TSTP Solution File: SWW191+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWW191+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 13:22:05 EDT 2022
% Result : Unknown 12.45s 12.35s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW191+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 02:53:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 12.38/12.29 ----- Otter 3.3f, August 2004 -----
% 12.38/12.29 The process was started by sandbox2 on n019.cluster.edu,
% 12.38/12.29 Wed Jul 27 02:53:52 2022
% 12.38/12.29 The command was "./otter". The process ID is 32166.
% 12.38/12.29
% 12.38/12.29 set(prolog_style_variables).
% 12.38/12.29 set(auto).
% 12.38/12.29 dependent: set(auto1).
% 12.38/12.29 dependent: set(process_input).
% 12.38/12.29 dependent: clear(print_kept).
% 12.38/12.29 dependent: clear(print_new_demod).
% 12.38/12.29 dependent: clear(print_back_demod).
% 12.38/12.29 dependent: clear(print_back_sub).
% 12.38/12.29 dependent: set(control_memory).
% 12.38/12.29 dependent: assign(max_mem, 12000).
% 12.38/12.29 dependent: assign(pick_given_ratio, 4).
% 12.38/12.29 dependent: assign(stats_level, 1).
% 12.38/12.29 dependent: assign(max_seconds, 10800).
% 12.38/12.29 clear(print_given).
% 12.38/12.29
% 12.38/12.29 formula_list(usable).
% 12.38/12.29 all A (A=A).
% 12.38/12.29 all V_g_2 V_f_2 ((all B_x (hAPP(V_f_2,B_x)=hAPP(V_g_2,B_x)))->V_f_2=V_g_2).
% 12.38/12.29 all B_z (hBOOL(hAPP(v_P,B_z))->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B_z,v_y____)).
% 12.38/12.29 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_y____,v_L____).
% 12.38/12.29 c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,v_L____,v_Y____).
% 12.38/12.29 all B_x (hBOOL(hAPP(v_P,B_x))->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B_x,v_L____)).
% 12.38/12.29 all V_x T_a (class_Orderings_Opreorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x)).
% 12.38/12.29 all V_z_2 (hBOOL(hAPP(v_P,V_z_2))-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_y____,V_z_2)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_y____,v_L____))).
% 12.38/12.29 all V_w c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_w).
% 12.38/12.29 all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z)).
% 12.38/12.29 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_j,V_k)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_k))).
% 12.38/12.29 all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z)->V_z=V_w)).
% 12.38/12.29 all B_z (hBOOL(hAPP(v_P,B_z))-> -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_y____,B_z)).
% 12.38/12.29 all V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)<-> (all B_x c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x))))).
% 12.38/12.29 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Oorder(T_a)-> (V_xa_2=V_ya_2<->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2))).
% 12.38/12.29 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (V_x=V_y->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y))).
% 12.38/12.29 hBOOL(hAPP(v_P,v_x____)).
% 12.38/12.29 exists B_x1 hBOOL(hAPP(v_P,B_x1)).
% 12.38/12.29 all B_x (hBOOL(hAPP(v_P,B_x))->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B_x,v_Y____)).
% 12.38/12.29 all V_x (hBOOL(hAPP(v_P,V_x))->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,v_Y____)).
% 12.38/12.29 exists B_z all B_x (hBOOL(hAPP(v_P,B_x))->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,B_z)).
% 12.38/12.29 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x____,v_Y____).
% 12.38/12.29 all V_x T_a (class_Orderings_Opreorder(T_a)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_x)).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (V_xa_2!=V_ya_2<->c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2))).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)|V_xa_2=V_ya_2)).
% 12.38/12.29 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x)).
% 12.38/12.29 all V_xa_2 V_ya_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->V_xa_2=V_ya_2))).
% 12.38/12.29 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 12.38/12.29 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)).
% 12.38/12.29 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 12.38/12.29 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 12.38/12.29 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)).
% 12.38/12.29 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_y!=V_x)).
% 12.38/12.29 all V_b V_a T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> -c_Orderings_Oord__class_Oless(T_a,V_b,V_a))).
% 12.38/12.29 all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> -c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 12.38/12.29 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))).
% 12.38/12.29 all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_b)->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))).
% 12.38/12.29 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))).
% 12.38/12.29 all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))).
% 12.38/12.29 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 12.38/12.29 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 12.38/12.29 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 12.38/12.29 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (V_x!=V_y->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 12.38/12.29 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 12.38/12.29 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 12.38/12.29 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 12.38/12.29 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 12.38/12.29 all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (V_a!=V_b->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 12.38/12.29 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (V_a!=V_b->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 12.38/12.29 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y)).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->V_xa_2=V_ya_2))).
% 12.38/12.29 all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y))).
% 12.38/12.29 all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_y))).
% 12.38/12.29 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 12.38/12.29 all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)<->V_xa_2=V_ya_2))).
% 12.38/12.29 all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y))).
% 12.38/12.29 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x))).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2)).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)& -c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2))).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)&V_xa_2!=V_ya_2)).
% 12.38/12.29 all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x)).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2))).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2))).
% 12.38/12.29 all V_ya_2 V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)|V_xa_2=V_ya_2).
% 12.38/12.29 all V_ya_2 V_xa_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)&V_xa_2!=V_ya_2).
% 12.38/12.29 all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x))).
% 12.38/12.29 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)))).
% 12.38/12.29 all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x)))).
% 12.38/12.29 all V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->V_x=V_y))).
% 12.38/12.29 all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_z)))).
% 12.38/12.29 all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)->V_x=V_y))).
% 12.38/12.29 all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (V_b=V_c->c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a)))).
% 12.38/12.29 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (V_b=V_c->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)))).
% 12.38/12.29 all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a)))).
% 12.38/12.29 all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)))).
% 12.38/12.29 all V_xa_2 V_ya_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)<->V_xa_2=V_ya_2))).
% 12.38/12.29 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)))).
% 12.38/12.29 c_Lubs_OisLub(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),c_Set_OCollect(tc_RealDef_Oreal,v_P),v_L____).
% 12.38/12.29 all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 12.38/12.29 -((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)))))).
% 12.38/12.29 all T_a V_g_2 V_f_2 T_b (class_Orderings_Oord(T_b)-> ((all B_x c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)))->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2))).
% 12.38/12.29 all V_z V_y T_a (class_Orderings_Odense__linorder(T_a)-> ((all B_x (c_Orderings_Oord__class_Oless(T_a,B_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,B_x,V_z)))->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z))).
% 12.38/12.29 all V_z V_y V_x T_a (class_Orderings_Odense__linorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> ((all B_w (c_Orderings_Oord__class_Oless(T_a,V_x,B_w)-> (c_Orderings_Oord__class_Oless(T_a,B_w,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,B_w,V_z))))->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)))).
% 12.38/12.29 all V_f_2 V_c_2 V_a_2 V_b_2 T_a T_b (class_Orderings_Oorder(T_b)&class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)-> (c_Orderings_Oord__class_Oless__e_q(T_b,V_c_2,hAPP(V_f_2,V_b_2))-> ((all B_x B_y (c_Orderings_Oord__class_Oless(T_a,B_y,B_x)->c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,B_y),hAPP(V_f_2,B_x))))->c_Orderings_Oord__class_Oless(T_b,V_c_2,hAPP(V_f_2,V_a_2)))))).
% 12.38/12.29 all V_f_2 V_c_2 V_a_2 V_b_2 T_a T_b (class_Orderings_Oorder(T_b)&class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2)-> (c_Orderings_Oord__class_Oless(T_b,V_c_2,hAPP(V_f_2,V_b_2))-> ((all B_x B_y (c_Orderings_Oord__class_Oless__e_q(T_a,B_y,B_x)->c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,B_y),hAPP(V_f_2,B_x))))->c_Orderings_Oord__class_Oless(T_b,V_c_2,hAPP(V_f_2,V_a_2)))))).
% 12.38/12.29 all V_c_2 V_f_2 V_b_2 V_a_2 T_b T_a (class_Orderings_Oorder(T_a)&class_Orderings_Oorder(T_b)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)-> (c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_b_2),V_c_2)-> ((all B_x B_y (c_Orderings_Oord__class_Oless(T_a,B_x,B_y)->c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,B_x),hAPP(V_f_2,B_y))))->c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_a_2),V_c_2))))).
% 12.38/12.29 all V_c_2 V_f_2 V_b_2 V_a_2 T_b T_a (class_Orderings_Oorder(T_a)&class_Orderings_Oorder(T_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_b_2),V_c_2)-> ((all B_x B_y (c_Orderings_Oord__class_Oless__e_q(T_a,B_x,B_y)->c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,B_x),hAPP(V_f_2,B_y))))->c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_a_2),V_c_2))))).
% 12.38/12.29 all V_c_2 V_b_2 V_f_2 V_a_2 T_b T_a (class_Orderings_Oorder(T_a)&class_Orderings_Oorder(T_b)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(V_f_2,V_b_2))-> (c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2,V_c_2)-> ((all B_x B_y (c_Orderings_Oord__class_Oless__e_q(T_b,B_x,B_y)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_f_2,B_x),hAPP(V_f_2,B_y))))->c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(V_f_2,V_c_2)))))).
% 12.38/12.29 all V_c_2 V_b_2 V_f_2 V_a_2 T_b T_a (class_Orderings_Oorder(T_a)&class_Orderings_Oorder(T_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,hAPP(V_f_2,V_b_2))-> (c_Orderings_Oord__class_Oless(T_b,V_b_2,V_c_2)-> ((all B_x B_y (c_Orderings_Oord__class_Oless(T_b,B_x,B_y)->c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,B_x),hAPP(V_f_2,B_y))))->c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(V_f_2,V_c_2)))))).
% 12.38/12.29 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)).
% 12.38/12.29 all V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)& -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2))).
% 12.38/12.29 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))).
% 12.38/12.29 -(all B_L (-c_Lubs_OisLub(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_L))).
% 12.38/12.29 exists B_x1 c_Lubs_OisLub(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).
% 12.38/12.29 all V_xa_2 T_a hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_xa_2)).
% 12.38/12.29 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)).
% 12.38/12.29 all V_ya_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_ya_2)->V_xa_2=V_ya_2)).
% 12.38/12.29 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))).
% 12.38/12.29 all V_Pa_2 T_a (c_Set_OCollect(T_a,V_Pa_2)=V_Pa_2).
% 12.38/12.29 exists B_x c_member(tc_RealDef_Oreal,B_x,c_Set_OCollect(tc_RealDef_Oreal,v_P)).
% 12.38/12.29 all V_c_2 V_a_2 V_b_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)&class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_f_2,V_b_2),V_a_2)-> (c_Orderings_Oord__class_Oless(T_b,V_c_2,V_b_2)-> ((all B_x B_y (c_Orderings_Oord__class_Oless(T_b,B_y,B_x)->c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,B_y),hAPP(V_f_2,B_x))))->c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,V_c_2),V_a_2))))).
% 12.38/12.29 all V_c_2 V_a_2 V_b_2 V_f_2 T_a T_b (class_Orderings_Oorder(T_b)&class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,V_b_2),V_a_2)-> (c_Orderings_Oord__class_Oless__e_q(T_b,V_c_2,V_b_2)-> ((all B_x B_y (c_Orderings_Oord__class_Oless__e_q(T_b,B_y,B_x)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_f_2,B_y),hAPP(V_f_2,B_x))))->c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,V_c_2),V_a_2))))).
% 12.38/12.29 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)))).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (c_member(T_a,V_xa_2,c_fe_qual(V_ya_2))<->V_xa_2=V_ya_2).
% 12.38/12.29 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))).
% 12.38/12.29 all V_A_2 T_a V_ya_2 V_xa_2 (V_xa_2=V_ya_2-> (c_member(T_a,V_xa_2,V_A_2)<->c_member(T_a,V_ya_2,V_A_2))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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)))).
% 12.38/12.29 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))).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)))).
% 12.38/12.29 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)).
% 12.38/12.29 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).
% 12.38/12.29 all V_ya_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_ya_2))->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)))).
% 12.38/12.29 all V_ya_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_ya_2,V_S_2)->c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2)))).
% 12.38/12.29 all V_ya_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_ya_2,V_S_2)->c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2)))).
% 12.38/12.29 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)))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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)))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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)))).
% 12.38/12.29 all V_ya_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_ya_2,c_Set_OCollect(T_a,V_Pa_2))->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))))).
% 12.38/12.29 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))).
% 12.38/12.29 all V_ya_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_ya_2,V_S_2)->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)))).
% 12.38/12.29 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)))).
% 12.38/12.29 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)))).
% 12.38/12.29 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)))).
% 12.38/12.29 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)))).
% 12.38/12.29 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))))).
% 12.38/12.29 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))))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 all V_ya_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_ya_2,V_S_2)->c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2)))).
% 12.38/12.29 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)))).
% 12.38/12.29 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))).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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).
% 12.38/12.29 all T_a exists B_x c_member(T_a,B_x,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.29 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Odecse_q(T_a,V_X_2)<-> (all B_m B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)))))).
% 12.38/12.29 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Oincse_q(T_a,V_X_2)<-> (all B_m B_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)))))).
% 12.38/12.29 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))).
% 12.38/12.29 all V_ya_2 V_xa_2 V_f_2 T_a T_b (class_Orderings_Oorder(T_b)&class_Orderings_Oorder(T_a)-> (c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2)-> (c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)->c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_f_2,V_ya_2))))).
% 12.38/12.29 all V_ya_2 V_xa_2 V_f_2 T_a T_b (class_Orderings_Oorder(T_b)&class_Orderings_Olinorder(T_a)-> (c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2)-> (c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_f_2,V_ya_2))<->c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)))).
% 12.38/12.29 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastAtMost(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_a_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_d_2)& (c_Orderings_Oord__class_Oless(T_a,V_c_2,V_a_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_d_2)))&c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_d_2))).
% 12.38/12.29 all V_ya_2 V_xa_2 V_f_2 T_a T_b (class_Orderings_Oorder(T_b)&class_Orderings_Olinorder(T_a)-> (c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2)-> (c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_f_2,V_ya_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)))).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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)).
% 12.38/12.29 all V_ya_2 V_xa_2 V_f_2 T_a T_b (class_Orderings_Oorder(T_b)&class_Orderings_Olinorder(T_a)-> (c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2)-> (hAPP(V_f_2,V_xa_2)=hAPP(V_f_2,V_ya_2)<->V_xa_2=V_ya_2))).
% 12.38/12.29 all V_xa_2 V_A_2 V_ya_2 T_a (hBOOL(hAPP(c_Set_Oinsert(T_a,V_ya_2,V_A_2),V_xa_2))<->V_ya_2=V_xa_2|hBOOL(hAPP(V_A_2,V_xa_2))).
% 12.38/12.29 all V_A_2 V_ya_2 V_xa_2 T_a (c_Set_Oinsert(T_a,V_xa_2,c_Set_Oinsert(T_a,V_ya_2,V_A_2))=c_Set_Oinsert(T_a,V_ya_2,c_Set_Oinsert(T_a,V_xa_2,V_A_2))).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastAtMost(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_a_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_d_2))).
% 12.38/12.29 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))).
% 12.38/12.29 all V_k_2 V_less__e_q_2 V_i_2 T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OatMost(T_a,V_less__e_q_2,V_k_2))<->hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_k_2))).
% 12.38/12.29 all V_k_2 V_less__e_q_2 V_i_2 T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeast(T_a,V_less__e_q_2,V_k_2))<->hBOOL(hAPP(hAPP(V_less__e_q_2,V_k_2),V_i_2))).
% 12.38/12.29 all V_k_2 V_less_2 V_i_2 T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))<->hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2))).
% 12.38/12.29 all V_k_2 V_less_2 V_i_2 T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))<->hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2))).
% 12.38/12.29 all V_u_2 V_l_2 V_less__e_q_2 V_i_2 T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__e_q_2,V_l_2,V_u_2))<->hBOOL(hAPP(hAPP(V_less__e_q_2,V_l_2),V_i_2))&hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_u_2))).
% 12.38/12.29 all V_u_2 V_l_2 V_less_2 V_i_2 T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2))<->hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))&hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))).
% 12.38/12.29 all V_u_2 V_l_2 V_less_2 V_less__e_q_2 V_i_2 T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__e_q_2,V_less_2,V_l_2,V_u_2))<->hBOOL(hAPP(hAPP(V_less__e_q_2,V_l_2),V_i_2))&hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))).
% 12.38/12.29 all V_u_2 V_l_2 V_less_2 V_less__e_q_2 V_i_2 T_a (c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__e_q_2,V_less_2,V_l_2,V_u_2))<->hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))&hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_u_2))).
% 12.38/12.29 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)))))).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.29 all V_y V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)).
% 12.38/12.29 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> (V_m!=V_n->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 12.38/12.29 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_m=V_n->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.29 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 12.38/12.29 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)).
% 12.38/12.29 all V_y V_x (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x))).
% 12.38/12.29 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 12.38/12.29 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)->V_m!=V_n).
% 12.38/12.29 all V_t V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)->V_s!=V_t).
% 12.38/12.29 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))))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->V_m=V_n)).
% 12.38/12.29 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_k))).
% 12.38/12.29 all V_n V_m (V_m=V_n->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.29 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)).
% 12.38/12.29 all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 all V_n_2 V_m_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_m_2),c_SetInterval_Oord__class_OlessThan(T_a,V_n_2))<->c_Orderings_Oord__class_Oless(T_a,V_m_2,V_n_2))).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(T_a,V_xa_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_ya_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2))).
% 12.38/12.29 all V_f_2 T_a T_b (class_Orderings_Oorder(T_b)&class_Orderings_Oorder(T_a)-> ((all B_x B_y (c_Orderings_Oord__class_Oless(T_a,B_x,B_y)->c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,B_x),hAPP(V_f_2,B_y))))->c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2))).
% 12.38/12.29 all V_k_2 V_i_2 T_a (class_Orderings_Oord(T_a)-> (c_member(T_a,V_i_2,c_SetInterval_Oord__class_OgreaterThan(T_a,V_k_2))<->c_Orderings_Oord__class_Oless(T_a,V_k_2,V_i_2))).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_xa_2),c_SetInterval_Oord__class_OlessThan(T_a,V_ya_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2))).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (c_SetInterval_Oord__class_OlessThan(T_a,V_xa_2)=c_SetInterval_Oord__class_OlessThan(T_a,V_ya_2)<->V_xa_2=V_ya_2)).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (c_SetInterval_Oord__class_OgreaterThan(T_a,V_xa_2)=c_SetInterval_Oord__class_OgreaterThan(T_a,V_ya_2)<->V_xa_2=V_ya_2)).
% 12.38/12.29 all V_k_2 V_i_2 T_a (class_Orderings_Oord(T_a)-> (c_member(T_a,V_i_2,c_SetInterval_Oord__class_OlessThan(T_a,V_k_2))<->c_Orderings_Oord__class_Oless(T_a,V_i_2,V_k_2))).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_xa_2),c_SetInterval_Oord__class_OatMost(T_a,V_ya_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2))).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeast(T_a,V_xa_2),c_SetInterval_Oord__class_OatLeast(T_a,V_ya_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2))).
% 12.38/12.29 all V_k_2 V_i_2 T_a (class_Orderings_Oord(T_a)-> (c_member(T_a,V_i_2,c_SetInterval_Oord__class_OatMost(T_a,V_k_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_i_2,V_k_2))).
% 12.38/12.29 all V_k_2 V_i_2 T_a (class_Orderings_Oord(T_a)-> (c_member(T_a,V_i_2,c_SetInterval_Oord__class_OatLeast(T_a,V_k_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_k_2,V_i_2))).
% 12.38/12.29 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y))).
% 12.38/12.29 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)))).
% 12.38/12.29 all V_A_2 V_xa_2 T_a (c_member(T_a,V_xa_2,V_A_2)-> -(all B_B (V_A_2=c_Set_Oinsert(T_a,V_xa_2,B_B)->c_member(T_a,V_xa_2,B_B)))).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (c_SetInterval_Oord__class_OatLeast(T_a,V_xa_2)=c_SetInterval_Oord__class_OatLeast(T_a,V_ya_2)<->V_xa_2=V_ya_2)).
% 12.38/12.29 all V_ya_2 V_xa_2 T_a (class_Orderings_Olinorder(T_a)-> (c_SetInterval_Oord__class_OatMost(T_a,V_xa_2)=c_SetInterval_Oord__class_OatMost(T_a,V_ya_2)<->V_xa_2=V_ya_2)).
