEPT (pick-wt=43): 427 [copy,426,flip.3] -c_Nitpick_Ofold__graph_H(A,B,C,D,E,hAPP(hAPP(C,F),G))|hAPP(hAPP(C,F),G)=D|hAPP(hAPP(C,$f54(G,F,E,D,C,B,A)),$f53(G,F,E,D,C,B,A))=hAPP(hAPP(C,F),G).
% 13.74/13.66 ** KEPT (pick-wt=29): 428 [] -c_Nitpick_Ofold__graph_H(A,B,C,D,E,hAPP(hAPP(C,F),G))|hAPP(hAPP(C,F),G)=D|c_member(A,$f54(G,F,E,D,C,B,A),E).
% 13.74/13.66 ** KEPT (pick-wt=50): 429 [] -c_Nitpick_Ofold__graph_H(A,B,C,D,E,hAPP(hAPP(C,F),G))|hAPP(hAPP(C,F),G)=D|c_Nitpick_Ofold__graph_H(A,B,C,D,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),E,c_Set_Oinsert(A,$f54(G,F,E,D,C,B,A),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))),$f53(G,F,E,D,C,B,A)).
% 13.74/13.66 ** KEPT (pick-wt=24): 430 [] c_Nitpick_Ofold__graph_H(A,B,C,D,E,hAPP(hAPP(C,F),G))|E!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|hAPP(hAPP(C,F),G)!=D.
% 13.74/13.66 ** KEPT (pick-wt=44): 431 [] c_Nitpick_Ofold__graph_H(A,B,C,D,E,hAPP(hAPP(C,F),G))|hAPP(hAPP(C,F),G)!=hAPP(hAPP(C,H),I)| -c_member(A,H,E)| -c_Nitpick_Ofold__graph_H(A,B,C,D,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),E,c_Set_Oinsert(A,H,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))),I).
% 13.74/13.66 ** KEPT (pick-wt=16): 432 [] -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,c_RealDef_Oreal(tc_Nat_Onat,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(A),B).
% 13.74/13.66 ** KEPT (pick-wt=16): 433 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,c_RComplete_Onatfloor(A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B),A).
% 13.74/13.66 ** KEPT (pick-wt=16): 434 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,c_RComplete_Onatfloor(A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B),A).
% 13.74/13.66 ** KEPT (pick-wt=30): 435 [] c_member(tc_fun(A,tc_HOL_Obool),B,C)|$f56(C,B,A)!=$f55(C,B,A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),C))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 13.74/13.66 ** KEPT (pick-wt=38): 436 [] c_member(tc_fun(A,tc_HOL_Obool),B,C)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),$f56(C,B,A),$f55(C,B,A))!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,c_Complete__Lattice_OSup__class_OSup(tc_fun(A,tc_HOL_Obool),C))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 13.74/13.66 ** KEPT (pick-wt=5): 437 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.74/13.66 ** KEPT (pick-wt=10): 438 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatfloor(A)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.66 ** KEPT (pick-wt=12): 439 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 13.74/13.66 ** KEPT (pick-wt=12): 440 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 13.74/13.66 ** KEPT (pick-wt=17): 441 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),B).
% 13.74/13.66 ** KEPT (pick-wt=11): 442 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.66 ** KEPT (pick-wt=11): 443 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 13.74/13.66 Following clause subsumed by 442 during input processing: 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 13.74/13.66 ** KEPT (pick-wt=17): 444 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=B.
% 13.74/13.66 Following clause subsumed by 437 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.74/13.66 Following clause subsumed by 183 during input processing: 0 [] A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 13.74/13.66 Following clause subsumed by 437 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 13.74/13.66 ** KEPT (pick-wt=8): 445 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.66 ** KEPT (pick-wt=9): 446 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.66 Following clause subsumed by 181 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.66 ** KEPT (pick-wt=10): 447 [] c_RealDef_Oreal(tc_Nat_Onat,A)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.66 ** KEPT (pick-wt=10): 448 [] c_RealDef_Oreal(tc_Nat_Onat,A)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.66 ** KEPT (pick-wt=10): 449 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatfloor(A),c_RComplete_Onatfloor(B)).
% 13.74/13.66 ** KEPT (pick-wt=19): 450 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),B)|c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,B,c_RealDef_Oreal(tc_Nat_Onat,A)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(B),A).
% 13.74/13.66 ** KEPT (pick-wt=11): 451 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.66 ** KEPT (pick-wt=11): 452 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.66 ** KEPT (pick-wt=10): 453 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatceiling(A)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.66 ** KEPT (pick-wt=12): 454 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),A)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(A)),A).
% 13.74/13.66 ** KEPT (pick-wt=11): 455 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_RComplete_Onatfloor(B)).
% 13.74/13.66 ** KEPT (pick-wt=12): 456 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,A))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 13.74/13.66 ** KEPT (pick-wt=12): 457 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,A))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 13.74/13.66 ** KEPT (pick-wt=33): 458 [] -c_Finite__Set_Ofold__graph(A,B,C,D,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),E,c_Set_Oinsert(A,F,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))),G)| -c_member(A,F,E)|c_Finite__Set_Ofold__graph(A,B,C,D,E,hAPP(hAPP(C,F),G)).
% 13.74/13.66 ** KEPT (pick-wt=11): 459 [] -class_GCD_Ogcd(A)|c_GCD_Ogcd__class_OGcd(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.66 ** KEPT (pick-wt=7): 460 [] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 13.74/13.66 Following clause subsumed by 460 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).
% 13.74/13.66 ** KEPT (pick-wt=5): 461 [] c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 13.74/13.66 ** KEPT (pick-wt=13): 462 [] -c_Finite__Set_Ofold__graph(A,B,C,D,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)),E)|E=D.
% 13.74/13.66 ** KEPT (pick-wt=8): 463 [] -class_Rings_Osemiring__1(A)|c_member(A,c_Groups_Oone__class_Oone(A),c_Nat_Osemiring__1__class_ONats(A)).
% 13.74/13.66 ** KEPT (pick-wt=10): 464 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)!=B|B=c_Groups_Oone__class_Oone(A).
% 13.74/13.66 ** KEPT (pick-wt=10): 465 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)=B|B!=c_Groups_Oone__class_Oone(A).
% 13.74/13.66 ** KEPT (pick-wt=8): 466 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.66 ** KEPT (pick-wt=8): 467 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)).
% 13.74/13.66 ** KEPT (pick-wt=8): 468 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.66 ** KEPT (pick-wt=8): 469 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)).
% 13.74/13.66 ** KEPT (pick-wt=25): 470 [] c_member(A,B,C)| -c_Finite__Set_Ofold__graph(A,D,E,F,C,G)|c_Finite__Set_Ofold__graph(A,D,E,F,c_Set_Oinsert(A,B,C),hAPP(hAPP(E,B),G)).
% 13.74/13.66 ** KEPT (pick-wt=8): 471 [] -class_Rings_Osemiring__1(A)|c_member(A,c_Groups_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_ONats(A)).
% 13.74/13.66 ** KEPT (pick-wt=11): 472 [] -class_GCD_Ogcd(A)|c_GCD_Ogcd__class_OLcm(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(A).
% 13.74/13.66 ** KEPT (pick-wt=19): 473 [] -c_Finite__Set_Ofold__graph(A,A,B,C,D,E)|c_member(A,C,D)|c_Finite__Set_Ofold1Set(A,B,c_Set_Oinsert(A,C,D),E).
% 13.74/13.66 ** KEPT (pick-wt=20): 474 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,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,c_RealDef_Oreal(tc_Nat_Onat,A),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatfloor(B)=A.
% 13.74/13.66 ** KEPT (pick-wt=40): 475 [] -class_Groups_Oab__semigroup__mult(A)| -c_Finite__Set_Ofold__graph(A,A,c_Groups_Otimes__class_Otimes(A),B,C,D)| -c_member(A,E,C)|c_member(A,B,C)|c_Finite__Set_Ofold__graph(A,A,c_Groups_Otimes__class_Otimes(A),E,c_Set_Oinsert(A,B,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),C,c_Set_Oinsert(A,E,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))),D).
% 13.74/13.66 ** KEPT (pick-wt=44): 476 [] -class_Rings_Olinordered__semiring__1(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),F)|c_Groups_Oplus__class_Oplus(A,E,F)!=c_Groups_Oone__class_Oone(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D)),C).