% 12.38/12.29 all V_u_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_u_2))=c_SetInterval_Oord__class_OatLeast(T_a,V_l_2))).
% 12.38/12.29 all V_u_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_l_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2))=c_SetInterval_Oord__class_OatMost(T_a,V_u_2))).
% 12.38/12.29 all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)).
% 12.38/12.29 all V_x c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)).
% 12.38/12.29 all V_A_2 V_a_2 T_a (c_member(T_a,V_a_2,V_A_2)-> (exists B_B (V_A_2=c_Set_Oinsert(T_a,V_a_2,B_B)& -c_member(T_a,V_a_2,B_B)))).
% 12.38/12.29 all V_n_2 V_f_2 (c_SEQ_Osubse_q(V_f_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,hAPP(V_f_2,V_n_2))).
% 12.38/12.29 all V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y))).
% 12.38/12.29 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)))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.38/12.29 all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 12.38/12.29 c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)).
% 12.38/12.29 all V_n_2 (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)=c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,V_n_2)).
% 12.38/12.29 all V_x c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)).
% 12.38/12.29 all V_n (c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n).
% 12.38/12.29 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).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))))).
% 12.38/12.29 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))))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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).
% 12.38/12.29 all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 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))).
% 12.38/12.29 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)))).
% 12.38/12.29 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))).
% 12.38/12.29 all V_n (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)).
% 12.38/12.29 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.29 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.38/12.29 all V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 12.38/12.29 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.38/12.29 all V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.29 all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 12.38/12.29 all V_n (c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 all V_x c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))).
% 12.38/12.29 all V_f_2 (c_SEQ_Osubse_q(V_f_2)<-> (all B_m B_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,B_m),hAPP(V_f_2,B_n))))).
% 12.38/12.29 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))).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 all V_Pa_2 V_n_2 ((all B_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,V_n_2)->hBOOL(hAPP(V_Pa_2,B_m))))<-> (all B_x (c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))->hBOOL(hAPP(V_Pa_2,B_x))))).
% 12.38/12.29 all V_Pa_2 V_n_2 ((exists B_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,V_n_2)&hBOOL(hAPP(V_Pa_2,B_m))))<-> (exists B_x (c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))&hBOOL(hAPP(V_Pa_2,B_x))))).
% 12.38/12.29 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)))).
% 12.38/12.29 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)))).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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)))).
% 12.38/12.29 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))))).
% 12.38/12.29 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)))).
% 12.38/12.29 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)))).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)))).
% 12.38/12.29 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)))).
% 12.38/12.29 all V_z_2 V_ya_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_ya_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_ya_2,V_z_2))).
% 12.38/12.29 all V_ya_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_ya_2)<->c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_ya_2)=V_ya_2)).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 all V_u_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_l_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OatLeast(T_a,V_u_2))=c_SetInterval_Oord__class_OgreaterThan(T_a,V_l_2))).
% 12.38/12.29 all V_u_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_l_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_l_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2))=c_SetInterval_Oord__class_OlessThan(T_a,V_u_2))).
% 12.38/12.29 all V_n V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n))).
% 12.38/12.29 all V_l_2 T_a (class_Orderings_Olinorder(T_a)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_l_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(T_a,V_l_2))=c_SetInterval_Oord__class_OatLeast(T_a,V_l_2)).
% 12.38/12.29 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)))).
% 12.38/12.29 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))).
% 12.38/12.29 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)))).
% 12.38/12.29 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).
% 12.38/12.29 all V_n c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 12.38/12.29 all V_k_2 V_l_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_k_2)->c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_k_2,V_l_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 12.38/12.29 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)))).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 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))))).
% 12.38/12.29 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))))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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)))).
% 12.38/12.29 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)).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 all V_ya_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_ya_2)=c_Orderings_Obot__class_Obot(T_a)<->V_xa_2=c_Orderings_Obot__class_Obot(T_a)&V_ya_2=c_Orderings_Obot__class_Obot(T_a))).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 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)))).
% 12.38/12.29 all V_b_2 V_a_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)<-> -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2))).
% 12.38/12.29 all V_b_2 V_a_2 T_a (class_Orderings_Oorder(T_a)-> (c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))<-> -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2))).
% 12.38/12.29 all V_a_2 V_b_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)->c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 12.38/12.29 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)).
% 12.38/12.29 all V_b_2 V_a_2 T_a (class_Orderings_Oorder(T_a)-> (V_a_2=V_b_2->c_SetInterval_Oord__class_OatLeastAtMost(T_a,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))))).
% 12.38/12.29 all V_c_2 V_b_2 V_a_2 T_a (class_Orderings_Oorder(T_a)-> (c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)=c_Set_Oinsert(T_a,V_c_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))<->V_a_2=V_b_2&V_b_2=V_c_2)).
% 12.38/12.29 all V_a_2 T_a (class_Orderings_Oorder(T_a)->c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_a_2)=c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 12.38/12.29 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.38/12.29 all V_n_2 (c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.29 all V_n (-c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 12.38/12.29 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)).
% 12.38/12.29 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.29 c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Set_Oinsert(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))).
% 12.38/12.29 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.29 all V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.29 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_RComplete_Onatfloor(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.29 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))->c_RComplete_Onatceiling(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.29 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x)).
% 12.38/12.29 all V_n_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 12.38/12.29 all V_u_2 T_a (class_Orderings_Olinorder(T_a)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_u_2),c_Set_Oinsert(T_a,V_u_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=c_SetInterval_Oord__class_OatMost(T_a,V_u_2)).
% 12.38/12.29 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).
% 12.38/12.29 all V_u_2 V_m_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_l_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_m_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2))=c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)))).
% 12.38/12.29 all V_u_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_l_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2),c_Set_Oinsert(T_a,V_u_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2))).
% 12.38/12.29 all V_u_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_l_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2))=c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2))).
% 12.38/12.29 all V_u_2 V_m_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_m_2)-> (c_Orderings_Oord__class_Oless(T_a,V_m_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2))=c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2)))).
% 12.38/12.29 all V_n_2 (c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)=c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,V_n_2)).
% 12.38/12.29 all V_m_2 (c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))).
% 12.38/12.29 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Orderings_Olinorder(T_a)-> (c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)=c_SetInterval_Oord__class_OatLeastLessThan(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)->V_b_2=V_d_2)))).
% 12.38/12.29 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Orderings_Olinorder(T_a)-> (c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)=c_SetInterval_Oord__class_OatLeastLessThan(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)->V_a_2=V_c_2)))).
% 12.38/12.29 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Orderings_Olinorder(T_a)-> (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)-> (c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)=c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2)<->V_a_2=V_c_2&V_b_2=V_d_2)))).
% 12.38/12.29 c_Orderings_Obot__class_Obot(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.29 all V_Pa_2 V_n_2 ((all B_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,V_n_2)->hBOOL(hAPP(V_Pa_2,B_m))))<-> (all B_x (c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))->hBOOL(hAPP(V_Pa_2,B_x))))).
% 12.38/12.29 all V_Pa_2 V_n_2 ((exists B_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,V_n_2)&hBOOL(hAPP(V_Pa_2,B_m))))<-> (exists B_x (c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))&hBOOL(hAPP(V_Pa_2,B_x))))).
% 12.38/12.29 all V_a_2 V_b_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2)->c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 12.38/12.29 all V_b_2 V_a_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)<-> -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2))).
% 12.38/12.29 all V_b_2 V_a_2 T_a (class_Orderings_Oorder(T_a)-> (c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))<-> -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2))).
% 12.38/12.29 all V_d_2 V_c_2 V_b_2 V_a_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2))->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_a_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_d_2))).
% 12.38/12.29 all V_u_2 V_m_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_m_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2,V_u_2))=c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2)))).
% 12.38/12.29 all V_k_2 V_l_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_k_2)->c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 12.38/12.29 all V_l_2 V_k_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2)<-> -c_Orderings_Oord__class_Oless(T_a,V_k_2,V_l_2))).
% 12.38/12.29 all V_l_2 V_k_2 T_a (class_Orderings_Oorder(T_a)-> (c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))<-> -c_Orderings_Oord__class_Oless(T_a,V_k_2,V_l_2))).
% 12.38/12.29 all V_u_2 V_m_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_m_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2))=c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2)))).
% 12.38/12.29 all V_u_2 V_m_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_m_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2))=c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)))).
% 12.38/12.29 all V_u_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_l_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2))=c_SetInterval_Oord__class_OlessThan(T_a,V_u_2))).
% 12.38/12.29 all V_u_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OatLeast(T_a,V_u_2))=c_SetInterval_Oord__class_OatLeast(T_a,V_l_2))).
% 12.38/12.29 all V_u_2 V_m_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_m_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2))=c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2)))).
% 12.38/12.29 all V_u_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_l_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2))=c_SetInterval_Oord__class_OatMost(T_a,V_u_2))).
% 12.38/12.29 all V_u_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_u_2))=c_SetInterval_Oord__class_OgreaterThan(T_a,V_l_2))).
% 12.38/12.29 all V_u_2 V_m_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_l_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_m_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2,V_u_2))=c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)))).
% 12.38/12.29 all V_u_2 V_m_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_m_2)-> (c_Orderings_Oord__class_Oless(T_a,V_m_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2))=c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2)))).
% 12.38/12.29 all V_u_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2),c_Set_Oinsert(T_a,V_u_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2))).
% 12.38/12.29 all V_u_2 V_l_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_l_2,V_u_2)->c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_l_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2))=c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2))).
% 12.38/12.29 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)))).
% 12.38/12.29 all V_n_2 T_a (class_Orderings_Oorder(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_n_2),c_SetInterval_Oord__class_OatLeast(T_a,V_n_2))=c_Set_Oinsert(T_a,V_n_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)))).
% 12.38/12.29 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)))).
% 12.38/12.29 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)))).
% 12.38/12.29 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))).
% 12.38/12.29 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)))).
% 12.38/12.29 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))).
% 12.38/12.29 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)))).
% 12.38/12.29 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))).
% 12.38/12.29 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).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 all V_ya_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_ya_2)=c_Orderings_Otop__class_Otop(T_a)<->V_xa_2=c_Orderings_Otop__class_Otop(T_a)&V_ya_2=c_Orderings_Otop__class_Otop(T_a))).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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))))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 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)))).
% 12.38/12.29 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)))).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 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)).
% 12.38/12.29 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)))).
% 12.38/12.29 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).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 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).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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)))).
% 12.38/12.29 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))))).
% 12.38/12.29 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))))).
% 12.38/12.29 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))))).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 all V_z_2 V_ya_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_ya_2,V_z_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_z_2))).
% 12.38/12.29 all V_ya_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_ya_2)<->c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_xa_2,V_ya_2)=V_xa_2)).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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)))).
% 12.38/12.29 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)))).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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))).
% 12.38/12.29 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))).
% 12.38/12.29 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)).
% 12.38/12.29 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)))).
% 12.38/12.29 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)).
% 12.38/12.29 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)).
% 12.38/12.29 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))))).
% 12.38/12.29 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))).
% 12.38/12.29 all V_m_2 V_n_2 V_i_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_i_2,V_n_2)->c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2,V_m_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2,V_n_2))=c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_n_2,V_m_2))).
% 12.38/12.29 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)).
% 12.38/12.30 all V_u_2 V_m_2 V_l_2 T_a (class_Orderings_Oorder(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.30 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).
% 12.38/12.30 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))).
% 12.38/12.30 all V_u_2 V_m_2 V_l_2 T_a (class_Orderings_Oorder(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.30 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).
% 12.38/12.30 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).
% 12.38/12.30 all V_u_2 V_m_2 V_l_2 T_a (class_Orderings_Oorder(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.30 all V_k_2 T_a (class_Orderings_Oorder(T_a)->c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_k_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(T_a,V_k_2))=c_Set_Oinsert(T_a,V_k_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 12.38/12.30 all V_u_2 V_l_2 T_a (class_Orderings_Oorder(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_l_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.30 all V_u_2 V_l_2 T_a (class_Orderings_Oorder(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_l_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.30 all V_u_2 V_m_2 V_l_2 T_a (class_Orderings_Oorder(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.30 all V_u_2 V_m_2 V_l_2 T_a (class_Orderings_Oorder(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.30 all V_u_2 V_m_2 V_l_2 T_a (class_Orderings_Oorder(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.30 all V_u_2 V_m_2 V_l_2 T_a (class_Orderings_Oorder(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.30 all V_u_2 V_l_2 T_a (class_Orderings_Oorder(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OatLeast(T_a,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.30 all V_u_2 V_l_2 T_a (class_Orderings_Oorder(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.30 all V_u_2 V_l_2 T_a (class_Orderings_Oorder(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_l_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.30 all V_u_2 V_l_2 T_a (class_Orderings_Oorder(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_l_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.30 all V_u_2 V_m_2 V_l_2 T_a (class_Orderings_Oorder(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.30 all V_u_2 V_l_2 T_a (class_Orderings_Oorder(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OatLeast(T_a,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.30 all V_u_2 V_l_2 T_a (class_Orderings_Oorder(T_a)->c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.30 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))).
% 12.38/12.30 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))).
% 12.38/12.30 all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))).
% 12.38/12.30 all V_b_2 V_a_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))).
% 12.38/12.30 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)))).
% 12.38/12.30 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)))).
% 12.38/12.30 all V_b_2 V_a_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=V_b_2)).
% 12.38/12.30 all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->V_m=V_n)).
% 12.38/12.30 all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.30 all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 12.38/12.30 all V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.30 all V_n V_k V_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k)).
% 12.38/12.30 all V_l V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)))).
% 12.38/12.30 all V_n V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m).
% 12.38/12.30 all V_l V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))).
% 12.38/12.30 all V_l V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l))).
% 12.38/12.30 all V_n V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i))=V_i).
% 12.38/12.30 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))).
% 12.38/12.30 all V_n V_m V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_m)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))).
% 12.38/12.30 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)))).
% 12.38/12.30 all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 12.38/12.30 all V_x V_a (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)->c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)).
% 12.38/12.30 all V_x V_a (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)->c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)).
% 12.38/12.30 all V_ya_2 V_xa_2 (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)<->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_xa_2,V_ya_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))).
% 12.38/12.30 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m))).
% 12.38/12.30 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)).
% 12.38/12.30 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.30 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)).
% 12.38/12.30 all V_c V_b V_a (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_c,V_a)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)))).
% 12.38/12.30 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)))).
% 12.38/12.30 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))).
% 12.38/12.30 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))).
% 12.38/12.30 all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 12.38/12.30 all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.30 all V_b_2 V_a_2 T_a (class_Groups_Oab__group__add(T_a)-> (V_a_2=V_b_2<->c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a))).
% 12.38/12.30 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))))).
% 12.38/12.30 all V_ya_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_ya_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_ya_2)))).
% 12.38/12.30 all V_p_2 T_a (class_Groups_Ozero(T_a)-> (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_p_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 12.38/12.30 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)).
% 12.38/12.30 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).
% 12.38/12.30 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).
% 12.38/12.30 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)))).
% 12.38/12.30 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))).
% 12.38/12.30 all V_n_2 V_m_2 ((c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)->c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))=c_Set_Oinsert(tc_Nat_Onat,V_n_2,c_SetInterval_Oord__class_OatLeastLessThan(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)->c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))).
% 12.38/12.30 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))).
% 12.38/12.30 all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)).
% 12.38/12.30 all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)).
% 12.38/12.30 all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.30 all V_k V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k)).
% 12.38/12.30 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.38/12.30 c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.38/12.30 all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m)).
% 12.38/12.30 all V_nat_H (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_nat_H)).
% 12.38/12.30 all V_m (c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.30 all V_nat_H_1 (c_Nat_OSuc(V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.30 all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m)).
% 12.38/12.30 all V_m (c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.30 all T_a (class_Rings_Ozero__ne_q__one(T_a)->c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.30 all T_a (class_Rings_Ozero__ne_q__one(T_a)->c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a)).
% 12.38/12.30 all V_k_2 (c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,c_Nat_OSuc(V_k_2))=c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,V_k_2)).
% 12.38/12.30 all V_u_2 V_l_2 (c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Nat_OSuc(V_l_2),V_u_2)=c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)).
% 12.38/12.30 all V_y V_x (c_Nat_OSuc(V_x)=c_Nat_OSuc(V_y)->V_x=V_y).
% 12.38/12.30 all V_nat_H_2 V_nat_2 (c_Nat_OSuc(V_nat_2)=c_Nat_OSuc(V_nat_H_2)<->V_nat_2=V_nat_H_2).
% 12.38/12.30 all V_n (c_Nat_OSuc(V_n)!=V_n).
% 12.38/12.30 all V_n (V_n!=c_Nat_OSuc(V_n)).
% 12.38/12.30 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.30 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))-> (-c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->V_m=c_Nat_OSuc(V_n))).
% 12.38/12.30 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))).
% 12.38/12.30 all V_m_2 V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2)).
% 12.38/12.30 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=c_Nat_OSuc(V_n_2)).
% 12.38/12.30 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__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2)).
% 12.38/12.30 all V_n (-c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n)).
% 12.38/12.30 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.30 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.30 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))-> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->V_m=V_n)).
% 12.38/12.30 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k))).
% 12.38/12.30 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)-> (c_Nat_OSuc(V_m)!=V_n->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n))).
% 12.38/12.30 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))).
% 12.38/12.30 all V_m V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))->V_m=V_n)).
% 12.38/12.30 all V_m_2 V_n_2 (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))<->V_n_2=V_m_2)).
% 12.38/12.30 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 12.38/12.30 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2).
% 12.38/12.30 all V_n_2 V_m_2 (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))).
% 12.38/12.30 all V_u_2 V_l_2 (c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Nat_OSuc(V_l_2),V_u_2)=c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)).
% 12.38/12.30 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))).
% 12.38/12.30 all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))).
% 12.38/12.30 all T_a (class_Rings_Olinordered__semidom(T_a)-> -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))).
% 12.38/12.30 all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))).
% 12.38/12.30 all T_a (class_Rings_Olinordered__semidom(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))).
% 12.38/12.30 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| (exists B_j (V_m_2=c_Nat_OSuc(B_j)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)))).
% 12.38/12.30 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.30 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)<-> (exists B_m (V_n_2=c_Nat_OSuc(B_m)))).
% 12.38/12.30 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_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2)).
% 12.38/12.30 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)).
% 12.38/12.30 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 12.38/12.30 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))).
% 12.38/12.30 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)).
% 12.38/12.30 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_n_2,c_Nat_OSuc(V_m_2))<->V_n_2=V_m_2)).
% 12.38/12.30 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.30 all V_n V_m c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)).
% 12.38/12.30 all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))).
% 12.38/12.30 all V_X_2 T_a (class_Orderings_Oorder(T_a)-> (c_SEQ_Omonose_q(T_a,V_X_2)<-> (all B_n c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,c_Nat_OSuc(B_n))))| (all B_n c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,c_Nat_OSuc(B_n)),hAPP(V_X_2,B_n))))).
% 12.38/12.30 all V_u_2 V_l_2 (c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2,c_Nat_OSuc(V_u_2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)).
% 12.38/12.30 all V_k_2 (c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_Nat_OSuc(V_k_2))=c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,V_k_2),c_Set_Oinsert(tc_Nat_Onat,c_Nat_OSuc(V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))).
% 12.38/12.30 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))).
% 12.38/12.30 all V_k_2 (c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,c_Nat_OSuc(V_k_2))=c_Set_Oinsert(tc_Nat_Onat,V_k_2,c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,V_k_2))).
% 12.38/12.30 all V_k_2 (c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,c_Nat_OSuc(V_k_2))=c_Set_Oinsert(tc_Nat_Onat,c_Nat_OSuc(V_k_2),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,V_k_2))).
% 12.38/12.30 all V_f_2 (c_SEQ_Osubse_q(V_f_2)<-> (all B_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,B_n),hAPP(V_f_2,c_Nat_OSuc(B_n))))).
% 12.38/12.30 all V_k_2 (c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,c_Nat_OSuc(V_k_2))=c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,V_k_2)).
% 12.38/12.30 all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n).
% 12.38/12.30 all V_i V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n)).
% 12.38/12.30 all V_n c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))).
% 12.38/12.30 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))->c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))=c_Set_Oinsert(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))).
% 12.38/12.30 all V_m_2 (c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_m_2))=c_Set_Oinsert(tc_Nat_Onat,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))).
% 12.38/12.30 all V_k_2 (c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,c_Nat_OSuc(V_k_2))=c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,V_k_2),c_Set_Oinsert(tc_Nat_Onat,V_k_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))).
% 12.38/12.30 all V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Nat_OSuc(V_j_2))->c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,c_Nat_OSuc(V_j_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2),c_Set_Oinsert(tc_Nat_Onat,c_Nat_OSuc(V_j_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))).
% 12.38/12.30 all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))->V_x=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.38/12.30 all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)).
% 12.38/12.30 c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.30 all V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n).
% 12.38/12.30 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.38/12.30 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.38/12.30 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.38/12.30 all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->V_n=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 12.38/12.30 all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=V_n).
% 12.38/12.30 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)).
% 12.38/12.30 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))).
% 12.38/12.30 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)).
% 12.38/12.30 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))))).
% 12.38/12.30 all V_r (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)-> (exists B_n (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B_n),V_r)&c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n)))))).
% 12.38/12.30 all V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j_2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))->c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j_2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2),c_Set_Oinsert(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j_2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))).
% 12.38/12.30 all V_n V_z (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 12.38/12.30 all V_x V_n (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))->c_RComplete_Onatfloor(V_x)=V_n)).
% 12.38/12.30 all V_a T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)))).
% 12.38/12.30 all V_n_2 V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.38/12.30 all V_n_2 V_m_2 (c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)<->V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.38/12.30 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)).
% 12.38/12.30 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)<-> (exists B_k (V_n_2=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k))))).
% 12.38/12.30 all V_m V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))).
% 12.38/12.30 all V_m V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))).
% 12.38/12.30 all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.30 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))).
% 12.38/12.30 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))).
% 12.38/12.30 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))).
% 12.38/12.30 all V_c V_b V_a T_a (class_Groups_Oab__semigroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))).
% 12.38/12.30 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)).
% 12.38/12.30 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)).
% 12.38/12.30 all V_c V_b V_a T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)->V_b=V_c)).
% 12.38/12.30 all V_c V_b V_a T_a (class_Groups_Ocancel__ab__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)->V_b=V_c)).
% 12.38/12.30 all V_c V_a V_b T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_b,V_a)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)->V_b=V_c)).
% 12.38/12.30 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))).
% 12.38/12.30 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))).
% 12.38/12.30 all V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))).
% 12.38/12.30 all V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)))).
% 12.38/12.30 all V_d V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 12.38/12.30 all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b))).
% 12.38/12.30 all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b))).
% 12.38/12.30 all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 12.38/12.30 all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 12.38/12.30 all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 12.38/12.30 all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)))).
% 12.38/12.30 all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))).
% 12.38/12.30 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))).
% 12.38/12.30 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))).
% 12.38/12.30 all V_z V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y))).
% 12.38/12.30 all V_j V_i (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i)).
% 12.38/12.30 all V_i V_j (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i)).
% 12.38/12.30 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)).
% 12.38/12.30 all V_m V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))).
% 12.38/12.30 all V_m V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))).
% 12.38/12.30 all V_z V_y V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 12.38/12.30 all V_y V_z V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 12.38/12.30 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))).
% 12.38/12.30 all V_l V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)))).
% 12.38/12.30 all V_n V_m V_l V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)-> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 12.38/12.30 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k)).
% 12.38/12.30 all V_m V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.30 all V_m V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)).
% 12.38/12.30 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)))).
% 12.38/12.30 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)).
% 12.38/12.30 all V_m V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))).
% 12.38/12.30 all V_m V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))).
% 12.38/12.30 all V_z V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 12.38/12.30 all V_y V_z V_x (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_z)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 12.38/12.30 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))).
% 12.38/12.30 all V_l V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)))).
% 12.38/12.30 all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)).
% 12.38/12.30 all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.30 all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)-> -(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n))).
% 12.38/12.30 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)).
% 12.38/12.30 all V_z V_y V_x (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z))).
% 12.38/12.30 all V_k V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))).
% 12.38/12.30 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).
% 12.38/12.30 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).
% 12.38/12.30 all V_n V_m (c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 12.38/12.30 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=V_m->V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.30 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)).
% 12.38/12.30 all V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 12.38/12.30 all V_n (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n).
% 12.38/12.30 all V_a T_a (class_Groups_Omonoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a).
% 12.38/12.30 all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a).
% 12.38/12.30 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.38/12.30 all V_a T_a (class_Groups_Omonoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 12.38/12.30 all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 12.38/12.30 all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)).
% 12.38/12.30 all V_a V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)).
% 12.38/12.30 all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 12.38/12.30 all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 12.38/12.30 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 12.38/12.30 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 12.38/12.30 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 12.38/12.30 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 12.38/12.30 all V_c V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 12.38/12.30 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 12.38/12.30 all V_a V_b V_c T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 12.38/12.30 all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 12.38/12.30 all V_ya_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_ya_2)-> (c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_xa_2=c_Groups_Ozero__class_Ozero(T_a)&V_ya_2=c_Groups_Ozero__class_Ozero(T_a))))).
% 12.38/12.30 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 12.38/12.30 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 12.38/12.30 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2))).
% 12.38/12.30 all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n)=V_m).
% 12.38/12.30 all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n)=V_m).
% 12.38/12.30 all V_k V_j V_i (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))).
% 12.38/12.30 all V_n V_m V_k (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.30 all V_n V_k V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.30 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=V_a).
% 12.38/12.30 all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b)=V_a).
% 12.38/12.30 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))).
% 12.38/12.30 all V_k_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2)).
% 12.38/12.30 all V_n V_m (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m).
% 12.38/12.30 all V_n (c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 12.38/12.30 all V_n (c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)).
% 12.38/12.30 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j)).
% 12.38/12.30 all V_i_2 V_k_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2))).
% 12.38/12.30 all V_m V_n V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k))).
% 12.38/12.30 all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m).
% 12.38/12.30 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)).
% 12.38/12.30 all V_i_2 V_j_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2))).
% 12.38/12.30 all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)=V_m).
% 12.38/12.30 all V_k_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_k_2<->V_j_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2))).
% 12.38/12.30 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))).
% 12.38/12.30 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)).
% 12.38/12.30 all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)).
% 12.38/12.30 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))))).
% 12.38/12.30 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 12.38/12.30 all V_x (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)->c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 12.38/12.30 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 12.38/12.30 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 12.38/12.30 all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 12.38/12.30 all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 12.38/12.30 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 12.38/12.30 all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 12.38/12.30 all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))).
% 12.38/12.30 all V_x V_n (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)-> (c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))->c_RComplete_Onatceiling(V_x)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 12.38/12.30 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))))).
% 12.38/12.30 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)))))).
% 12.38/12.30 all V_m V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m))).
% 12.38/12.30 all V_m V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j))).
% 12.38/12.30 all V_n (c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 12.38/12.30 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_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j_2,V_k_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2,V_j_2),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j_2,V_k_2)))).
% 12.38/12.30 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))).
% 12.38/12.30 all V_n V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=V_n)& (V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)))).
% 12.38/12.30 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)))).
% 12.38/12.30 all V_x c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 12.38/12.30 all V_a_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 12.38/12.30 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)<-> (exists B_n (V_l_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n)))).
% 12.38/12.30 all V_a_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.38/12.30 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))))).
% 12.38/12.30 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a).
% 12.38/12.30 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))).
% 12.38/12.30 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))))).
% 12.38/12.30 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))))).
% 12.38/12.30 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))).
% 12.38/12.30 all V_d V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))).
% 12.38/12.30 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b)).
% 12.38/12.30 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))).
% 12.38/12.30 all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d)).
% 12.38/12.30 all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d))).
% 12.38/12.30 all V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)).
% 12.38/12.30 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)).
% 12.38/12.30 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)))).
% 12.38/12.30 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))).
% 12.38/12.30 all V_a_2 V_b_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_b_2=c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.38/12.30 all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 12.38/12.30 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)))))))).
% 12.38/12.30 all V_v (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v))->c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 12.38/12.30 all V_w_2 T_a (class_Int_Onumber__ring(T_a)->c_member(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Int_Oring__1__class_OInts(T_a))).
% 12.38/12.30 all V_ya_2 V_xa_2 T_a (class_Int_Onumber__ring(T_a)&class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,V_ya_2))).
% 12.38/12.30 all V_ya_2 V_xa_2 T_a (class_Int_Onumber__ring(T_a)&class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_xa_2,V_ya_2))).
% 12.38/12.30 all V_ya_2 V_xa_2 T_a (class_Int_Onumber__ring(T_a)&class_Int_Oring__char__0(T_a)-> (c_Int_Onumber__class_Onumber__of(T_a,V_xa_2)=c_Int_Onumber__class_Onumber__of(T_a,V_ya_2)<->V_xa_2=V_ya_2)).
% 12.38/12.30 all V_xa_2 V_w_2 T_a (class_Int_Onumber(T_a)-> (c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=V_xa_2<->V_xa_2=c_Int_Onumber__class_Onumber__of(T_a,V_w_2))).
% 12.38/12.30 all V_w_2 V_v_2 T_a (class_Int_Onumber(T_a)&class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))<-> -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)))).
% 12.38/12.30 all V_w V_v T_a (class_Int_Onumber__ring(T_a)->c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_v,V_w))=c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))).
% 12.38/12.30 all V_c V_w V_v T_a (class_Int_Onumber__ring(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_c))=c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_c)).
% 12.38/12.30 all V_w V_v T_a (class_Int_Onumber__ring(T_a)->c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w))=c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))).
% 12.38/12.30 all V_w V_v T_a (class_Int_Onumber__ring(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))=c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w))).
% 12.38/12.30 all V_z V_w V_v T_a (class_Int_Onumber__ring(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z))=c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_z)).
% 12.38/12.30 all V_M_2 (c_Finite__Set_Ofinite(tc_Nat_Onat,V_M_2)->c_GCD_Ogcd__class_OGcd(tc_Nat_Onat,V_M_2)=c_GCD_Ogcd__class_OGcd(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool),V_M_2,c_Set_Oinsert(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))).
% 12.38/12.30 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,c_Groups_Otimes__class_Otimes(T_a,V_u,V_x),c_Groups_Otimes__class_Otimes(T_a,V_v,V_y)),V_a))))))).
% 12.38/12.30 all V_u_2 V_l_2 c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2,V_u_2)).
% 12.38/12.30 all V_u_2 V_l_2 c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)).
% 12.38/12.30 all V_k_2 c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,V_k_2)).
% 12.38/12.30 all V_k_2 c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,V_k_2)).
% 12.38/12.30 all V_u_2 V_l_2 c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)).
% 12.38/12.30 all V_u_2 V_l_2 c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)).
% 12.38/12.30 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_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Int_Oring__1__class_OInts(T_a))))).
% 12.38/12.30 all V_n (c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n)).
% 12.38/12.30 all V_n (c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n)).
% 12.38/12.30 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)).
% 12.38/12.30 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2)).
% 12.38/12.30 all V_z V_w V_v T_a (class_Int_Onumber__ring(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z))=c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)),V_z)).
% 12.38/12.30 all V_w V_v T_a (class_Int_Onumber__ring(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))=c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w))).
% 12.38/12.30 all V_w V_v T_a (class_Int_Onumber__ring(T_a)->c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w))=c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))).
% 12.38/12.30 all V_v V_b V_a T_b (class_Int_Onumber(T_b)&class_Rings_Oring(T_b)->c_Groups_Otimes__class_Otimes(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))=c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)))).
% 12.38/12.30 all V_c V_b V_v T_b (class_Int_Onumber(T_b)&class_Rings_Oring(T_b)->c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Ominus__class_Ominus(T_b,V_b,V_c))=c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c))).
% 12.38/12.30 all V_w V_v (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))=c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w))).
% 12.38/12.30 all V_c V_b V_v T_b (class_Int_Onumber(T_b)&class_Rings_Osemiring(T_b)->c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Oplus__class_Oplus(T_b,V_b,V_c))=c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c))).
% 12.38/12.30 all V_v V_b V_a T_b (class_Int_Onumber(T_b)&class_Rings_Osemiring(T_b)->c_Groups_Otimes__class_Otimes(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))=c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)))).
% 12.38/12.30 all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.38/12.30 all V_z (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z))).
% 12.38/12.30 all V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 12.38/12.30 all V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))->c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2),c_Set_Oinsert(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))))).
% 12.38/12.30 all V_u_2 V_l_2 (c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_l_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2)=c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2)).
% 12.38/12.30 all V_u_2 V_l_2 (c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_u_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)).
% 12.38/12.30 all V_z V_w (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)).
% 12.38/12.30 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)).
% 12.38/12.30 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,V_z_2)).
% 12.38/12.30 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)|V_w_2=V_z_2).
% 12.38/12.30 all V_u_2 V_l_2 (c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_l_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2)=c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2)).
% 12.38/12.30 all V_n V_m (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n))).
% 12.38/12.30 all V_n V_m (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n))).
% 12.38/12.30 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k))).
% 12.38/12.30 all V_n V_m V_k (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,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n))).
% 12.38/12.30 all V_k V_n V_m (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,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k))).
% 12.38/12.30 all V_z V_z_H V_w V_w_H (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_H,V_z)->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)))).
% 12.38/12.30 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j))).
% 12.38/12.30 all V_w V_z2 V_z1 (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,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2,V_w))).
% 12.38/12.30 all V_w V_z2 V_z1 (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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_w))).
% 12.38/12.30 all V_z3 V_z2 V_z1 (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3))).
% 12.38/12.30 all V_z2 V_z1 V_w (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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z2))).
% 12.38/12.30 all V_z V_y V_x (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z))).
% 12.38/12.30 all V_w V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)).
% 12.38/12.30 all V_c V_b V_a T_a (class_Rings_Ocomm__semiring(T_a)->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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))).
% 12.38/12.30 all V_c V_b V_e V_a T_a (class_Rings_Osemiring(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_e),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_e),V_c))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_e),V_c)).
% 12.38/12.30 all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z).
% 12.38/12.30 all V_z (c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)=V_z).
% 12.38/12.30 all V_b V_a V_y V_x T_a (class_Rings_Oring(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b))).
% 12.38/12.30 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,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2)=c_Groups_Oplus__class_Oplus(T_a,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,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_e_2),V_d_2))).
% 12.38/12.30 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,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2)<->c_Groups_Oplus__class_Oplus(T_a,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)).
% 12.38/12.30 all V_ya_2 V_xa_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(T_a,V_ya_2,V_ya_2))=c_Groups_Ozero__class_Ozero(T_a)<->V_xa_2=c_Groups_Ozero__class_Ozero(T_a)&V_ya_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.38/12.30 all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 12.38/12.30 all V_z2 V_z1 V_w (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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z2))).
% 12.38/12.30 all V_w V_z2 V_z1 (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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_w))).
% 12.38/12.30 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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_j)))).
% 12.38/12.30 all V_w c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_w).
% 12.38/12.30 all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z)).
% 12.38/12.30 all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_j,V_k)->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_k))).
% 12.38/12.30 all V_w V_z (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)-> (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z)->V_z=V_w)).
% 12.38/12.30 all V_w_2 V_z_2 (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_w_2)&V_z_2!=V_w_2).
% 12.38/12.30 all V_y V_x (c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x)).
% 12.38/12.30 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 12.38/12.30 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)-> (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))).
% 12.38/12.30 all V_z_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)<->c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)).
% 12.38/12.30 all V_z_2 V_w_2 (c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))<->c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)).
% 12.38/12.30 all V_ya_2 V_xa_2 (c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ya_2,V_ya_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)<->V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)&V_ya_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.38/12.30 all V_M_2 (c_Finite__Set_Ofinite(tc_Nat_Onat,V_M_2)-> (V_M_2!=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))-> (c_GCD_Ogcd__class_OLcm(tc_Nat_Onat,V_M_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->c_member(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_M_2)))).
% 12.38/12.30 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_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))))).
% 12.38/12.30 all V_z (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_z)=V_z).
% 12.38/12.30 all V_n_2 V_m_2 (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)).
% 12.38/12.30 all V_n (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n).
% 12.38/12.30 all V_n_2 V_m_2 (c_Groups_Oone__class_Oone(tc_Nat_Onat)=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)).
% 12.38/12.30 all V_n (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)=V_n).
% 12.38/12.30 all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a).
% 12.38/12.30 all V_a T_a (class_Groups_Omonoid__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a).
% 12.38/12.30 all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a)=V_a).
% 12.38/12.30 all V_a T_a (class_Groups_Omonoid__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a)=V_a).
% 12.38/12.30 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),c_Groups_Otimes__class_Otimes(T_a,V_m,V_n))))).
% 12.38/12.30 all V_M_2 (c_Finite__Set_Ofinite(tc_Nat_Onat,V_M_2)-> (c_member(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_M_2)->c_GCD_Ogcd__class_OLcm(tc_Nat_Onat,V_M_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.38/12.30 all V_n_2 V_m_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.38/12.30 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,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_j)))).
% 12.38/12.30 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,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_k)))).
% 12.38/12.30 all V_n_2 V_k_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),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)).
% 12.38/12.30 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),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)).
% 12.38/12.30 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_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)).
% 12.38/12.30 all V_ya_2 V_xa_2 V_z_2 (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)-> (c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_z_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ya_2,V_z_2))<->c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2))).
% 12.38/12.30 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),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_y)))).
% 12.38/12.30 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,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_x),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_y)))).
% 12.38/12.30 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 12.38/12.30 all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)).
% 12.38/12.30 all V_n_2 V_m_2 V_k_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2)<->V_m_2=V_n_2).
% 12.38/12.30 all V_c V_b V_a T_a (class_Groups_Oab__semigroup__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)=c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))).
% 12.38/12.30 all V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_m)).
% 12.38/12.30 all V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_m))).
% 12.38/12.30 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_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_k))).
% 12.38/12.30 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_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_j))).
% 12.38/12.30 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_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_l)))).
% 12.38/12.30 all V_a T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,V_a)=V_a).
% 12.38/12.30 all V_x T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_x,V_x)=V_x).
% 12.38/12.30 all V_b V_a T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)).
% 12.38/12.30 all V_n V_m (c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n))=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n))).
% 12.38/12.30 all V_N_2 (c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)<-> (exists B_m all B_x (c_member(tc_Nat_Onat,B_x,V_N_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_x,B_m)))).
% 12.38/12.30 all V_N_2 (c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)<-> (exists B_m all B_x (c_member(tc_Nat_Onat,B_x,V_N_2)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_x,B_m)))).
% 12.38/12.30 all V_b V_a T_a (class_Rings_Ono__zero__divisors(T_a)-> (c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)=c_Groups_Ozero__class_Ozero(T_a)->V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a))).
% 12.38/12.30 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)->c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)!=c_Groups_Ozero__class_Ozero(T_a)))).
% 12.38/12.30 all V_b_2 V_a_2 T_a (class_Rings_Oring__no__zero__divisors(T_a)-> (c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_a_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a))).
% 12.38/12.30 all V_a T_a (class_Rings_Omult__zero(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.30 all V_a T_a (class_Rings_Omult__zero(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.30 all V_n_2 V_k_2 V_m_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2)=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)).
% 12.38/12.30 all V_n_2 V_m_2 V_k_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2)=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)).
% 12.38/12.30 all V_n_2 V_m_2 (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)).
% 12.38/12.30 all V_m (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.30 all V_n (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.30 all V_b_2 V_a_2 V_c_2 (V_c_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2,V_c_2)=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2,V_c_2)<->V_a_2=V_b_2)).
% 12.38/12.30 all V_b_2 V_a_2 V_c_2 (V_c_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)-> (c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_a_2)=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_b_2)<->V_a_2=V_b_2)).
% 12.38/12.30 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,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_RComplete_Onatfloor(V_a),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a,V_b))))).
% 12.38/12.30 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,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))))).
% 12.38/12.30 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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))))).
% 12.38/12.30 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,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))))).
% 12.38/12.30 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,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))))).
% 12.38/12.30 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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))))).
% 12.38/12.30 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),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))))).
% 12.38/12.30 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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 12.38/12.30 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,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),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)))).
% 12.38/12.30 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),c_Groups_Otimes__class_Otimes(T_a,V_b,V_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)))).
% 12.38/12.30 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),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)))).
% 12.38/12.30 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,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a))))).
% 12.38/12.30 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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 12.38/12.30 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),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))))).
% 12.38/12.30 all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oidom(tc_Polynomial_Opoly(T_1))).
% 12.38/12.30 all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 12.38/12.30 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))).