% 13.74/13.66 ** KEPT (pick-wt=19): 477 [] -class_Rings_Ono__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.66 Following clause subsumed by 477 during input processing: 0 [] -class_Rings_Ono__zero__divisors(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)!=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.66 ** KEPT (pick-wt=19): 478 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.66 ** KEPT (pick-wt=15): 479 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.66 ** KEPT (pick-wt=15): 480 [] -class_Rings_Oring__no__zero__divisors(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.66 ** KEPT (pick-wt=12): 481 [] -class_Rings_Omult__zero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.66 ** KEPT (pick-wt=12): 482 [] -class_Rings_Omult__zero(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ozero__class_Ozero(A)),B)=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.67 ** KEPT (pick-wt=9): 483 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 13.74/13.67 ** KEPT (pick-wt=9): 484 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 13.74/13.67 ** KEPT (pick-wt=13): 485 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oplus__class_Oplus(A,B,B)|B=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.67 ** KEPT (pick-wt=13): 486 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)=c_Groups_Oplus__class_Oplus(A,B,B)|B!=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.67 ** KEPT (pick-wt=9): 487 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 13.74/13.67 ** KEPT (pick-wt=9): 488 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 13.74/13.67 ** KEPT (pick-wt=20): 489 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)|B=C.
% 13.74/13.67 ** KEPT (pick-wt=20): 490 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),C)|B!=C.
% 13.74/13.67 ** KEPT (pick-wt=20): 491 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)|B=C.
% 13.74/13.67 ** KEPT (pick-wt=20): 492 [] A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),A)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),C),A)|B!=C.
% 13.74/13.67 ** KEPT (pick-wt=21): 493 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.74/13.67 ** KEPT (pick-wt=21): 494 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.74/13.67 ** KEPT (pick-wt=25): 495 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),A),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),B),B))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|B!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 13.74/13.67 ** KEPT (pick-wt=16): 497 [copy,496,flip.1] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=A|B=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.67 ** KEPT (pick-wt=20): 498 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)|A=C|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.67 ** KEPT (pick-wt=16): 499 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)|A!=C.
% 13.74/13.67 ** KEPT (pick-wt=17): 500 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.67 ** KEPT (pick-wt=20): 501 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B=C|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.67 ** KEPT (pick-wt=16): 502 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|B!=C.
% 13.74/13.67 ** KEPT (pick-wt=17): 503 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.67 ** KEPT (pick-wt=17): 504 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.67 ** KEPT (pick-wt=13): 505 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.67 ** KEPT (pick-wt=13): 506 [] hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 13.74/13.67 ** KEPT (pick-wt=27): 508 [copy,507,flip.2] -class_Rings_Oring__1(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))),c_Groups_Ominus__class_Ominus(A,B,c_Groups_Oone__class_Oone(A)))=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),c_Groups_Oone__class_Oone(A)).
% 13.74/13.67 ** KEPT (pick-wt=11): 509 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 13.74/13.67 ** KEPT (pick-wt=11): 510 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Oone__class_Oone(A))=B.
% 13.74/13.67 ** KEPT (pick-wt=11): 511 [] -class_Groups_Ocomm__monoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 13.74/13.67 ** KEPT (pick-wt=11): 512 [] -class_Groups_Omonoid__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oone__class_Oone(A)),B)=B.
% 13.74/13.67 ** KEPT (pick-wt=16): 513 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.74/13.67 ** KEPT (pick-wt=16): 514 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))| -c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.74/13.67 ** KEPT (pick-wt=16): 515 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 13.74/13.67 ** KEPT (pick-wt=16): 516 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))| -c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 13.74/13.67 ** KEPT (pick-wt=16): 517 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)).
% 13.74/13.67 ** KEPT (pick-wt=16): 518 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)).
% 13.74/13.67 ** KEPT (pick-wt=20): 519 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 13.74/13.67 Following clause subsumed by 513 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 13.74/13.67 Following clause subsumed by 515 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 13.74/13.67 ** KEPT (pick-wt=17): 520 [] -class_Groups_Oab__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 13.74/13.67 ** KEPT (pick-wt=25): 521 [] -class_Groups_Oab__semigroup__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 13.74/13.67 ** KEPT (pick-wt=14): 522 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 13.74/13.67 ** KEPT (pick-wt=14): 523 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,B,D)|C!=D.