% 12.38/12.30 all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))).
% 12.38/12.30 all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1))).
% 12.38/12.30 class_Rings_Oidom(tc_RealDef_Oreal).
% 12.38/12.30 class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal).
% 12.38/12.30 class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal).
% 12.38/12.30 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal).
% 12.38/12.30 class_Rings_Ocomm__ring(tc_RealDef_Oreal).
% 12.38/12.30 class_Lattices_Obounded__lattice(tc_HOL_Obool).
% 12.38/12.30 class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat).
% 12.38/12.30 class_Rings_Ocomm__semiring__0(tc_Nat_Onat).
% 12.38/12.30 class_Rings_Oidom(tc_Int_Oint).
% 12.38/12.30 class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint).
% 12.38/12.30 class_Rings_Ocomm__semiring__0(tc_Int_Oint).
% 12.38/12.30 class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 12.38/12.30 class_Rings_Ocomm__ring(tc_Int_Oint).
% 12.38/12.30 all T_2 T_1 (class_Lattices_Obounded__lattice(T_1)->class_Lattices_Obounded__lattice(tc_fun(T_2,T_1))).
% 12.38/12.30 all T_2 T_1 (class_Lattices_Obounded__lattice(T_1)->class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1))).
% 12.38/12.30 all T_2 T_1 (class_Lattices_Obounded__lattice(T_1)->class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1))).
% 12.38/12.30 all T_2 T_1 (class_Lattices_Olattice(T_1)->class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1))).
% 12.38/12.30 all T_2 T_1 (class_Lattices_Olattice(T_1)->class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1))).
% 12.38/12.30 all T_2 T_1 (class_Lattices_Odistrib__lattice(T_1)->class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1))).
% 12.38/12.30 all T_2 T_1 (class_Orderings_Opreorder(T_1)->class_Orderings_Opreorder(tc_fun(T_2,T_1))).
% 12.38/12.30 all T_2 T_1 (class_Lattices_Olattice(T_1)->class_Lattices_Olattice(tc_fun(T_2,T_1))).
% 12.38/12.30 all T_2 T_1 (class_Orderings_Oorder(T_1)->class_Orderings_Oorder(tc_fun(T_2,T_1))).
% 12.38/12.30 all T_2 T_1 (class_Orderings_Otop(T_1)->class_Orderings_Otop(tc_fun(T_2,T_1))).
% 12.38/12.30 all T_2 T_1 (class_Orderings_Oord(T_1)->class_Orderings_Oord(tc_fun(T_2,T_1))).
% 12.38/12.30 all T_2 T_1 (class_Orderings_Obot(T_1)->class_Orderings_Obot(tc_fun(T_2,T_1))).
% 12.38/12.30 all T_2 T_1 (class_Groups_Ominus(T_1)->class_Groups_Ominus(tc_fun(T_2,T_1))).
% 12.38/12.30 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 12.38/12.30 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 12.38/12.30 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 12.38/12.30 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 12.38/12.30 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint).
% 12.38/12.30 class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 12.38/12.30 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint).
% 12.38/12.30 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 12.38/12.30 class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 12.38/12.30 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 12.38/12.30 class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 12.38/12.30 class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 12.38/12.30 class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 12.38/12.30 class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 12.38/12.30 class_Rings_Olinordered__semidom(tc_Int_Oint).
% 12.38/12.30 class_Lattices_Osemilattice__sup(tc_Int_Oint).
% 12.38/12.30 class_Lattices_Osemilattice__inf(tc_Int_Oint).
% 12.38/12.30 class_Lattices_Odistrib__lattice(tc_Int_Oint).
% 12.38/12.30 class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 12.38/12.30 class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 12.38/12.30 class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 12.38/12.30 class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 12.38/12.30 class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 12.38/12.30 class_Rings_Olinordered__idom(tc_Int_Oint).
% 12.38/12.30 class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 12.38/12.30 class_Rings_Ocomm__semiring(tc_Int_Oint).
% 12.38/12.30 class_Groups_Oab__group__add(tc_Int_Oint).
% 12.38/12.30 class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 12.38/12.30 class_Orderings_Opreorder(tc_Int_Oint).
% 12.38/12.30 class_Orderings_Olinorder(tc_Int_Oint).
% 12.38/12.30 class_Groups_Omonoid__mult(tc_Int_Oint).
% 12.38/12.30 class_Groups_Omonoid__add(tc_Int_Oint).
% 12.38/12.30 class_Rings_Osemiring__1(tc_Int_Oint).
% 12.38/12.30 class_Lattices_Olattice(tc_Int_Oint).
% 12.38/12.30 class_Groups_Ogroup__add(tc_Int_Oint).
% 12.38/12.30 class_Rings_Omult__zero(tc_Int_Oint).
% 12.38/12.30 class_Orderings_Oorder(tc_Int_Oint).
% 12.38/12.30 class_Int_Oring__char__0(tc_Int_Oint).
% 12.38/12.30 class_Int_Onumber__ring(tc_Int_Oint).
% 12.38/12.30 class_Rings_Osemiring(tc_Int_Oint).
% 12.38/12.30 class_Orderings_Oord(tc_Int_Oint).
% 12.38/12.30 class_Rings_Oring__1(tc_Int_Oint).
% 12.38/12.30 class_Groups_Ominus(tc_Int_Oint).
% 12.38/12.30 class_Groups_Ozero(tc_Int_Oint).
% 12.38/12.30 class_Rings_Oring(tc_Int_Oint).
% 12.38/12.30 class_Int_Onumber(tc_Int_Oint).
% 12.38/12.30 class_Groups_Oone(tc_Int_Oint).
% 12.38/12.30 class_GCD_Ogcd(tc_Int_Oint).
% 12.38/12.30 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 12.38/12.30 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 12.38/12.30 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 12.38/12.30 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 12.38/12.30 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 12.38/12.30 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 12.38/12.30 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 12.38/12.30 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 12.38/12.30 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 12.38/12.30 class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 12.38/12.30 class_Lattices_Osemilattice__sup(tc_Nat_Onat).
% 12.38/12.30 class_Lattices_Osemilattice__inf(tc_Nat_Onat).
% 12.38/12.30 class_Lattices_Odistrib__lattice(tc_Nat_Onat).
% 12.38/12.30 class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 12.38/12.30 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 12.38/12.30 class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 12.38/12.30 class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 12.38/12.30 class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 12.38/12.30 class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 12.38/12.30 class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 12.38/12.30 class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 12.38/12.30 class_Orderings_Opreorder(tc_Nat_Onat).
% 12.38/12.30 class_Orderings_Olinorder(tc_Nat_Onat).
% 12.38/12.30 class_Groups_Omonoid__mult(tc_Nat_Onat).
% 12.38/12.30 class_Groups_Omonoid__add(tc_Nat_Onat).
% 12.38/12.30 class_Rings_Osemiring__1(tc_Nat_Onat).
% 12.38/12.30 class_Lattices_Olattice(tc_Nat_Onat).
% 12.38/12.30 class_Rings_Omult__zero(tc_Nat_Onat).
% 12.38/12.30 class_Orderings_Oorder(tc_Nat_Onat).
% 12.38/12.30 class_Rings_Osemiring(tc_Nat_Onat).
% 12.38/12.30 class_Orderings_Oord(tc_Nat_Onat).
% 12.38/12.30 class_Orderings_Obot(tc_Nat_Onat).
% 12.38/12.30 class_Groups_Ominus(tc_Nat_Onat).
% 12.38/12.30 class_Groups_Ozero(tc_Nat_Onat).
% 12.38/12.30 class_Int_Onumber(tc_Nat_Onat).
% 12.38/12.30 class_Groups_Oone(tc_Nat_Onat).
% 12.38/12.30 class_GCD_Ogcd(tc_Nat_Onat).
% 12.38/12.30 class_Lattices_Obounded__lattice__top(tc_HOL_Obool).
% 12.38/12.30 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool).
% 12.38/12.31 class_Lattices_Osemilattice__sup(tc_HOL_Obool).
% 12.38/12.31 class_Lattices_Osemilattice__inf(tc_HOL_Obool).
% 12.38/12.31 class_Lattices_Odistrib__lattice(tc_HOL_Obool).
% 12.38/12.31 class_Orderings_Opreorder(tc_HOL_Obool).
% 12.38/12.31 class_Lattices_Olattice(tc_HOL_Obool).
% 12.38/12.31 class_Orderings_Oorder(tc_HOL_Obool).
% 12.38/12.31 class_Orderings_Otop(tc_HOL_Obool).
% 12.38/12.31 class_Orderings_Oord(tc_HOL_Obool).
% 12.38/12.31 class_Orderings_Obot(tc_HOL_Obool).
% 12.38/12.31 class_Groups_Ominus(tc_HOL_Obool).
% 12.38/12.31 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal).
% 12.38/12.31 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal).
% 12.38/12.31 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal).
% 12.38/12.31 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal).
% 12.38/12.31 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal).
% 12.38/12.31 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal).
% 12.38/12.31 class_Rings_Olinordered__semidom(tc_RealDef_Oreal).
% 12.38/12.31 class_Orderings_Odense__linorder(tc_RealDef_Oreal).
% 12.38/12.31 class_Lattices_Osemilattice__sup(tc_RealDef_Oreal).
% 12.38/12.31 class_Lattices_Osemilattice__inf(tc_RealDef_Oreal).
% 12.38/12.31 class_Lattices_Odistrib__lattice(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal).
% 12.38/12.31 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal).
% 12.38/12.31 class_Rings_Olinordered__idom(tc_RealDef_Oreal).
% 12.38/12.31 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal).
% 12.38/12.31 class_Rings_Ocomm__semiring(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Oab__group__add(tc_RealDef_Oreal).
% 12.38/12.31 class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal).
% 12.38/12.31 class_Orderings_Opreorder(tc_RealDef_Oreal).
% 12.38/12.31 class_Orderings_Olinorder(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Omonoid__mult(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Omonoid__add(tc_RealDef_Oreal).
% 12.38/12.31 class_Rings_Osemiring__1(tc_RealDef_Oreal).
% 12.38/12.31 class_Lattices_Olattice(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Ogroup__add(tc_RealDef_Oreal).
% 12.38/12.31 class_Rings_Omult__zero(tc_RealDef_Oreal).
% 12.38/12.31 class_Orderings_Oorder(tc_RealDef_Oreal).
% 12.38/12.31 class_Int_Oring__char__0(tc_RealDef_Oreal).
% 12.38/12.31 class_Int_Onumber__ring(tc_RealDef_Oreal).
% 12.38/12.31 class_Rings_Osemiring(tc_RealDef_Oreal).
% 12.38/12.31 class_Orderings_Oord(tc_RealDef_Oreal).
% 12.38/12.31 class_Rings_Oring__1(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Ominus(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Ozero(tc_RealDef_Oreal).
% 12.38/12.31 class_Rings_Oring(tc_RealDef_Oreal).
% 12.38/12.31 class_Int_Onumber(tc_RealDef_Oreal).
% 12.38/12.31 class_Groups_Oone(tc_RealDef_Oreal).
% 12.38/12.31 all T_1 (class_Rings_Oidom(T_1)->class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Oidom(T_1)->class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Osemiring__1(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Oorder(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Osemiring(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Oord(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Oring__1(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ominus(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Groups_Ozero(T_1)->class_Groups_Ozero(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Oring(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Int_Onumber(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Oone(tc_Polynomial_Opoly(T_1))).
% 12.38/12.31 all V_y_2 V_x_2 (-hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2))|V_x_2=V_y_2).
% 12.38/12.31 all V_y_2 V_x_2 (V_x_2!=V_y_2|hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2))).
% 12.38/12.31 -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,v_L____,v_y____).
% 12.38/12.31 end_of_list.
% 12.38/12.31
% 12.38/12.31 -------> usable clausifies to:
% 12.38/12.31
% 12.38/12.31 list(usable).
% 12.38/12.31 0 [] A=A.
% 12.38/12.31 0 [] hAPP(V_f_2,$f1(V_g_2,V_f_2))!=hAPP(V_g_2,$f1(V_g_2,V_f_2))|V_f_2=V_g_2.
% 12.38/12.31 0 [] -hBOOL(hAPP(v_P,B_z))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B_z,v_y____).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_y____,v_L____).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,v_L____,v_Y____).
% 12.38/12.31 0 [] -hBOOL(hAPP(v_P,B_x))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B_x,v_L____).
% 12.38/12.31 0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x).
% 12.38/12.31 0 [] -hBOOL(hAPP(v_P,V_z_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_y____,V_z_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_y____,v_L____).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_w).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_j,V_k)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_i,V_k).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_z,V_w)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_w,V_z)|V_z=V_w.
% 12.38/12.31 0 [] -hBOOL(hAPP(v_P,B_z))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_y____,B_z).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_b)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,$f2(V_g_2,V_f_2,T_a,T_b)),hAPP(V_g_2,$f2(V_g_2,V_f_2,T_a,T_b))).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|V_xa_2!=V_ya_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|V_xa_2!=V_ya_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|V_xa_2=V_ya_2| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Opreorder(T_a)|V_x!=V_y|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 12.38/12.31 0 [] hBOOL(hAPP(v_P,v_x____)).
% 12.38/12.31 0 [] hBOOL(hAPP(v_P,$c1)).
% 12.38/12.31 0 [] -hBOOL(hAPP(v_P,B_x))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B_x,v_Y____).
% 12.38/12.31 0 [] -hBOOL(hAPP(v_P,V_x))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,v_Y____).
% 12.38/12.31 0 [] -hBOOL(hAPP(v_P,B_x))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,$c2).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_x____,v_Y____).
% 12.38/12.31 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_x).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|V_xa_2=V_ya_2|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|V_xa_2!=V_ya_2| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|V_xa_2!=V_ya_2| -c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)|V_xa_2=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 12.38/12.31 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 12.38/12.31 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_y!=V_x.
% 12.38/12.31 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_c).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_c,V_b)|c_Orderings_Oord__class_Oless(T_a,V_c,V_a).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_a,V_c).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_c,V_a).
% 12.38/12.31 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 12.38/12.31 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 12.38/12.31 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 12.38/12.31 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|V_a=V_b|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|V_a=V_b|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2).
% 12.38/12.31 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)|V_xa_2=V_ya_2.
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2.
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2.
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)|V_xa_2=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x).
% 12.38/12.31 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)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|V_x=V_y.
% 12.38/12.31 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_z).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)|V_x=V_y.
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|V_b!=V_c|c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|V_b!=V_c|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|V_xa_2=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|V_xa_2!=V_ya_2.
% 12.38/12.31 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)).
% 12.38/12.31 0 [] c_Lubs_OisLub(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),c_Set_OCollect(tc_RealDef_Oreal,v_P),v_L____).
% 12.38/12.31 0 [] -class_Rings_Olinordered__idom(T_a)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 12.38/12.31 0 [] hBOOL(hAPP(v_P,$c3)).
% 12.38/12.31 0 [] -hBOOL(hAPP(v_P,B_x))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_x,$c4).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,$f3(T_a,V_g_2,V_f_2,T_b)),hAPP(V_g_2,$f3(T_a,V_g_2,V_f_2,T_b)))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2).
% 12.38/12.31 0 [] -class_Orderings_Odense__linorder(T_a)|c_Orderings_Oord__class_Oless(T_a,$f4(V_z,V_y,T_a),V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z).
% 12.38/12.31 0 [] -class_Orderings_Odense__linorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,$f4(V_z,V_y,T_a),V_z)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z).
% 12.38/12.31 0 [] -class_Orderings_Odense__linorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_x,$f5(V_z,V_y,V_x,T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z).
% 12.38/12.31 0 [] -class_Orderings_Odense__linorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,$f5(V_z,V_y,V_x,T_a),V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z).
% 12.38/12.31 0 [] -class_Orderings_Odense__linorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,$f5(V_z,V_y,V_x,T_a),V_z)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,V_c_2,hAPP(V_f_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,$f6(V_f_2,V_c_2,V_a_2,V_b_2,T_a,T_b),$f7(V_f_2,V_c_2,V_a_2,V_b_2,T_a,T_b))|c_Orderings_Oord__class_Oless(T_b,V_c_2,hAPP(V_f_2,V_a_2)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,V_c_2,hAPP(V_f_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,$f6(V_f_2,V_c_2,V_a_2,V_b_2,T_a,T_b)),hAPP(V_f_2,$f7(V_f_2,V_c_2,V_a_2,V_b_2,T_a,T_b)))|c_Orderings_Oord__class_Oless(T_b,V_c_2,hAPP(V_f_2,V_a_2)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2)| -c_Orderings_Oord__class_Oless(T_b,V_c_2,hAPP(V_f_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,$f8(V_f_2,V_c_2,V_a_2,V_b_2,T_a,T_b),$f9(V_f_2,V_c_2,V_a_2,V_b_2,T_a,T_b))|c_Orderings_Oord__class_Oless(T_b,V_c_2,hAPP(V_f_2,V_a_2)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2)| -c_Orderings_Oord__class_Oless(T_b,V_c_2,hAPP(V_f_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,$f8(V_f_2,V_c_2,V_a_2,V_b_2,T_a,T_b)),hAPP(V_f_2,$f9(V_f_2,V_c_2,V_a_2,V_b_2,T_a,T_b)))|c_Orderings_Oord__class_Oless(T_b,V_c_2,hAPP(V_f_2,V_a_2)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -class_Orderings_Oorder(T_b)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_b_2),V_c_2)|c_Orderings_Oord__class_Oless(T_a,$f11(V_c_2,V_f_2,V_b_2,V_a_2,T_b,T_a),$f10(V_c_2,V_f_2,V_b_2,V_a_2,T_b,T_a))|c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_a_2),V_c_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -class_Orderings_Oorder(T_b)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_b_2),V_c_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,$f11(V_c_2,V_f_2,V_b_2,V_a_2,T_b,T_a)),hAPP(V_f_2,$f10(V_c_2,V_f_2,V_b_2,V_a_2,T_b,T_a)))|c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_a_2),V_c_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -class_Orderings_Oorder(T_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_b_2),V_c_2)|c_Orderings_Oord__class_Oless__e_q(T_a,$f13(V_c_2,V_f_2,V_b_2,V_a_2,T_b,T_a),$f12(V_c_2,V_f_2,V_b_2,V_a_2,T_b,T_a))|c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_a_2),V_c_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -class_Orderings_Oorder(T_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_b_2),V_c_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,$f13(V_c_2,V_f_2,V_b_2,V_a_2,T_b,T_a)),hAPP(V_f_2,$f12(V_c_2,V_f_2,V_b_2,V_a_2,T_b,T_a)))|c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_a_2),V_c_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -class_Orderings_Oorder(T_b)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(V_f_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2,V_c_2)|c_Orderings_Oord__class_Oless__e_q(T_b,$f15(V_c_2,V_b_2,V_f_2,V_a_2,T_b,T_a),$f14(V_c_2,V_b_2,V_f_2,V_a_2,T_b,T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(V_f_2,V_c_2)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -class_Orderings_Oorder(T_b)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(V_f_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_b,V_b_2,V_c_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_f_2,$f15(V_c_2,V_b_2,V_f_2,V_a_2,T_b,T_a)),hAPP(V_f_2,$f14(V_c_2,V_b_2,V_f_2,V_a_2,T_b,T_a)))|c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(V_f_2,V_c_2)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -class_Orderings_Oorder(T_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,hAPP(V_f_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_b,V_b_2,V_c_2)|c_Orderings_Oord__class_Oless(T_b,$f17(V_c_2,V_b_2,V_f_2,V_a_2,T_b,T_a),$f16(V_c_2,V_b_2,V_f_2,V_a_2,T_b,T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(V_f_2,V_c_2)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -class_Orderings_Oorder(T_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,hAPP(V_f_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_b,V_b_2,V_c_2)| -c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,$f17(V_c_2,V_b_2,V_f_2,V_a_2,T_b,T_a)),hAPP(V_f_2,$f16(V_c_2,V_b_2,V_f_2,V_a_2,T_b,T_a)))|c_Orderings_Oord__class_Oless(T_a,V_a_2,hAPP(V_f_2,V_c_2)).
% 12.38/12.31 0 [] -class_Orderings_Otop(T_a)|hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_xa_2)=c_Orderings_Otop__class_Otop(T_a).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_b)|c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2).
% 12.38/12.31 0 [] -class_Orderings_Otop(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Orderings_Otop__class_Otop(T_a)).
% 12.38/12.31 0 [] c_Lubs_OisLub(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),c_Set_OCollect(tc_RealDef_Oreal,v_P),$c5).
% 12.38/12.31 0 [] c_Lubs_OisLub(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),c_Set_OCollect(tc_RealDef_Oreal,v_P),$c6).
% 12.38/12.31 0 [] hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_xa_2)).
% 12.38/12.31 0 [] hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),c_Set_OCollect(tc_RealDef_Oreal,v_P)),$c7)).
% 12.38/12.31 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_ya_2)|V_xa_2=V_ya_2.
% 12.38/12.31 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))).
% 12.38/12.31 0 [] c_Set_OCollect(T_a,V_Pa_2)=V_Pa_2.
% 12.38/12.31 0 [] c_member(tc_RealDef_Oreal,$c8,c_Set_OCollect(tc_RealDef_Oreal,v_P)).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_b)| -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_f_2,V_b_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,V_c_2,V_b_2)|c_Orderings_Oord__class_Oless(T_b,$f18(V_c_2,V_a_2,V_b_2,V_f_2,T_a,T_b),$f19(V_c_2,V_a_2,V_b_2,V_f_2,T_a,T_b))|c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,V_c_2),V_a_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_b)| -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_f_2,V_b_2),V_a_2)| -c_Orderings_Oord__class_Oless(T_b,V_c_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,$f18(V_c_2,V_a_2,V_b_2,V_f_2,T_a,T_b)),hAPP(V_f_2,$f19(V_c_2,V_a_2,V_b_2,V_f_2,T_a,T_b)))|c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,V_c_2),V_a_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,V_b_2),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,V_c_2,V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_b,$f20(V_c_2,V_a_2,V_b_2,V_f_2,T_a,T_b),$f21(V_c_2,V_a_2,V_b_2,V_f_2,T_a,T_b))|c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,V_c_2),V_a_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,V_b_2),V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,V_c_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_f_2,$f20(V_c_2,V_a_2,V_b_2,V_f_2,T_a,T_b)),hAPP(V_f_2,$f21(V_c_2,V_a_2,V_b_2,V_f_2,T_a,T_b)))|c_Orderings_Oord__class_Oless(T_a,hAPP(V_f_2,V_c_2),V_a_2).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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.
% 12.38/12.31 0 [] c_member(T_a,V_xa_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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).
% 12.38/12.31 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.
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 0 [] -c_member(T_a,V_xa_2,V_A_2)|hBOOL(hAPP(V_A_2,V_xa_2)).
% 12.38/12.31 0 [] c_member(T_a,V_xa_2,V_A_2)| -hBOOL(hAPP(V_A_2,V_xa_2)).
% 12.38/12.31 0 [] -c_member(T_a,V_xa_2,c_fe_qual(V_ya_2))|V_xa_2=V_ya_2.
% 12.38/12.31 0 [] c_member(T_a,V_xa_2,c_fe_qual(V_ya_2))|V_xa_2!=V_ya_2.
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 0 [] V_xa_2!=V_ya_2| -c_member(T_a,V_xa_2,V_A_2)|c_member(T_a,V_ya_2,V_A_2).
% 12.38/12.31 0 [] V_xa_2!=V_ya_2|c_member(T_a,V_xa_2,V_A_2)| -c_member(T_a,V_ya_2,V_A_2).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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)).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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)).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2).
% 12.38/12.31 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_ya_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2).
% 12.38/12.31 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_ya_2,V_S_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 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_ya_2,V_S_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 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)).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 0 [] c_member(T_a,V_xa_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.31 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,$f22(V_S_2)).
% 12.38/12.31 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,$f23(V_S_2)).
% 12.38/12.31 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).
% 12.38/12.31 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)).
% 12.38/12.31 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).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_OleastP(T_a,V_Pa_2,V_xa_2)| -c_member(T_a,V_ya_2,c_Set_OCollect(T_a,V_Pa_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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)).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_Osetge(T_a,V_xa_2,V_S_2)| -c_member(T_a,V_ya_2,V_S_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)|c_Lubs_Osetle(T_a,V_S_2,V_xa_2)|c_member(T_a,$f24(V_xa_2,V_S_2,T_a),V_S_2).
% 12.38/12.31 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,$f24(V_xa_2,V_S_2,T_a),V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_Osetge(T_a,V_xa_2,V_S_2)| -c_member(T_a,B_x,V_S_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,B_x).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)|c_Lubs_Osetge(T_a,V_xa_2,V_S_2)|c_member(T_a,$f25(V_S_2,V_xa_2,T_a),V_S_2).
% 12.38/12.31 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,$f25(V_S_2,V_xa_2,T_a)).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_OisLub(T_a,V_R_2,V_S_2,V_xa_2)|c_Lubs_Osetle(T_a,V_S_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)| -hBOOL(hAPP(c_Lubs_OisUb(T_a,V_R_2,V_S_2),V_xa_2))|c_Lubs_Osetle(T_a,V_S_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)| -c_Lubs_Osetle(T_a,V_S_2,V_xa_2)| -c_member(T_a,V_ya_2,V_S_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)|c_member(T_a,$f26(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)).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,$f26(V_u_2,V_S_2,T_a),V_u_2)|hBOOL(hAPP(c_Lubs_OisUb(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_u_2)).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_Predicate_OPowp(T_a,V_A_2),c_Predicate_OPowp(T_a,V_B_2)).
% 12.38/12.31 0 [] c_member(T_a,$f27(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).
% 12.38/12.31 0 [] -c_member(T_a,$f27(V_B_2,V_A_2,T_a),V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)|c_member(T_a,$f28(V_xa_2,V_S_2,T_a),V_S_2)|c_Lubs_Osetle(T_a,V_S_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,$f28(V_xa_2,V_S_2,T_a),V_xa_2)|c_Lubs_Osetle(T_a,V_S_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)|c_member(T_a,$f29(V_xa_2,V_S_2,T_a),V_S_2)|c_Lubs_Osetge(T_a,V_xa_2,V_S_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,$f29(V_xa_2,V_S_2,T_a))|c_Lubs_Osetge(T_a,V_xa_2,V_S_2).
% 12.38/12.31 0 [] hBOOL(hAPP(V_Pa_2,$f30(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)).
% 12.38/12.31 0 [] -hBOOL(hAPP(V_Q_2,$f30(T_a,V_Q_2,V_Pa_2)))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_OCollect(T_a,V_Pa_2),c_Set_OCollect(T_a,V_Q_2)).
% 12.38/12.31 0 [] -c_member(T_a,$f31(V_A_2,T_a),V_A_2)|c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))=V_A_2.
% 12.38/12.31 0 [] c_member(T_a,$f32(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Odecse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Odecse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f34(V_X_2,T_a),$f33(V_X_2,T_a)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Odecse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f33(V_X_2,T_a)),hAPP(V_X_2,$f34(V_X_2,T_a))).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Oincse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Oincse_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f36(V_X_2,T_a),$f35(V_X_2,T_a)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Oincse_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f36(V_X_2,T_a)),hAPP(V_X_2,$f35(V_X_2,T_a))).
% 12.38/12.31 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)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Oorder(T_a)| -c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2)| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_f_2,V_ya_2)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2)| -c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_f_2,V_ya_2))|c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2)|c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_f_2,V_ya_2))| -c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastAtMost(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_a_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastAtMost(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_b_2,V_d_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastAtMost(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(T_a,V_c_2,V_a_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_d_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_d_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastAtMost(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).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_d_2)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_d_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_d_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_d_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_d_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_f_2,V_ya_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_f_2,V_ya_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 0 [] c_member(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OPow(T_a,V_A_2)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2)|hAPP(V_f_2,V_xa_2)!=hAPP(V_f_2,V_ya_2)|V_xa_2=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2)|hAPP(V_f_2,V_xa_2)=hAPP(V_f_2,V_ya_2)|V_xa_2!=V_ya_2.
% 12.38/12.31 0 [] -hBOOL(hAPP(c_Set_Oinsert(T_a,V_ya_2,V_A_2),V_xa_2))|V_ya_2=V_xa_2|hBOOL(hAPP(V_A_2,V_xa_2)).
% 12.38/12.31 0 [] hBOOL(hAPP(c_Set_Oinsert(T_a,V_ya_2,V_A_2),V_xa_2))|V_ya_2!=V_xa_2.
% 12.38/12.31 0 [] hBOOL(hAPP(c_Set_Oinsert(T_a,V_ya_2,V_A_2),V_xa_2))| -hBOOL(hAPP(V_A_2,V_xa_2)).
% 12.38/12.31 0 [] c_Set_Oinsert(T_a,V_xa_2,c_Set_Oinsert(T_a,V_ya_2,V_A_2))=c_Set_Oinsert(T_a,V_ya_2,c_Set_Oinsert(T_a,V_xa_2,V_A_2)).
% 12.38/12.31 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).
% 12.38/12.31 0 [] c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)).
% 12.38/12.31 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).
% 12.38/12.31 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.
% 12.38/12.31 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).
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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)).
% 12.38/12.31 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.
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastAtMost(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_a_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastAtMost(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_b_2,V_d_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_a_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_d_2).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OatMost(T_a,V_less__e_q_2,V_k_2))|hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_k_2)).
% 12.38/12.31 0 [] c_member(T_a,V_i_2,c_SetInterval_Oord_OatMost(T_a,V_less__e_q_2,V_k_2))| -hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_k_2)).
% 12.38/12.31 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeast(T_a,V_less__e_q_2,V_k_2))|hBOOL(hAPP(hAPP(V_less__e_q_2,V_k_2),V_i_2)).
% 12.38/12.31 0 [] c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeast(T_a,V_less__e_q_2,V_k_2))| -hBOOL(hAPP(hAPP(V_less__e_q_2,V_k_2),V_i_2)).
% 12.38/12.31 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))|hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)).
% 12.38/12.31 0 [] c_member(T_a,V_i_2,c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))| -hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)).
% 12.38/12.31 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))|hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)).
% 12.38/12.31 0 [] c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))| -hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)).
% 12.38/12.31 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__e_q_2,V_l_2,V_u_2))|hBOOL(hAPP(hAPP(V_less__e_q_2,V_l_2),V_i_2)).
% 12.38/12.31 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__e_q_2,V_l_2,V_u_2))|hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_u_2)).
% 12.38/12.31 0 [] c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__e_q_2,V_l_2,V_u_2))| -hBOOL(hAPP(hAPP(V_less__e_q_2,V_l_2),V_i_2))| -hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_u_2)).
% 12.38/12.31 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2))|hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)).
% 12.38/12.31 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2))|hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)).
% 12.38/12.31 0 [] c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2))| -hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))| -hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)).
% 12.38/12.31 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__e_q_2,V_less_2,V_l_2,V_u_2))|hBOOL(hAPP(hAPP(V_less__e_q_2,V_l_2),V_i_2)).
% 12.38/12.31 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__e_q_2,V_less_2,V_l_2,V_u_2))|hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)).
% 12.38/12.31 0 [] c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__e_q_2,V_less_2,V_l_2,V_u_2))| -hBOOL(hAPP(hAPP(V_less__e_q_2,V_l_2),V_i_2))| -hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)).
% 12.38/12.31 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__e_q_2,V_less_2,V_l_2,V_u_2))|hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)).
% 12.38/12.31 0 [] -c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__e_q_2,V_less_2,V_l_2,V_u_2))|hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_u_2)).
% 12.38/12.31 0 [] c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__e_q_2,V_less_2,V_l_2,V_u_2))| -hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))| -hBOOL(hAPP(hAPP(V_less__e_q_2,V_i_2),V_u_2)).
% 12.38/12.31 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)).
% 12.38/12.31 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,$f38(V_X_2,T_a),$f37(V_X_2,T_a)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f38(V_X_2,T_a)),hAPP(V_X_2,$f37(V_X_2,T_a))).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f40(V_X_2,T_a),$f39(V_X_2,T_a)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f39(V_X_2,T_a)),hAPP(V_X_2,$f40(V_X_2,T_a))).
% 12.38/12.31 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).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=V_n_2.
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=V_n_2.
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|V_m=V_n|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 12.38/12.31 0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 12.38/12.31 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).
% 12.38/12.31 0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 12.38/12.31 0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 12.38/12.31 0 [] V_x=V_y|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)|V_m!=V_n.
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)|V_s!=V_t.
% 12.38/12.31 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)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Oincse_q(T_a,V_X_2)|c_SEQ_Omonose_q(T_a,V_X_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_SEQ_Odecse_q(T_a,V_X_2)|c_SEQ_Omonose_q(T_a,V_X_2).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|V_m=V_n.
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_k).
% 12.38/12.31 0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f42(V_X_2,T_a),$f41(V_X_2,T_a))|c_SEQ_Omonose_q(T_a,V_X_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f41(V_X_2,T_a)),hAPP(V_X_2,$f42(V_X_2,T_a)))|c_SEQ_Omonose_q(T_a,V_X_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f44(V_X_2,T_a),$f43(V_X_2,T_a))|c_SEQ_Omonose_q(T_a,V_X_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,$f44(V_X_2,T_a)),hAPP(V_X_2,$f43(V_X_2,T_a)))|c_SEQ_Omonose_q(T_a,V_X_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_m_2),c_SetInterval_Oord__class_OlessThan(T_a,V_n_2))|c_Orderings_Oord__class_Oless(T_a,V_m_2,V_n_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_m_2),c_SetInterval_Oord__class_OlessThan(T_a,V_n_2))| -c_Orderings_Oord__class_Oless(T_a,V_m_2,V_n_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(T_a,V_xa_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_ya_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(T_a,V_xa_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_ya_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless(T_a,$f46(V_f_2,T_a,T_b),$f45(V_f_2,T_a,T_b))|c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_b)| -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,$f46(V_f_2,T_a,T_b)),hAPP(V_f_2,$f45(V_f_2,T_a,T_b)))|c_Orderings_Oorder__class_Ostrict__mono(T_a,T_b,V_f_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)| -c_member(T_a,V_i_2,c_SetInterval_Oord__class_OgreaterThan(T_a,V_k_2))|c_Orderings_Oord__class_Oless(T_a,V_k_2,V_i_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)|c_member(T_a,V_i_2,c_SetInterval_Oord__class_OgreaterThan(T_a,V_k_2))| -c_Orderings_Oord__class_Oless(T_a,V_k_2,V_i_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_xa_2),c_SetInterval_Oord__class_OlessThan(T_a,V_ya_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_xa_2),c_SetInterval_Oord__class_OlessThan(T_a,V_ya_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_SetInterval_Oord__class_OlessThan(T_a,V_xa_2)!=c_SetInterval_Oord__class_OlessThan(T_a,V_ya_2)|V_xa_2=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_SetInterval_Oord__class_OlessThan(T_a,V_xa_2)=c_SetInterval_Oord__class_OlessThan(T_a,V_ya_2)|V_xa_2!=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_SetInterval_Oord__class_OgreaterThan(T_a,V_xa_2)!=c_SetInterval_Oord__class_OgreaterThan(T_a,V_ya_2)|V_xa_2=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_SetInterval_Oord__class_OgreaterThan(T_a,V_xa_2)=c_SetInterval_Oord__class_OgreaterThan(T_a,V_ya_2)|V_xa_2!=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)| -c_member(T_a,V_i_2,c_SetInterval_Oord__class_OlessThan(T_a,V_k_2))|c_Orderings_Oord__class_Oless(T_a,V_i_2,V_k_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)|c_member(T_a,V_i_2,c_SetInterval_Oord__class_OlessThan(T_a,V_k_2))| -c_Orderings_Oord__class_Oless(T_a,V_i_2,V_k_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_xa_2),c_SetInterval_Oord__class_OatMost(T_a,V_ya_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_xa_2),c_SetInterval_Oord__class_OatMost(T_a,V_ya_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeast(T_a,V_xa_2),c_SetInterval_Oord__class_OatLeast(T_a,V_ya_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeast(T_a,V_xa_2),c_SetInterval_Oord__class_OatLeast(T_a,V_ya_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_xa_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)| -c_member(T_a,V_i_2,c_SetInterval_Oord__class_OatMost(T_a,V_k_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_i_2,V_k_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)|c_member(T_a,V_i_2,c_SetInterval_Oord__class_OatMost(T_a,V_k_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_i_2,V_k_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)| -c_member(T_a,V_i_2,c_SetInterval_Oord__class_OatLeast(T_a,V_k_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_k_2,V_i_2).
% 12.38/12.31 0 [] -class_Orderings_Oord(T_a)|c_member(T_a,V_i_2,c_SetInterval_Oord__class_OatLeast(T_a,V_k_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_k_2,V_i_2).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f48(V_j_2,V_i_2,V_f_2),$f47(V_j_2,V_i_2,V_f_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(V_f_2,V_i_2),hAPP(V_f_2,V_j_2)).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,$f48(V_j_2,V_i_2,V_f_2)),hAPP(V_f_2,$f47(V_j_2,V_i_2,V_f_2)))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(V_f_2,V_i_2),hAPP(V_f_2,V_j_2)).
% 12.38/12.31 0 [] -c_member(T_a,V_xa_2,V_A_2)|V_A_2=c_Set_Oinsert(T_a,V_xa_2,$f49(V_A_2,V_xa_2,T_a)).
% 12.38/12.31 0 [] -c_member(T_a,V_xa_2,V_A_2)| -c_member(T_a,V_xa_2,$f49(V_A_2,V_xa_2,T_a)).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_SetInterval_Oord__class_OatLeast(T_a,V_xa_2)!=c_SetInterval_Oord__class_OatLeast(T_a,V_ya_2)|V_xa_2=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_SetInterval_Oord__class_OatLeast(T_a,V_xa_2)=c_SetInterval_Oord__class_OatLeast(T_a,V_ya_2)|V_xa_2!=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_SetInterval_Oord__class_OatMost(T_a,V_xa_2)!=c_SetInterval_Oord__class_OatMost(T_a,V_ya_2)|V_xa_2=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_SetInterval_Oord__class_OatMost(T_a,V_xa_2)=c_SetInterval_Oord__class_OatMost(T_a,V_ya_2)|V_xa_2!=V_ya_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_u_2))=c_SetInterval_Oord__class_OatLeast(T_a,V_l_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_l_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2))=c_SetInterval_Oord__class_OatMost(T_a,V_u_2).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)).
% 12.38/12.31 0 [] -c_member(T_a,V_a_2,V_A_2)|V_A_2=c_Set_Oinsert(T_a,V_a_2,$f50(V_A_2,V_a_2,T_a)).
% 12.38/12.31 0 [] -c_member(T_a,V_a_2,V_A_2)| -c_member(T_a,V_a_2,$f50(V_A_2,V_a_2,T_a)).
% 12.38/12.31 0 [] -c_SEQ_Osubse_q(V_f_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,hAPP(V_f_2,V_n_2)).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 12.38/12.31 0 [] c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)).
% 12.38/12.31 0 [] c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)=c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,V_n_2).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)).
% 12.38/12.31 0 [] c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n.
% 12.38/12.31 0 [] c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)=V_A_2.
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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,$f51(V_Pa_2,V_B_2,V_A_2,T_a),V_A_2)|c_member(T_a,$f52(V_Pa_2,V_B_2,V_A_2,T_a),V_B_2).
% 12.38/12.31 0 [] -c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -hBOOL(hAPP(V_Pa_2,B_x))|c_member(T_a,$f51(V_Pa_2,V_B_2,V_A_2,T_a),V_A_2)|hBOOL(hAPP(V_Pa_2,$f52(V_Pa_2,V_B_2,V_A_2,T_a))).
% 12.38/12.31 0 [] -c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -hBOOL(hAPP(V_Pa_2,B_x))|hBOOL(hAPP(V_Pa_2,$f51(V_Pa_2,V_B_2,V_A_2,T_a)))|c_member(T_a,$f52(V_Pa_2,V_B_2,V_A_2,T_a),V_B_2).
% 12.38/12.31 0 [] -c_member(T_a,B_x,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -hBOOL(hAPP(V_Pa_2,B_x))|hBOOL(hAPP(V_Pa_2,$f51(V_Pa_2,V_B_2,V_A_2,T_a)))|hBOOL(hAPP(V_Pa_2,$f52(V_Pa_2,V_B_2,V_A_2,T_a))).
% 12.38/12.31 0 [] c_member(T_a,$f53(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_A_2)| -hBOOL(hAPP(V_Pa_2,X3)).