% 13.74/13.67 ** KEPT (pick-wt=14): 524 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,D,C)|B=D.
% 13.74/13.67 ** KEPT (pick-wt=14): 525 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,D,C)|B!=D.
% 13.74/13.67 Following clause subsumed by 522 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 13.74/13.67 ** KEPT (pick-wt=14): 526 [] -class_Groups_Ocancel__ab__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 13.74/13.67 Following clause subsumed by 524 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,D,C)|B=D.
% 13.74/13.67 ** KEPT (pick-wt=16): 527 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless(A,C,D).
% 13.74/13.67 ** KEPT (pick-wt=16): 528 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless(A,B,D).
% 13.74/13.67 ** KEPT (pick-wt=20): 529 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 13.74/13.67 ** KEPT (pick-wt=16): 530 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)).
% 13.74/13.67 ** KEPT (pick-wt=16): 531 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)).
% 13.74/13.67 Following clause subsumed by 527 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless(A,C,D).
% 13.74/13.67 ** KEPT (pick-wt=16): 532 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))| -c_Orderings_Oord__class_Oless(A,C,D).
% 13.74/13.67 Following clause subsumed by 528 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless(A,B,D).
% 13.74/13.67 ** KEPT (pick-wt=16): 533 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))| -c_Orderings_Oord__class_Oless(A,B,D).
% 13.74/13.67 ** KEPT (pick-wt=22): 534 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),D)).
% 13.74/13.67 ** KEPT (pick-wt=18): 535 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),C),B)).
% 13.74/13.67 ** KEPT (pick-wt=18): 536 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),A),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B),C)).
% 13.74/13.67 ** KEPT (pick-wt=26): 537 [] -class_Rings_Ocomm__semiring(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 13.74/13.67 ** KEPT (pick-wt=32): 539 [copy,538,flip.2] -class_Rings_Osemiring(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Oplus__class_Oplus(A,B,C)),D),E)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),E)).
% 13.74/13.67 ** KEPT (pick-wt=14): 540 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,A),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,C,B)).
% 13.74/13.67 ** KEPT (pick-wt=10): 541 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=B.
% 13.74/13.67 Following clause subsumed by 541 during input processing: 0 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)=B.
% 13.74/13.67 ** KEPT (pick-wt=20): 542 [] -class_Lattices_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))=hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C).
% 13.74/13.67 ** KEPT (pick-wt=35): 543 [] -class_Rings_Oring(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D)!=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D)=F.
% 13.74/13.67 ** KEPT (pick-wt=35): 544 [] -class_Rings_Oring(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D)!=F.
% 13.74/13.67 ** KEPT (pick-wt=35): 545 [] -class_Rings_Oring(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D)!=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F)|D=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F).
% 13.74/13.67 ** KEPT (pick-wt=35): 546 [] -class_Rings_Oring(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D)=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F)|D!=c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F).
% 13.74/13.67 ** KEPT (pick-wt=11): 547 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,B,C),C)=B.
% 13.74/13.67 ** KEPT (pick-wt=11): 548 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,C),C)=B.
% 13.74/13.67 ** KEPT (pick-wt=37): 550 [copy,549,flip.2] -class_Rings_Oring(A)|c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),c_Groups_Ominus__class_Ominus(A,C,D)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),D))=c_Groups_Ominus__class_Ominus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),D)).
% 13.74/13.67 ** KEPT (pick-wt=23): 552 [copy,551,flip.2] -class_Groups_Oab__group__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ominus__class_Ominus(A,D,E))=c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 13.74/13.67 ** KEPT (pick-wt=37): 553 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D),F).
% 13.74/13.67 ** KEPT (pick-wt=37): 554 [] -class_Rings_Oordered__ring(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F))| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D),F).
% 13.74/13.67 ** KEPT (pick-wt=37): 555 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F))|c_Orderings_Oord__class_Oless(A,D,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F)).
% 13.74/13.67 ** KEPT (pick-wt=37): 556 [] -class_Rings_Oordered__ring(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F))| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F)).