% 12.38/12.31 0 [] c_member(T_a,$f53(V_Pa_2,V_B_2,V_A_2,T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,X4,V_B_2)| -hBOOL(hAPP(V_Pa_2,X4)).
% 12.38/12.31 0 [] hBOOL(hAPP(V_Pa_2,$f53(V_Pa_2,V_B_2,V_A_2,T_a)))| -c_member(T_a,X3,V_A_2)| -hBOOL(hAPP(V_Pa_2,X3)).
% 12.38/12.31 0 [] hBOOL(hAPP(V_Pa_2,$f53(V_Pa_2,V_B_2,V_A_2,T_a)))| -c_member(T_a,X4,V_B_2)| -hBOOL(hAPP(V_Pa_2,X4)).
% 12.38/12.31 0 [] c_member(T_a,$f54(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)).
% 12.38/12.31 0 [] c_member(T_a,$f54(V_Pa_2,V_B_2,V_A_2,T_a),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))| -c_member(T_a,X5,V_B_2)|hBOOL(hAPP(V_Pa_2,X5)).
% 12.38/12.31 0 [] -hBOOL(hAPP(V_Pa_2,$f54(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)).
% 12.38/12.31 0 [] -hBOOL(hAPP(V_Pa_2,$f54(V_Pa_2,V_B_2,V_A_2,T_a)))| -c_member(T_a,X5,V_B_2)|hBOOL(hAPP(V_Pa_2,X5)).
% 12.38/12.31 0 [] -c_member(T_a,X6,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|hBOOL(hAPP(V_Pa_2,X6))|c_member(T_a,$f55(V_Pa_2,V_B_2,V_A_2,T_a),V_A_2)|c_member(T_a,$f56(V_Pa_2,V_B_2,V_A_2,T_a),V_B_2).
% 12.38/12.31 0 [] -c_member(T_a,X6,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|hBOOL(hAPP(V_Pa_2,X6))|c_member(T_a,$f55(V_Pa_2,V_B_2,V_A_2,T_a),V_A_2)| -hBOOL(hAPP(V_Pa_2,$f56(V_Pa_2,V_B_2,V_A_2,T_a))).
% 12.38/12.31 0 [] -c_member(T_a,X6,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|hBOOL(hAPP(V_Pa_2,X6))| -hBOOL(hAPP(V_Pa_2,$f55(V_Pa_2,V_B_2,V_A_2,T_a)))|c_member(T_a,$f56(V_Pa_2,V_B_2,V_A_2,T_a),V_B_2).
% 12.38/12.31 0 [] -c_member(T_a,X6,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))|hBOOL(hAPP(V_Pa_2,X6))| -hBOOL(hAPP(V_Pa_2,$f55(V_Pa_2,V_B_2,V_A_2,T_a)))| -hBOOL(hAPP(V_Pa_2,$f56(V_Pa_2,V_B_2,V_A_2,T_a))).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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).
% 12.38/12.31 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)).
% 12.38/12.31 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))).
% 12.38/12.31 0 [] V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.31 0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 12.38/12.31 0 [] V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 12.38/12.31 0 [] c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n))=V_n.
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))).
% 12.38/12.31 0 [] -c_SEQ_Osubse_q(V_f_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,B_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,B_m),hAPP(V_f_2,B_n)).
% 12.38/12.31 0 [] c_SEQ_Osubse_q(V_f_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f58(V_f_2),$f57(V_f_2)).
% 12.38/12.31 0 [] c_SEQ_Osubse_q(V_f_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,$f58(V_f_2)),hAPP(V_f_2,$f57(V_f_2))).
% 12.38/12.31 0 [] -class_Lattices_Olattice(T_a)|hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,T_a),V_f_2,V_g_2),V_xa_2)=c_Lattices_Osemilattice__sup__class_Osup(T_a,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_2)).
% 12.38/12.31 0 [] -class_Lattices_Obounded__lattice__top(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,c_Orderings_Otop__class_Otop(T_a))=c_Orderings_Otop__class_Otop(T_a).
% 12.38/12.31 0 [] -class_Lattices_Obounded__lattice__top(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,c_Orderings_Otop__class_Otop(T_a),V_x)=c_Orderings_Otop__class_Otop(T_a).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f59(V_Pa_2,V_n_2),V_n_2)| -c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))|hBOOL(hAPP(V_Pa_2,B_x)).
% 12.38/12.31 0 [] -hBOOL(hAPP(V_Pa_2,$f59(V_Pa_2,V_n_2)))| -c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))|hBOOL(hAPP(V_Pa_2,B_x)).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,V_n_2)|hBOOL(hAPP(V_Pa_2,B_m))|c_member(tc_Nat_Onat,$f60(V_Pa_2,V_n_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,V_n_2)|hBOOL(hAPP(V_Pa_2,B_m))| -hBOOL(hAPP(V_Pa_2,$f60(V_Pa_2,V_n_2))).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,V_n_2)| -hBOOL(hAPP(V_Pa_2,B_m))|c_member(tc_Nat_Onat,$f61(V_Pa_2,V_n_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,V_n_2)| -hBOOL(hAPP(V_Pa_2,B_m))|hBOOL(hAPP(V_Pa_2,$f61(V_Pa_2,V_n_2))).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f62(V_Pa_2,V_n_2),V_n_2)| -c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))| -hBOOL(hAPP(V_Pa_2,B_x)).
% 12.38/12.31 0 [] hBOOL(hAPP(V_Pa_2,$f62(V_Pa_2,V_n_2)))| -c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))| -hBOOL(hAPP(V_Pa_2,B_x)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_a,V_a)=V_a.
% 12.38/12.31 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_x,V_x)=V_x.
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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)).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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_ya_2),V_z_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_z_2).
% 12.38/12.31 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_ya_2),V_z_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_ya_2,V_z_2).
% 12.38/12.31 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_ya_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_ya_2,V_z_2).
% 12.38/12.31 0 [] -class_Lattices_Osemilattice__sup(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_ya_2)=V_ya_2.
% 12.38/12.31 0 [] -class_Lattices_Osemilattice__sup(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_ya_2)!=V_ya_2.
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_l_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OatLeast(T_a,V_u_2))=c_SetInterval_Oord__class_OgreaterThan(T_a,V_l_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_l_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_l_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2))=c_SetInterval_Oord__class_OlessThan(T_a,V_u_2).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_l_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(T_a,V_l_2))=c_SetInterval_Oord__class_OatLeast(T_a,V_l_2).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 0 [] -c_member(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.31 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).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_k_2)|c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_k_2,V_l_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.31 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))).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 0 [] -c_member(T_a,V_c_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.31 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)).
% 12.38/12.31 0 [] c_member(T_a,$f63(V_A_2,T_a),V_A_2)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.31 0 [] c_member(T_a,$f64(V_A_2,T_a),V_A_2)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.31 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)).
% 12.38/12.31 0 [] c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)).
% 12.38/12.31 0 [] c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))!=c_Set_Oinsert(T_a,V_a_2,V_A_2).
% 12.38/12.31 0 [] c_Set_Oinsert(T_a,V_a_2,V_A_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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)).
% 12.38/12.31 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,$f65(V_Pa_2,T_a))).
% 12.38/12.31 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)).
% 12.38/12.31 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,$f66(V_Pa_2,T_a))).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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))).
% 12.38/12.31 0 [] -class_Orderings_Obot(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Orderings_Obot__class_Obot(T_a),V_x).
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 0 [] -class_Lattices_Obounded__lattice__bot(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_ya_2)!=c_Orderings_Obot__class_Obot(T_a)|V_xa_2=c_Orderings_Obot__class_Obot(T_a).
% 12.38/12.31 0 [] -class_Lattices_Obounded__lattice__bot(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_ya_2)!=c_Orderings_Obot__class_Obot(T_a)|V_ya_2=c_Orderings_Obot__class_Obot(T_a).
% 12.38/12.31 0 [] -class_Lattices_Obounded__lattice__bot(T_a)|c_Lattices_Osemilattice__sup__class_Osup(T_a,V_xa_2,V_ya_2)=c_Orderings_Obot__class_Obot(T_a)|V_xa_2!=c_Orderings_Obot__class_Obot(T_a)|V_ya_2!=c_Orderings_Obot__class_Obot(T_a).
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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))).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))!=c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)|c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.31 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).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|V_a_2!=V_b_2|c_SetInterval_Oord__class_OatLeastAtMost(T_a,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))).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)!=c_Set_Oinsert(T_a,V_c_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))|V_a_2=V_b_2.
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)!=c_Set_Oinsert(T_a,V_c_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))|V_b_2=V_c_2.
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)=c_Set_Oinsert(T_a,V_c_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))|V_a_2!=V_b_2|V_b_2!=V_c_2.
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_a_2)=c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.31 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.38/12.31 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.31 0 [] c_RealDef_Oreal(tc_Nat_Onat,V_n_2)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.38/12.31 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)).
% 12.38/12.31 0 [] c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.31 0 [] c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Set_Oinsert(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))).
% 12.38/12.31 0 [] c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatfloor(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatceiling(V_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_u_2),c_Set_Oinsert(T_a,V_u_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=c_SetInterval_Oord__class_OatMost(T_a,V_u_2).
% 12.38/12.31 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.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_l_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_m_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2))=c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_l_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2),c_Set_Oinsert(T_a,V_u_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_l_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2))=c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_m_2)| -c_Orderings_Oord__class_Oless(T_a,V_m_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2))=c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2).
% 12.38/12.31 0 [] c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)=c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,V_n_2).
% 12.38/12.31 0 [] c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)!=c_SetInterval_Oord__class_OatLeastLessThan(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)|V_b_2=V_d_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)|c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)!=c_SetInterval_Oord__class_OatLeastLessThan(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)|V_a_2=V_c_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -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)|c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)!=c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2)|V_a_2=V_c_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -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)|c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)!=c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2)|V_b_2=V_d_2.
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -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)|c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)=c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2)|V_a_2!=V_c_2|V_b_2!=V_d_2.
% 12.38/12.31 0 [] c_Orderings_Obot__class_Obot(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f67(V_Pa_2,V_n_2),V_n_2)| -c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))|hBOOL(hAPP(V_Pa_2,B_x)).
% 12.38/12.31 0 [] -hBOOL(hAPP(V_Pa_2,$f67(V_Pa_2,V_n_2)))| -c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))|hBOOL(hAPP(V_Pa_2,B_x)).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,V_n_2)|hBOOL(hAPP(V_Pa_2,B_m))|c_member(tc_Nat_Onat,$f68(V_Pa_2,V_n_2),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,V_n_2)|hBOOL(hAPP(V_Pa_2,B_m))| -hBOOL(hAPP(V_Pa_2,$f68(V_Pa_2,V_n_2))).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,V_n_2)| -hBOOL(hAPP(V_Pa_2,B_m))|c_member(tc_Nat_Onat,$f69(V_Pa_2,V_n_2),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 12.38/12.31 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,V_n_2)| -hBOOL(hAPP(V_Pa_2,B_m))|hBOOL(hAPP(V_Pa_2,$f69(V_Pa_2,V_n_2))).
% 12.38/12.31 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f70(V_Pa_2,V_n_2),V_n_2)| -c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))| -hBOOL(hAPP(V_Pa_2,B_x)).
% 12.38/12.31 0 [] hBOOL(hAPP(V_Pa_2,$f70(V_Pa_2,V_n_2)))| -c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))| -hBOOL(hAPP(V_Pa_2,B_x)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2)|c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))!=c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_a_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_a_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_d_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_m_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2,V_u_2))=c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_k_2)|c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))!=c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2)| -c_Orderings_Oord__class_Oless(T_a,V_k_2,V_l_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2)|c_Orderings_Oord__class_Oless(T_a,V_k_2,V_l_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))| -c_Orderings_Oord__class_Oless(T_a,V_k_2,V_l_2).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_k_2,V_l_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|c_Orderings_Oord__class_Oless(T_a,V_k_2,V_l_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_m_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2))=c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_m_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2))=c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_l_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2))=c_SetInterval_Oord__class_OlessThan(T_a,V_u_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OatLeast(T_a,V_u_2))=c_SetInterval_Oord__class_OatLeast(T_a,V_l_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_m_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2))=c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_l_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2))=c_SetInterval_Oord__class_OatMost(T_a,V_u_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_u_2))=c_SetInterval_Oord__class_OgreaterThan(T_a,V_l_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_l_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_m_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2,V_u_2))=c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_m_2)| -c_Orderings_Oord__class_Oless(T_a,V_m_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2))=c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_l_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2),c_Set_Oinsert(T_a,V_u_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2).
% 12.38/12.31 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_l_2,V_u_2)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_l_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2))=c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 0 [] -class_Orderings_Oorder(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_n_2),c_SetInterval_Oord__class_OatLeast(T_a,V_n_2))=c_Set_Oinsert(T_a,V_n_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.31 0 [] c_member(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Nat_Osemiring__1__class_ONats(tc_RealDef_Oreal)).
% 12.38/12.31 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).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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)).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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.
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 0 [] -class_Lattices_Obounded__lattice__top(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_xa_2,V_ya_2)!=c_Orderings_Otop__class_Otop(T_a)|V_xa_2=c_Orderings_Otop__class_Otop(T_a).
% 12.38/12.31 0 [] -class_Lattices_Obounded__lattice__top(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_xa_2,V_ya_2)!=c_Orderings_Otop__class_Otop(T_a)|V_ya_2=c_Orderings_Otop__class_Otop(T_a).
% 12.38/12.31 0 [] -class_Lattices_Obounded__lattice__top(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_xa_2,V_ya_2)=c_Orderings_Otop__class_Otop(T_a)|V_xa_2!=c_Orderings_Otop__class_Otop(T_a)|V_ya_2!=c_Orderings_Otop__class_Otop(T_a).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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.
% 12.38/12.31 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,$f72(V_B_2,V_A_2,T_a),V_A_2).
% 12.38/12.31 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,$f71(V_B_2,V_A_2,T_a),V_B_2).
% 12.38/12.31 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|$f72(V_B_2,V_A_2,T_a)=$f71(V_B_2,V_A_2,T_a).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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.
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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.
% 12.38/12.31 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.
% 12.38/12.31 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).
% 12.38/12.31 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).
% 12.38/12.31 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.
% 12.38/12.31 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)).
% 12.38/12.31 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).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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)).
% 12.38/12.31 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).
% 12.38/12.32 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).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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.
% 12.38/12.32 0 [] -class_Lattices_Osemilattice__inf(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_a,V_a)=V_a.
% 12.38/12.32 0 [] -class_Lattices_Osemilattice__inf(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_x,V_x)=V_x.
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 0 [] c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2)=V_A_2.
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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.
% 12.38/12.32 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.
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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_ya_2,V_z_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2).
% 12.38/12.32 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_ya_2,V_z_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_z_2).
% 12.38/12.32 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_ya_2,V_z_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_z_2).
% 12.38/12.32 0 [] -class_Lattices_Osemilattice__inf(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_xa_2,V_ya_2)=V_xa_2.
% 12.38/12.32 0 [] -class_Lattices_Osemilattice__inf(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_xa_2,V_ya_2)|c_Lattices_Osemilattice__inf__class_Oinf(T_a,V_xa_2,V_ya_2)!=V_xa_2.
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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))).
% 12.38/12.32 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))).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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)).
% 12.38/12.32 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).
% 12.38/12.32 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)).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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)).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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)))).
% 12.38/12.32 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)).
% 12.38/12.32 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_i_2,V_n_2)|c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2,V_m_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_i_2,V_n_2))=c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_n_2,V_m_2).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.32 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.
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.32 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.
% 12.38/12.32 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.
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_k_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(T_a,V_k_2))=c_Set_Oinsert(T_a,V_k_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_l_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(T_a,V_l_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_m_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_m_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_m_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OatLeast(T_a,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_l_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(T_a,V_l_2),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_m_2),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_m_2,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OatLeast(T_a,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_l_2,V_u_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_u_2))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 12.38/12.32 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)).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=V_b_2.
% 12.38/12.32 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=V_b_2.
% 12.38/12.32 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m=V_n.
% 12.38/12.32 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 12.38/12.32 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i))=V_i.
% 12.38/12.32 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.
% 12.38/12.32 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.
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_m)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)|c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)|c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_xa_2,V_ya_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_xa_2,V_ya_2)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_xa_2,V_ya_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_c,V_a)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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.
% 12.38/12.32 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.
% 12.38/12.32 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 12.38/12.32 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] -class_Groups_Oab__group__add(T_a)|V_a_2!=V_b_2|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] -class_Groups_Oab__group__add(T_a)|V_a_2=V_b_2|c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 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,$f73(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))).
% 12.38/12.32 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,$f73(V_Q_2,V_Pa_2,V_B_2,V_A_2,T_a)))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_OCollect(T_a,V_Pa_2)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_OCollect(T_a,V_Q_2))).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -hBOOL(hAPP(V_Q_2,$f73(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))).
% 12.38/12.32 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_ya_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_ya_2)).
% 12.38/12.32 0 [] -class_Groups_Ozero(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_p_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 12.38/12.32 0 [] -class_Groups_Ozero(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_p_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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,$f75(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a)),$f74(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a)).
% 12.38/12.32 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,$f75(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a),V_a2_2).
% 12.38/12.32 0 [] -c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))|V_a2_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_a2_2,c_Set_Oinsert(T_a,$f75(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)))),$f74(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a)).
% 12.38/12.32 0 [] -c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))|hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)=V_a4_2|hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)=hAPP(hAPP(V_a3_2,$f75(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a)),$f74(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a)).
% 12.38/12.32 0 [] -c_Nitpick_Ofold__graph_H(T_a,T_b,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))|hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)=V_a4_2|c_member(T_a,$f75(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a),V_a2_2).
% 12.38/12.32 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,$f75(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))),$f74(V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a)).
% 12.38/12.32 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.
% 12.38/12.32 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).
% 12.38/12.32 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))).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))=c_Set_Oinsert(tc_Nat_Onat,V_n_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_n_2)).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)).
% 12.38/12.32 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 12.38/12.32 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k).
% 12.38/12.32 0 [] c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)!=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.38/12.32 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.38/12.32 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m).
% 12.38/12.32 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_nat_H).
% 12.38/12.32 0 [] c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] c_Nat_OSuc(V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m).
% 12.38/12.32 0 [] c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a).
% 12.38/12.32 0 [] c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,c_Nat_OSuc(V_k_2))=c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,V_k_2).
% 12.38/12.32 0 [] c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Nat_OSuc(V_l_2),V_u_2)=c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2).
% 12.38/12.32 0 [] c_Nat_OSuc(V_x)!=c_Nat_OSuc(V_y)|V_x=V_y.
% 12.38/12.32 0 [] c_Nat_OSuc(V_nat_2)!=c_Nat_OSuc(V_nat_H_2)|V_nat_2=V_nat_H_2.
% 12.38/12.32 0 [] c_Nat_OSuc(V_nat_2)=c_Nat_OSuc(V_nat_H_2)|V_nat_2!=V_nat_H_2.
% 12.38/12.32 0 [] c_Nat_OSuc(V_n)!=V_n.
% 12.38/12.32 0 [] V_n!=c_Nat_OSuc(V_n).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|V_m=c_Nat_OSuc(V_n).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=c_Nat_OSuc(V_n_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2!=c_Nat_OSuc(V_n_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_m=V_n.
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Nat_OSuc(V_m)=V_n|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))|V_m=V_n.
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))|V_n_2=V_m_2.
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))|V_n_2!=V_m_2.
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2.
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2!=V_n_2.
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)).
% 12.38/12.32 0 [] c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Nat_OSuc(V_l_2),V_u_2)=c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Nat_OSuc($f76(V_n_2,V_m_2)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f76(V_n_2,V_m_2),V_n_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2!=c_Nat_OSuc(B_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)|V_n_2=c_Nat_OSuc($f77(V_n_2)).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)|V_n_2!=c_Nat_OSuc(B_m).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n).
% 12.38/12.32 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_n_2,c_Nat_OSuc(V_m_2))|V_n_2=V_m_2.
% 12.38/12.32 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_n_2,c_Nat_OSuc(V_m_2))|V_n_2!=V_m_2.
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.32 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,B_n),hAPP(V_X_2,c_Nat_OSuc(B_n)))|c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,c_Nat_OSuc(X7)),hAPP(V_X_2,X7)).
% 12.38/12.32 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,$f78(V_X_2,T_a)),hAPP(V_X_2,c_Nat_OSuc($f78(V_X_2,T_a)))).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_a)|c_SEQ_Omonose_q(T_a,V_X_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,hAPP(V_X_2,c_Nat_OSuc($f79(V_X_2,T_a))),hAPP(V_X_2,$f79(V_X_2,T_a))).
% 12.38/12.32 0 [] c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2,c_Nat_OSuc(V_u_2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2).
% 12.38/12.32 0 [] c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_Nat_OSuc(V_k_2))=c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,V_k_2),c_Set_Oinsert(tc_Nat_Onat,c_Nat_OSuc(V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))).
% 12.38/12.32 0 [] -class_Rings_Osemiring__1(T_a)|c_member(T_a,c_Groups_Oone__class_Oone(T_a),c_Nat_Osemiring__1__class_ONats(T_a)).
% 12.38/12.32 0 [] c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,c_Nat_OSuc(V_k_2))=c_Set_Oinsert(tc_Nat_Onat,V_k_2,c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,V_k_2)).
% 12.38/12.32 0 [] c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,c_Nat_OSuc(V_k_2))=c_Set_Oinsert(tc_Nat_Onat,c_Nat_OSuc(V_k_2),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,V_k_2)).
% 12.38/12.32 0 [] -c_SEQ_Osubse_q(V_f_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,B_n),hAPP(V_f_2,c_Nat_OSuc(B_n))).
% 12.38/12.32 0 [] c_SEQ_Osubse_q(V_f_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_f_2,$f80(V_f_2)),hAPP(V_f_2,c_Nat_OSuc($f80(V_f_2)))).
% 12.38/12.32 0 [] c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,c_Nat_OSuc(V_k_2))=c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,V_k_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n.
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))=c_Set_Oinsert(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)).
% 12.38/12.32 0 [] c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_m_2))=c_Set_Oinsert(tc_Nat_Onat,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))).
% 12.38/12.32 0 [] c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,c_Nat_OSuc(V_k_2))=c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat,V_k_2),c_Set_Oinsert(tc_Nat_Onat,V_k_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Nat_OSuc(V_j_2))|c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,c_Nat_OSuc(V_j_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2),c_Set_Oinsert(tc_Nat_Onat,c_Nat_OSuc(V_j_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.32 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n).
% 12.38/12.32 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.32 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 12.38/12.32 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_RealDef_Oreal).
% 12.38/12.32 0 [] c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.38/12.32 0 [] c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|V_n=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=V_n.
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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).
% 12.38/12.32 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,$f81(V_r),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_r).
% 12.38/12.32 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,$f81(V_r))).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,$f82(V_r)),V_r).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc($f82(V_r)))).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j_2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j_2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2),c_Set_Oinsert(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j_2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatfloor(V_x)=V_n.
% 12.38/12.32 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.32 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.32 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.32 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,$f83(V_n_2,V_m_2))).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2!=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))).
% 12.38/12.32 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.32 0 [] -class_Groups_Oab__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 12.38/12.32 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.
% 12.38/12.32 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.
% 12.38/12.32 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.
% 12.38/12.32 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.
% 12.38/12.32 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)!=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)|V_b=V_c.
% 12.38/12.32 0 [] -class_Groups_Ocancel__ab__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)!=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)|V_b=V_c.
% 12.38/12.32 0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_b,V_a)!=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)|V_b=V_c.
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 12.38/12.32 0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)).
% 12.38/12.32 0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 12.38/12.32 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b).
% 12.38/12.32 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b).
% 12.38/12.32 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 12.38/12.32 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 12.38/12.32 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 12.38/12.32 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)).
% 12.38/12.32 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)).
% 12.38/12.32 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,$f84(V_n_2,V_m_2)).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_z)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)).
% 12.38/12.32 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.
% 12.38/12.32 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.
% 12.38/12.32 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.
% 12.38/12.32 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.
% 12.38/12.32 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)!=V_m|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n.
% 12.38/12.32 0 [] -class_Groups_Omonoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a.
% 12.38/12.32 0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a.
% 12.38/12.32 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] -class_Groups_Omonoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 12.38/12.32 0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a).
% 12.38/12.32 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 12.38/12.32 0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 12.38/12.32 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.38/12.32 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.38/12.32 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 12.38/12.32 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 12.38/12.32 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 12.38/12.32 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 12.38/12.32 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_ya_2)|c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 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_ya_2)|c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 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_ya_2)|c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2)=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 12.38/12.32 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.38/12.32 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2).
% 12.38/12.32 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n)=V_m.
% 12.38/12.32 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n)=V_m.
% 12.38/12.32 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)).
% 12.38/12.32 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 12.38/12.32 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 12.38/12.32 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=V_a.
% 12.38/12.32 0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b)=V_a.
% 12.38/12.32 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)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m.
% 12.38/12.32 0 [] c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 12.38/12.32 0 [] c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m.
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)=V_m.
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)!=V_k_2|V_j_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_k_2|V_j_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i).
% 12.38/12.32 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)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)|c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 12.38/12.32 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 12.38/12.32 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 12.38/12.32 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 12.38/12.32 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 12.38/12.32 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))|c_RComplete_Onatceiling(V_x)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 12.38/12.32 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))).
% 12.38/12.32 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)).
% 12.38/12.32 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,$f85(V_b_2,V_a_2,V_Pa_2)).
% 12.38/12.32 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,$f85(V_b_2,V_a_2,V_Pa_2))).
% 12.38/12.32 0 [] hBOOL(hAPP(V_Pa_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f85(V_b_2,V_a_2,V_Pa_2)).
% 12.38/12.32 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,$f85(V_b_2,V_a_2,V_Pa_2))).
% 12.38/12.32 0 [] -hBOOL(hAPP(V_Pa_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 12.38/12.32 0 [] -hBOOL(hAPP(V_Pa_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|V_a_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)|hBOOL(hAPP(V_Pa_2,B_d)).
% 12.38/12.32 0 [] hBOOL(hAPP(V_Pa_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f86(V_b_2,V_a_2,V_Pa_2)).
% 12.38/12.32 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,$f86(V_b_2,V_a_2,V_Pa_2))).
% 12.38/12.32 0 [] hBOOL(hAPP(V_Pa_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))| -hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_a_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f86(V_b_2,V_a_2,V_Pa_2)).
% 12.38/12.32 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,$f86(V_b_2,V_a_2,V_Pa_2))).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j)).
% 12.38/12.32 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))=c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j_2,V_k_2))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2,V_j_2),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j_2,V_k_2))).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 0 [] V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=V_n.
% 12.38/12.32 0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)).
% 12.38/12.32 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))).
% 12.38/12.32 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))).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 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,$f87(V_l_2,V_k_2)).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)|V_l_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n).
% 12.38/12.32 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a.
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 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)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a).
% 12.38/12.32 0 [] c_member(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Int_Oring__1__class_OInts(tc_RealDef_Oreal)).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 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).
% 12.38/12.32 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_b_2!=c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_b_2=c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 12.38/12.32 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,$f88(V_n_2,V_Pa_2),V_n_2).
% 12.38/12.32 0 [] hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_Pa_2,V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i,$f88(V_n_2,V_Pa_2))| -hBOOL(hAPP(V_Pa_2,B_i)).
% 12.38/12.32 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,$f88(V_n_2,V_Pa_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 12.38/12.32 0 [] -class_Int_Onumber__ring(T_a)|c_member(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Int_Oring__1__class_OInts(T_a)).
% 12.38/12.32 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,V_ya_2).
% 12.38/12.32 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,V_ya_2).
% 12.38/12.32 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_xa_2,V_ya_2).
% 12.38/12.32 0 [] -class_Int_Onumber__ring(T_a)| -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_xa_2,V_ya_2).
% 12.38/12.32 0 [] -class_Int_Onumber__ring(T_a)| -class_Int_Oring__char__0(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_xa_2)!=c_Int_Onumber__class_Onumber__of(T_a,V_ya_2)|V_xa_2=V_ya_2.
% 12.38/12.32 0 [] -class_Int_Onumber__ring(T_a)| -class_Int_Oring__char__0(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_xa_2)=c_Int_Onumber__class_Onumber__of(T_a,V_ya_2)|V_xa_2!=V_ya_2.
% 12.38/12.32 0 [] -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)!=V_xa_2|V_xa_2=c_Int_Onumber__class_Onumber__of(T_a,V_w_2).
% 12.38/12.32 0 [] -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(T_a,V_w_2)=V_xa_2|V_xa_2!=c_Int_Onumber__class_Onumber__of(T_a,V_w_2).
% 12.38/12.32 0 [] -class_Int_Onumber(T_a)| -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))| -c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)).
% 12.38/12.32 0 [] -class_Int_Onumber(T_a)| -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))|c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)).
% 12.38/12.32 0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_v,V_w))=c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)).
% 12.38/12.32 0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_c))=c_Groups_Ominus__class_Ominus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_c).
% 12.38/12.32 0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w))=c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)).
% 12.38/12.32 0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))=c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)).
% 12.38/12.32 0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z))=c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_z).
% 12.38/12.32 0 [] -c_Finite__Set_Ofinite(tc_Nat_Onat,V_M_2)|c_GCD_Ogcd__class_OGcd(tc_Nat_Onat,V_M_2)=c_GCD_Ogcd__class_OGcd(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool),V_M_2,c_Set_Oinsert(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))).
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(T_a,V_u,V_x),c_Groups_Otimes__class_Otimes(T_a,V_v,V_y)),V_a).
% 12.38/12.32 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2,V_u_2)).
% 12.38/12.32 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)).
% 12.38/12.32 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat,V_k_2)).
% 12.38/12.32 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatMost(tc_Nat_Onat,V_k_2)).
% 12.38/12.32 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)).
% 12.38/12.32 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)).
% 12.38/12.32 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_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Int_Oring__1__class_OInts(T_a)).
% 12.38/12.32 0 [] c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n).
% 12.38/12.32 0 [] c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_n))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_n).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_k_2,V_l_2).
% 12.38/12.32 0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z))=c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)),V_z).
% 12.38/12.32 0 [] -class_Int_Onumber__ring(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))=c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w)).
% 12.38/12.32 0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v,V_w))=c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)).
% 12.38/12.32 0 [] -class_Int_Onumber(T_b)| -class_Rings_Oring(T_b)|c_Groups_Otimes__class_Otimes(T_b,c_Groups_Ominus__class_Ominus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))=c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v))).
% 12.38/12.32 0 [] -class_Int_Onumber(T_b)| -class_Rings_Oring(T_b)|c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Ominus__class_Ominus(T_b,V_b,V_c))=c_Groups_Ominus__class_Ominus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c)).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w))=c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)).
% 12.38/12.32 0 [] -class_Int_Onumber(T_b)| -class_Rings_Osemiring(T_b)|c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),c_Groups_Oplus__class_Oplus(T_b,V_b,V_c))=c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_b),c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v),V_c)).
% 12.38/12.32 0 [] -class_Int_Onumber(T_b)| -class_Rings_Osemiring(T_b)|c_Groups_Otimes__class_Otimes(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))=c_Groups_Oplus__class_Oplus(T_b,c_Groups_Otimes__class_Otimes(T_b,V_a,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Otimes__class_Otimes(T_b,V_b,c_Int_Onumber__class_Onumber__of(T_b,V_v))).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))=c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2),c_Set_Oinsert(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))).
% 12.38/12.32 0 [] c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_l_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2)=c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2).
% 12.38/12.32 0 [] c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_u_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,V_z_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,V_z_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)|V_w_2=V_z_2.
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|V_w_2!=V_z_2.
% 12.38/12.32 0 [] c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_l_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2)=c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2).
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)).
% 12.38/12.32 0 [] 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,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n)).
% 12.38/12.32 0 [] 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,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_H,V_z)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j)).
% 12.38/12.32 0 [] 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,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2,V_w)).
% 12.38/12.32 0 [] 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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_w)).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)).
% 12.38/12.32 0 [] 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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z2)).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring(T_a)|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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)).
% 12.38/12.32 0 [] -class_Rings_Osemiring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_e),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_e),V_c))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_e),V_c).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z.
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)=V_z.
% 12.38/12.32 0 [] -class_Rings_Oring(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)).
% 12.38/12.32 0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2)!=c_Groups_Oplus__class_Oplus(T_a,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,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_e_2),V_d_2).
% 12.38/12.32 0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2)=c_Groups_Oplus__class_Oplus(T_a,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,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2),V_e_2),V_d_2).
% 12.38/12.32 0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2)!=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2)|c_Groups_Oplus__class_Oplus(T_a,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.
% 12.38/12.32 0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_e_2),V_c_2)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2)|c_Groups_Oplus__class_Oplus(T_a,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.
% 12.38/12.32 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(T_a,V_ya_2,V_ya_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(T_a,V_ya_2,V_ya_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(T_a,V_ya_2,V_ya_2))=c_Groups_Ozero__class_Ozero(T_a)|V_xa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_ya_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 12.38/12.32 0 [] 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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w,V_z2)).
% 12.38/12.32 0 [] 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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1,V_w),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2,V_w)).
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k,V_j)).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_w).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_j,V_k)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_i,V_k).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z,V_w)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w,V_z)|V_z=V_w.
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)|c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_w_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)|V_z_2!=V_w_2.
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_z_2,V_w_2)|V_z_2=V_w_2.
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)|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).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)|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).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)|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).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))|c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ya_2,V_ya_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ya_2,V_ya_2))!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_ya_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.38/12.32 0 [] c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_xa_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ya_2,V_ya_2))=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_xa_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|V_ya_2!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal).
% 12.38/12.32 0 [] -c_Finite__Set_Ofinite(tc_Nat_Onat,V_M_2)|V_M_2=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|c_GCD_Ogcd__class_OLcm(tc_Nat_Onat,V_M_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_member(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_M_2).
% 12.38/12.32 0 [] -c_Finite__Set_Ofinite(tc_Nat_Onat,V_M_2)|V_M_2=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))|c_GCD_Ogcd__class_OLcm(tc_Nat_Onat,V_M_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_member(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_M_2).
% 12.38/12.32 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_Otimes__class_Otimes(T_a,V_a_2,V_b_2),c_Nat_Osemiring__1__class_ONats(T_a)).
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_z)=V_z.
% 12.38/12.32 0 [] 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).
% 12.38/12.32 0 [] 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).
% 12.38/12.32 0 [] 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).
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 12.38/12.32 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=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).
% 12.38/12.32 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=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).
% 12.38/12.32 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=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).
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)=V_n.
% 12.38/12.32 0 [] -class_Groups_Ocomm__monoid__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a.
% 12.38/12.32 0 [] -class_Groups_Omonoid__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a.
% 12.38/12.32 0 [] -class_Groups_Ocomm__monoid__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a)=V_a.
% 12.38/12.32 0 [] -class_Groups_Omonoid__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a)=V_a.
% 12.38/12.32 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),c_Groups_Otimes__class_Otimes(T_a,V_m,V_n)).
% 12.38/12.32 0 [] -c_Finite__Set_Ofinite(tc_Nat_Onat,V_M_2)| -c_member(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_M_2)|c_GCD_Ogcd__class_OLcm(tc_Nat_Onat,V_M_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_j)).
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_k)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),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).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),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).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),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).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),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).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),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).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),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).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),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).
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_z_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ya_2,V_z_2))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2).
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_xa_2,V_z_2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ya_2,V_z_2))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2).
% 12.38/12.32 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),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x,V_y)).
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_x),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z,V_y)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2)!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2)|V_m_2=V_n_2.
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2)|V_m_2!=V_n_2.
% 12.38/12.32 0 [] -class_Groups_Oab__semigroup__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)=c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_m)).
% 12.38/12.32 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_m))).
% 12.38/12.32 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_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_k)).
% 12.38/12.32 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_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_j)).
% 12.38/12.32 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_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_l)).
% 12.38/12.32 0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,V_a)=V_a.
% 12.38/12.32 0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_x,V_x)=V_x.
% 12.38/12.32 0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,V_a,V_b).
% 12.38/12.32 0 [] c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n))=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)).
% 12.38/12.32 0 [] -c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)| -c_member(tc_Nat_Onat,B_x,V_N_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_x,$f89(V_N_2)).
% 12.38/12.32 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)|c_member(tc_Nat_Onat,$f90(V_N_2,B_m),V_N_2).
% 12.38/12.32 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f90(V_N_2,B_m),B_m).
% 12.38/12.32 0 [] -c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)| -c_member(tc_Nat_Onat,B_x,V_N_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_x,$f91(V_N_2)).
% 12.38/12.32 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)|c_member(tc_Nat_Onat,$f92(V_N_2,B_m),V_N_2).
% 12.38/12.32 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f92(V_N_2,B_m),B_m).
% 12.38/12.32 0 [] -class_Rings_Ono__zero__divisors(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)!=c_Groups_Ozero__class_Ozero(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 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)|c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)!=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] -class_Rings_Oring__no__zero__divisors(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] -class_Rings_Oring__no__zero__divisors(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] -class_Rings_Oring__no__zero__divisors(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_b_2!=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] -class_Rings_Omult__zero(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] -class_Rings_Omult__zero(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2)!=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).
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2)|V_m_2!=V_n_2.
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2)!=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).
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)|V_m_2!=V_n_2.
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] 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).
% 12.38/12.32 0 [] 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).
% 12.38/12.32 0 [] 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).
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2,V_c_2)!=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2,V_c_2)|V_a_2=V_b_2.
% 12.38/12.32 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2,V_c_2)=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_b_2,V_c_2)|V_a_2!=V_b_2.
% 12.38/12.32 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_a_2)!=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_b_2)|V_a_2=V_b_2.
% 12.38/12.32 0 [] V_c_2=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_a_2)=c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_c_2,V_b_2)|V_a_2!=V_b_2.
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_RComplete_Onatfloor(V_a),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a,V_b))).
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)).
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)).
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)).
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)).
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)).
% 12.38/12.32 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),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)).
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),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).
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_a_2),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).
% 12.38/12.32 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_b,V_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b).
% 12.38/12.32 0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b).
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 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,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 12.38/12.32 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),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)).
% 12.38/12.32 0 [] -class_Rings_Oidom(T_1)|class_Rings_Oidom(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] class_Rings_Oidom(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Ocomm__ring__1(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Ocomm__ring(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Lattices_Obounded__lattice(tc_HOL_Obool).
% 12.38/12.32 0 [] class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Rings_Ocomm__semiring__0(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Rings_Oidom(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Ocomm__semiring__0(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Ocomm__ring__1(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Ocomm__ring(tc_Int_Oint).
% 12.38/12.32 0 [] -class_Lattices_Obounded__lattice(T_1)|class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)).
% 12.38/12.32 0 [] -class_Lattices_Obounded__lattice(T_1)|class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)).
% 12.38/12.32 0 [] -class_Lattices_Obounded__lattice(T_1)|class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)).
% 12.38/12.32 0 [] -class_Lattices_Olattice(T_1)|class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)).
% 12.38/12.32 0 [] -class_Lattices_Olattice(T_1)|class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)).
% 12.38/12.32 0 [] -class_Lattices_Odistrib__lattice(T_1)|class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)).
% 12.38/12.32 0 [] -class_Orderings_Opreorder(T_1)|class_Orderings_Opreorder(tc_fun(T_2,T_1)).
% 12.38/12.32 0 [] -class_Lattices_Olattice(T_1)|class_Lattices_Olattice(tc_fun(T_2,T_1)).
% 12.38/12.32 0 [] -class_Orderings_Oorder(T_1)|class_Orderings_Oorder(tc_fun(T_2,T_1)).
% 12.38/12.32 0 [] -class_Orderings_Otop(T_1)|class_Orderings_Otop(tc_fun(T_2,T_1)).
% 12.38/12.32 0 [] -class_Orderings_Oord(T_1)|class_Orderings_Oord(tc_fun(T_2,T_1)).
% 12.38/12.32 0 [] -class_Orderings_Obot(T_1)|class_Orderings_Obot(tc_fun(T_2,T_1)).
% 12.38/12.32 0 [] -class_Groups_Ominus(T_1)|class_Groups_Ominus(tc_fun(T_2,T_1)).
% 12.38/12.32 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Olinordered__semiring__strict(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Olinordered__ring__strict(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Oring__no__zero__divisors(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Olinordered__semidom(tc_Int_Oint).
% 12.38/12.32 0 [] class_Lattices_Osemilattice__sup(tc_Int_Oint).
% 12.38/12.32 0 [] class_Lattices_Osemilattice__inf(tc_Int_Oint).