% 13.74/13.67 ** KEPT (pick-wt=37): 557 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D),F).
% 13.74/13.67 ** KEPT (pick-wt=37): 558 [] -class_Rings_Oordered__ring(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,B,E)),C),D),F).
% 13.74/13.67 ** KEPT (pick-wt=37): 559 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F))|c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F)).
% 13.74/13.67 ** KEPT (pick-wt=37): 560 [] -class_Rings_Oordered__ring(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),D),c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),C),F))| -c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),c_Groups_Ominus__class_Ominus(A,E,B)),C),F)).
% 13.74/13.67 ** KEPT (pick-wt=44): 561 [] -class_Rings_Olinordered__semiring__1__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),F)|c_Groups_Oplus__class_Oplus(A,E,F)!=c_Groups_Oone__class_Oone(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),E),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),F),D)),C).
% 13.74/13.67 ** KEPT (pick-wt=15): 562 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.74/13.67 ** KEPT (pick-wt=15): 563 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.74/13.67 ** KEPT (pick-wt=15): 564 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 ** KEPT (pick-wt=15): 565 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 ** KEPT (pick-wt=20): 566 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 13.74/13.67 ** KEPT (pick-wt=23): 567 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.67 ** KEPT (pick-wt=23): 568 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.67 ** KEPT (pick-wt=27): 569 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 13.74/13.67 ** KEPT (pick-wt=18): 570 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 13.74/13.67 ** KEPT (pick-wt=18): 571 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Oplus__class_Oplus(A,D,B)).
% 13.74/13.67 ** KEPT (pick-wt=20): 572 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 ** KEPT (pick-wt=15): 573 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.74/13.67 ** KEPT (pick-wt=15): 574 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.74/13.67 ** KEPT (pick-wt=15): 575 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 ** KEPT (pick-wt=15): 576 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 ** KEPT (pick-wt=20): 577 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 13.74/13.67 ** KEPT (pick-wt=18): 578 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 13.74/13.67 ** KEPT (pick-wt=20): 579 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 ** KEPT (pick-wt=20): 580 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 13.74/13.67 ** KEPT (pick-wt=20): 581 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 13.74/13.67 ** KEPT (pick-wt=10): 582 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))).
% 13.74/13.67 ** KEPT (pick-wt=22): 583 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 ** KEPT (pick-wt=22): 584 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 ** KEPT (pick-wt=22): 585 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.74/13.67 ** KEPT (pick-wt=22): 586 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.74/13.67 ** KEPT (pick-wt=34): 587 [] -class_Rings_Oordered__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 13.74/13.67 ** KEPT (pick-wt=34): 588 [] -class_Rings_Oordered__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),E)).
% 13.74/13.67 ** KEPT (pick-wt=25): 589 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)).
% 13.74/13.67 ** KEPT (pick-wt=25): 590 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 13.74/13.67 ** KEPT (pick-wt=25): 591 [] -class_Rings_Oordered__comm__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)).
% 13.74/13.67 ** KEPT (pick-wt=25): 592 [] -class_Rings_Oordered__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)).
% 13.74/13.67 ** KEPT (pick-wt=25): 593 [] -class_Rings_Oordered__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 13.74/13.67 Following clause subsumed by 586 during input processing: 0 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.74/13.67 Following clause subsumed by 584 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 Following clause subsumed by 584 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),B),c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 Following clause subsumed by 583 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 ** KEPT (pick-wt=22): 594 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.74/13.67 ** KEPT (pick-wt=22): 595 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 ** KEPT (pick-wt=22): 596 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C).
% 13.74/13.67 ** KEPT (pick-wt=22): 597 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 ** KEPT (pick-wt=22): 598 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C).
% 13.74/13.67 ** KEPT (pick-wt=22): 599 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 ** KEPT (pick-wt=22): 600 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C).
% 13.74/13.67 ** KEPT (pick-wt=22): 601 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 ** KEPT (pick-wt=22): 602 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 ** KEPT (pick-wt=22): 603 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 ** KEPT (pick-wt=22): 604 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 ** KEPT (pick-wt=22): 605 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C).
% 13.74/13.67 ** KEPT (pick-wt=22): 606 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)).
% 13.74/13.67 ** KEPT (pick-wt=12): 607 [] -class_Rings_Olinordered__ring(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B)).
% 13.74/13.67 ** KEPT (pick-wt=25): 608 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B)).
% 13.74/13.67 ** KEPT (pick-wt=25): 609 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D)).
% 13.74/13.67 ** KEPT (pick-wt=25): 610 [] -class_Rings_Olinordered__comm__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)).
% 13.74/13.67 ** KEPT (pick-wt=25): 611 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C)).
% 13.74/13.67 ** KEPT (pick-wt=25): 612 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),C),D)).
% 13.74/13.67 ** KEPT (pick-wt=22): 613 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.77/13.67 ** KEPT (pick-wt=22): 614 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)).
% 13.77/13.67 ** KEPT (pick-wt=25): 615 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,D,C).
% 13.77/13.67 Following clause subsumed by 608 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -c_Orderings_Oord__class_Oless(A,D,C).
% 13.77/13.67 ** KEPT (pick-wt=22): 616 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 13.77/13.67 ** KEPT (pick-wt=22): 617 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C).
% 13.77/13.67 Following clause subsumed by 614 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)).
% 13.77/13.67 ** KEPT (pick-wt=22): 618 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),c_Groups_Ozero__class_Ozero(A)).
% 13.77/13.67 ** KEPT (pick-wt=22): 619 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C)).
% 13.77/13.67 ** KEPT (pick-wt=25): 620 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,C,D).
% 13.77/13.67 ** KEPT (pick-wt=25): 621 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))| -c_Orderings_Oord__class_Oless(A,C,D).
% 13.77/13.67 ** KEPT (pick-wt=26): 622 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.77/13.67 ** KEPT (pick-wt=25): 623 [] -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_
% 13.77/13.67 Search stopped in tp_alloc by max_mem option.
% 13.77/13.67 Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,D,C).
% 13.77/13.67 ** KEPT (pick-wt=25): 624 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 13.77/13.67 ** KEPT (pick-wt=24): 625 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),D))|c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,D,C).
% 13.77/13.67 Following clause subsumed by 621 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).
% 13.77/13.67 Following clause subsumed by 608 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).
% 13.77/13.67 ** KEPT (pick-wt=26): 626 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)).
% 13.77/13.67 ** KEPT (pick-wt=25): 627 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,D,B).
% 13.77/13.67 ** KEPT (pick-wt=25): 628 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|c_Orderings_Oord__class_Oless(A,B,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)).
% 13.77/13.67 ** KEPT (pick-wt=24): 629 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))|c_Orderings_Oord__class_Oless(A,B,D)|c_Orderings_Oord__class_Oless(A,D,B).
% 13.77/13.67 ** KEPT (pick-wt=25): 630 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),D),C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless(A,B,D).
% 13.77/13.67 Following clause subsumed by 609 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).
% 13.77/13.67 ** KEPT (pick-wt=12): 631 [] -class_Rings_Olinordered__ring(A)| -c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Otimes__class_Otimes(A),B),B),c_Groups_Ozero__class_Ozero(A)).
% 13.77/13.67
% 13.77/13.67 Search stopped in tp_alloc by max_mem option.
% 13.77/13.67
% 13.77/13.67 ============ end of search ============
% 13.77/13.67
% 13.77/13.67 -------------- statistics -------------
% 13.77/13.67 clauses given 0
% 13.77/13.67 clauses generated 0
% 13.77/13.67 clauses kept 618
% 13.77/13.67 clauses forward subsumed 161
% 13.77/13.67 clauses back subsumed 0
% 13.77/13.67 Kbytes malloced 11718
% 13.77/13.67
% 13.77/13.67 ----------- times (seconds) -----------
% 13.77/13.67 user CPU time 0.09 (0 hr, 0 min, 0 sec)
% 13.77/13.67 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 13.77/13.67 wall-clock time 13 (0 hr, 0 min, 13 sec)
% 13.77/13.67
% 13.77/13.67 Process 3801 finished Wed Jul 27 02:52:34 2022
% 13.77/13.67 Otter interrupted
% 13.77/13.67 PROOF NOT FOUND
%------------------------------------------------------------------------------