% 12.38/12.32 0 [] class_Lattices_Odistrib__lattice(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Oab__semigroup__mult(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Ocomm__monoid__mult(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Ono__zero__divisors(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Olinordered__idom(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Ocomm__semiring(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Oab__group__add(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Ozero__ne_q__one(tc_Int_Oint).
% 12.38/12.32 0 [] class_Orderings_Opreorder(tc_Int_Oint).
% 12.38/12.32 0 [] class_Orderings_Olinorder(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Omonoid__mult(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Omonoid__add(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Osemiring__1(tc_Int_Oint).
% 12.38/12.32 0 [] class_Lattices_Olattice(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Ogroup__add(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Omult__zero(tc_Int_Oint).
% 12.38/12.32 0 [] class_Orderings_Oorder(tc_Int_Oint).
% 12.38/12.32 0 [] class_Int_Oring__char__0(tc_Int_Oint).
% 12.38/12.32 0 [] class_Int_Onumber__ring(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Osemiring(tc_Int_Oint).
% 12.38/12.32 0 [] class_Orderings_Oord(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Oring__1(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Ominus(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Ozero(tc_Int_Oint).
% 12.38/12.32 0 [] class_Rings_Oring(tc_Int_Oint).
% 12.38/12.32 0 [] class_Int_Onumber(tc_Int_Oint).
% 12.38/12.32 0 [] class_Groups_Oone(tc_Int_Oint).
% 12.38/12.32 0 [] class_GCD_Ogcd(tc_Int_Oint).
% 12.38/12.32 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Lattices_Osemilattice__sup(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Lattices_Osemilattice__inf(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Lattices_Odistrib__lattice(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Orderings_Opreorder(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Orderings_Olinorder(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Groups_Omonoid__mult(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Groups_Omonoid__add(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Rings_Osemiring__1(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Lattices_Olattice(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Rings_Omult__zero(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Orderings_Oorder(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Rings_Osemiring(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Orderings_Oord(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Orderings_Obot(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Groups_Ominus(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Groups_Ozero(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Int_Onumber(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Groups_Oone(tc_Nat_Onat).
% 12.38/12.32 0 [] class_GCD_Ogcd(tc_Nat_Onat).
% 12.38/12.32 0 [] class_Lattices_Obounded__lattice__top(tc_HOL_Obool).
% 12.38/12.32 0 [] class_Lattices_Obounded__lattice__bot(tc_HOL_Obool).
% 12.38/12.32 0 [] class_Lattices_Osemilattice__sup(tc_HOL_Obool).
% 12.38/12.32 0 [] class_Lattices_Osemilattice__inf(tc_HOL_Obool).
% 12.38/12.32 0 [] class_Lattices_Odistrib__lattice(tc_HOL_Obool).
% 12.38/12.32 0 [] class_Orderings_Opreorder(tc_HOL_Obool).
% 12.38/12.32 0 [] class_Lattices_Olattice(tc_HOL_Obool).
% 12.38/12.32 0 [] class_Orderings_Oorder(tc_HOL_Obool).
% 12.38/12.32 0 [] class_Orderings_Otop(tc_HOL_Obool).
% 12.38/12.32 0 [] class_Orderings_Oord(tc_HOL_Obool).
% 12.38/12.32 0 [] class_Orderings_Obot(tc_HOL_Obool).
% 12.38/12.32 0 [] class_Groups_Ominus(tc_HOL_Obool).
% 12.38/12.32 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Olinordered__semidom(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Orderings_Odense__linorder(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Lattices_Osemilattice__sup(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Lattices_Osemilattice__inf(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Lattices_Odistrib__lattice(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Oab__semigroup__add(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Ono__zero__divisors(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Olinordered__idom(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Ocomm__semiring(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Oab__group__add(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Ozero__ne_q__one(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Orderings_Opreorder(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Orderings_Olinorder(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Omonoid__mult(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Omonoid__add(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Osemiring__1(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Lattices_Olattice(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Ogroup__add(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Omult__zero(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Orderings_Oorder(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Int_Oring__char__0(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Int_Onumber__ring(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Osemiring(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Orderings_Oord(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Oring__1(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Ominus(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Ozero(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Rings_Oring(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Int_Onumber(tc_RealDef_Oreal).
% 12.38/12.32 0 [] class_Groups_Oone(tc_RealDef_Oreal).
% 12.38/12.32 0 [] -class_Rings_Oidom(T_1)|class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Oidom(T_1)|class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Oidom(T_1)|class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Osemiring__1(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_1)|class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Oord(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ominus(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Groups_Ozero(T_1)|class_Groups_Ozero(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Oring(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Int_Onumber(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Oone(tc_Polynomial_Opoly(T_1)).
% 12.38/12.32 0 [] -hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2))|V_x_2=V_y_2.
% 12.38/12.32 0 [] V_x_2!=V_y_2|hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2)).
% 12.38/12.32 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,v_L____,v_y____).
% 12.38/12.32 end_of_list.
% 12.38/12.32
% 12.38/12.32 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 12.38/12.32
% 12.38/12.32 This ia a non-Horn set with equality. The strategy will be
% 12.38/12.32 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 12.38/12.32 deletion, with positive clauses in sos and nonpositive
% 12.38/12.32 clauses in usable.
% 12.38/12.32
% 12.38/12.32 dependent: set(knuth_bendix).
% 12.38/12.32 dependent: set(anl_eq).
% 12.38/12.32 dependent: set(para_from).
% 12.38/12.32 dependent: set(para_into).
% 12.38/12.32 dependent: clear(para_from_right).
% 12.38/12.32 dependent: clear(para_into_right).
% 12.38/12.32 dependent: set(para_from_vars).
% 12.38/12.32 dependent: set(eq_units_both_ways).
% 12.38/12.32 dependent: set(dynamic_demod_all).
% 12.38/12.32 dependent: set(dynamic_demod).
% 12.38/12.32 dependent: set(order_eq).
% 12.38/12.32 dependent: set(back_demod).
% 12.38/12.32 dependent: set(lrpo).
% 12.38/12.32 dependent: set(hyper_res).
% 12.38/12.32 dependent: set(unit_deletion).
% 12.38/12.32 dependent: set(factor).
% 12.38/12.32
% 12.38/12.32 ------------> process usable:
% 12.38/12.32 ** KEPT (pick-wt=14): 1 [] hAPP(A,$f1(B,A))!=hAPP(B,$f1(B,A))|A=B.
% 12.38/12.32 ** KEPT (pick-wt=8): 2 [] -hBOOL(hAPP(v_P,A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,v_y____).
% 12.38/12.32 ** KEPT (pick-wt=8): 3 [] -hBOOL(hAPP(v_P,A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,v_L____).
% 12.38/12.32 ** KEPT (pick-wt=6): 4 [] -class_Orderings_Opreorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,B).
% 12.38/12.32 ** KEPT (pick-wt=12): 5 [] -hBOOL(hAPP(v_P,A))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_y____,A)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_y____,v_L____).
% 12.38/12.32 ** KEPT (pick-wt=12): 6 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,C).
% 12.38/12.32 ** KEPT (pick-wt=11): 7 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,B,A)|A=B.
% 12.38/12.32 ** KEPT (pick-wt=8): 8 [] -hBOOL(hAPP(v_P,A))| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_y____,A).
% 12.38/12.32 ** KEPT (pick-wt=16): 9 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 12.38/12.32 ** KEPT (pick-wt=24): 10 [] -class_Orderings_Oord(A)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,$f2(D,C,B,A)),hAPP(D,$f2(D,C,B,A))).
% 12.38/12.32 ** KEPT (pick-wt=10): 11 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.32 ** KEPT (pick-wt=9): 12 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.38/12.32 ** KEPT (pick-wt=9): 13 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.32 ** KEPT (pick-wt=13): 14 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.32 ** KEPT (pick-wt=9): 15 [] -class_Orderings_Opreorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.38/12.32 ** KEPT (pick-wt=8): 16 [] -hBOOL(hAPP(v_P,A))|c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,v_Y____).
% 12.38/12.32 ** KEPT (pick-wt=8): 17 [] -hBOOL(hAPP(v_P,A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,v_Y____).
% 12.38/12.32 ** KEPT (pick-wt=8): 18 [] -hBOOL(hAPP(v_P,A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,$c2).
% 12.38/12.32 ** KEPT (pick-wt=6): 19 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,B).
% 12.38/12.32 ** KEPT (pick-wt=13): 20 [] -class_Orderings_Olinorder(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.32 ** KEPT (pick-wt=9): 21 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,B,C).
% 12.38/12.32 ** KEPT (pick-wt=9): 22 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.32 Following clause subsumed by 20 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B)|B=C.
% 12.38/12.32 ** KEPT (pick-wt=10): 23 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.32 Following clause subsumed by 21 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 12.38/12.32 Following clause subsumed by 20 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.32 Following clause subsumed by 20 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B)|C=B.
% 12.38/12.32 Following clause subsumed by 21 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B)|C!=B.
% 12.38/12.32 Following clause subsumed by 20 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.32 ** KEPT (pick-wt=9): 24 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 12.38/12.32 ** KEPT (pick-wt=10): 25 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.32 Following clause subsumed by 25 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.32 Following clause subsumed by 24 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 12.38/12.32 ** KEPT (pick-wt=9): 26 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=B.
% 12.38/12.32 Following clause subsumed by 25 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.32 ** KEPT (pick-wt=10): 27 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.32 ** KEPT (pick-wt=13): 28 [] -class_Orderings_Oord(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 12.38/12.32 ** KEPT (pick-wt=13): 29 [] -class_Orderings_Oorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,D,C)|c_Orderings_Oord__class_Oless(A,D,B).
% 12.38/12.32 ** KEPT (pick-wt=13): 30 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=D|c_Orderings_Oord__class_Oless(A,B,D).
% 12.38/12.32 ** KEPT (pick-wt=13): 31 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=D|c_Orderings_Oord__class_Oless(A,D,C).
% 12.38/12.32 ** KEPT (pick-wt=14): 32 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 12.38/12.32 ** KEPT (pick-wt=14): 33 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C).
% 12.38/12.32 Following clause subsumed by 25 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.32 Following clause subsumed by 20 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.32 ** KEPT (pick-wt=14): 34 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C).
% 12.38/12.32 ** KEPT (pick-wt=14): 35 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 12.38/12.32 ** KEPT (pick-wt=14): 36 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C).
% 12.38/12.32 ** KEPT (pick-wt=14): 37 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 12.38/12.32 ** KEPT (pick-wt=13): 38 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|C=B|c_Orderings_Oord__class_Oless(A,B,C).
% 12.38/12.32 ** KEPT (pick-wt=13): 39 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,B,C).
% 12.38/12.32 Following clause subsumed by 39 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 12.38/12.32 ** KEPT (pick-wt=13): 40 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 12.38/12.32 Following clause subsumed by 21 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 12.38/12.32 ** KEPT (pick-wt=10): 41 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.38/12.32 ** KEPT (pick-wt=10): 42 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.32 Following clause subsumed by 38 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.32 Following clause subsumed by 39 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C).
% 12.38/12.32 Following clause subsumed by 40 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C.
% 12.38/12.32 ** KEPT (pick-wt=13): 43 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C.
% 12.38/12.32 ** KEPT (pick-wt=10): 44 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.32 Following clause subsumed by 44 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.32 Following clause subsumed by 39 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 12.38/12.32 ** KEPT (pick-wt=10): 45 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,B,C).
% 12.38/12.32 Following clause subsumed by 12 during input processing: 0 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C.
% 12.38/12.32 Following clause subsumed by 41 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.38/12.32 ** KEPT (pick-wt=10): 46 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.33 ** KEPT (pick-wt=14): 47 [] -class_Orderings_Opreorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.33 Following clause subsumed by 45 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.38/12.33 Following clause subsumed by 24 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 12.38/12.33 Following clause subsumed by 39 during input processing: 0 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C.
% 12.38/12.33 Following clause subsumed by 44 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.33 Following clause subsumed by 44 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.33 Following clause subsumed by 42 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.33 Following clause subsumed by 44 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.33 Following clause subsumed by 42 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.33 ** KEPT (pick-wt=11): 48 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|A=B.
% 12.38/12.33 ** KEPT (pick-wt=8): 49 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B).
% 12.38/12.33 ** KEPT (pick-wt=7): 50 [] c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|A!=B.
% 12.38/12.33 Following clause subsumed by 49 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).
% 12.38/12.33 ** KEPT (pick-wt=7): 51 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|A!=B.
% 12.38/12.33 Following clause subsumed by 48 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.
% 12.38/12.33 Following clause subsumed by 11 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.33 Following clause subsumed by 9 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 12.38/12.33 ** KEPT (pick-wt=14): 52 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,B)|c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 12.38/12.33 Following clause subsumed by 14 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|C=B.
% 12.38/12.33 ** KEPT (pick-wt=14): 53 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 12.38/12.33 Following clause subsumed by 14 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|B=C.
% 12.38/12.33 ** KEPT (pick-wt=13): 54 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=D|c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 12.38/12.33 ** KEPT (pick-wt=13): 55 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|C!=D|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 12.38/12.33 ** KEPT (pick-wt=13): 56 [] -class_Orderings_Oorder(A)|B!=C| -c_Orderings_Oord__class_Oless__e_q(A,D,C)|c_Orderings_Oord__class_Oless__e_q(A,D,B).
% 12.38/12.33 ** KEPT (pick-wt=13): 57 [] -class_Orderings_Oord(A)|B!=C| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 12.38/12.33 Following clause subsumed by 14 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|C=B.
% 12.38/12.33 Following clause subsumed by 12 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B)|C!=B.
% 12.38/12.33 Following clause subsumed by 9 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 12.38/12.33 ** KEPT (pick-wt=13): 58 [] -class_Rings_Olinordered__idom(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.33 ** KEPT (pick-wt=8): 59 [] -hBOOL(hAPP(v_P,A))|c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,$c4).
% 12.38/12.33 ** KEPT (pick-wt=24): 60 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f3(C,D,B,A)),hAPP(D,$f3(C,D,B,A)))|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,A),B,D).
% 12.38/12.33 ** KEPT (pick-wt=13): 61 [] -class_Orderings_Odense__linorder(A)|c_Orderings_Oord__class_Oless(A,$f4(B,C,A),C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.33 ** KEPT (pick-wt=13): 62 [] -class_Orderings_Odense__linorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,$f4(B,C,A),B)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.33 ** KEPT (pick-wt=18): 63 [] -class_Orderings_Odense__linorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,B,$f5(D,C,B,A))|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 12.38/12.33 ** KEPT (pick-wt=18): 64 [] -class_Orderings_Odense__linorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,$f5(D,C,B,A),C)|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 12.38/12.33 ** KEPT (pick-wt=18): 65 [] -class_Orderings_Odense__linorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,$f5(D,C,B,A),D)|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 12.38/12.33 ** KEPT (pick-wt=36): 66 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless(B,C,D)| -c_Orderings_Oord__class_Oless__e_q(A,E,hAPP(F,C))|c_Orderings_Oord__class_Oless(B,$f6(F,E,D,C,B,A),$f7(F,E,D,C,B,A))|c_Orderings_Oord__class_Oless(A,E,hAPP(F,D)).
% 12.38/12.33 ** KEPT (pick-wt=40): 67 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless(B,C,D)| -c_Orderings_Oord__class_Oless__e_q(A,E,hAPP(F,C))| -c_Orderings_Oord__class_Oless(A,hAPP(F,$f6(F,E,D,C,B,A)),hAPP(F,$f7(F,E,D,C,B,A)))|c_Orderings_Oord__class_Oless(A,E,hAPP(F,D)).
% 12.38/12.33 ** KEPT (pick-wt=36): 68 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless__e_q(B,C,D)| -c_Orderings_Oord__class_Oless(A,E,hAPP(F,C))|c_Orderings_Oord__class_Oless__e_q(B,$f8(F,E,D,C,B,A),$f9(F,E,D,C,B,A))|c_Orderings_Oord__class_Oless(A,E,hAPP(F,D)).
% 12.38/12.33 ** KEPT (pick-wt=40): 69 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless__e_q(B,C,D)| -c_Orderings_Oord__class_Oless(A,E,hAPP(F,C))| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(F,$f8(F,E,D,C,B,A)),hAPP(F,$f9(F,E,D,C,B,A)))|c_Orderings_Oord__class_Oless(A,E,hAPP(F,D)).
% 12.38/12.33 ** KEPT (pick-wt=36): 70 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless(A,C,D)| -c_Orderings_Oord__class_Oless__e_q(B,hAPP(E,D),F)|c_Orderings_Oord__class_Oless(A,$f11(F,E,D,C,B,A),$f10(F,E,D,C,B,A))|c_Orderings_Oord__class_Oless(B,hAPP(E,C),F).
% 12.38/12.33 ** KEPT (pick-wt=40): 71 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless(A,C,D)| -c_Orderings_Oord__class_Oless__e_q(B,hAPP(E,D),F)| -c_Orderings_Oord__class_Oless(B,hAPP(E,$f11(F,E,D,C,B,A)),hAPP(E,$f10(F,E,D,C,B,A)))|c_Orderings_Oord__class_Oless(B,hAPP(E,C),F).
% 12.38/12.33 ** KEPT (pick-wt=36): 72 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)| -c_Orderings_Oord__class_Oless(B,hAPP(E,D),F)|c_Orderings_Oord__class_Oless__e_q(A,$f13(F,E,D,C,B,A),$f12(F,E,D,C,B,A))|c_Orderings_Oord__class_Oless(B,hAPP(E,C),F).
% 12.38/12.33 ** KEPT (pick-wt=40): 73 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)| -c_Orderings_Oord__class_Oless(B,hAPP(E,D),F)| -c_Orderings_Oord__class_Oless__e_q(B,hAPP(E,$f13(F,E,D,C,B,A)),hAPP(E,$f12(F,E,D,C,B,A)))|c_Orderings_Oord__class_Oless(B,hAPP(E,C),F).
% 12.38/12.33 ** KEPT (pick-wt=36): 74 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless(A,C,hAPP(D,E))| -c_Orderings_Oord__class_Oless__e_q(B,E,F)|c_Orderings_Oord__class_Oless__e_q(B,$f15(F,E,D,C,B,A),$f14(F,E,D,C,B,A))|c_Orderings_Oord__class_Oless(A,C,hAPP(D,F)).
% 12.38/12.33 ** KEPT (pick-wt=40): 75 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless(A,C,hAPP(D,E))| -c_Orderings_Oord__class_Oless__e_q(B,E,F)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(D,$f15(F,E,D,C,B,A)),hAPP(D,$f14(F,E,D,C,B,A)))|c_Orderings_Oord__class_Oless(A,C,hAPP(D,F)).
% 12.38/12.33 ** KEPT (pick-wt=36): 76 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(D,E))| -c_Orderings_Oord__class_Oless(B,E,F)|c_Orderings_Oord__class_Oless(B,$f17(F,E,D,C,B,A),$f16(F,E,D,C,B,A))|c_Orderings_Oord__class_Oless(A,C,hAPP(D,F)).
% 12.38/12.33 ** KEPT (pick-wt=40): 77 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless__e_q(A,C,hAPP(D,E))| -c_Orderings_Oord__class_Oless(B,E,F)| -c_Orderings_Oord__class_Oless(A,hAPP(D,$f17(F,E,D,C,B,A)),hAPP(D,$f16(F,E,D,C,B,A)))|c_Orderings_Oord__class_Oless(A,C,hAPP(D,F)).
% 12.38/12.33 ** KEPT (pick-wt=11): 78 [] -class_Orderings_Otop(A)|hAPP(c_Orderings_Otop__class_Otop(tc_fun(B,A)),C)=c_Orderings_Otop__class_Otop(A).
% 12.38/12.33 ** KEPT (pick-wt=14): 79 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D).
% 12.38/12.33 ** KEPT (pick-wt=14): 80 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D,C).
% 12.38/12.33 ** KEPT (pick-wt=20): 81 [] -class_Orderings_Oord(A)|c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D,C).
% 12.38/12.33 ** KEPT (pick-wt=7): 82 [] -class_Orderings_Otop(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Orderings_Otop__class_Otop(A)).
% 12.38/12.33 ** KEPT (pick-wt=13): 83 [] -c_Lubs_OisLub(tc_RealDef_Oreal,A,B,C)| -c_Lubs_OisLub(tc_RealDef_Oreal,A,B,D)|C=D.
% 12.38/12.33 ** KEPT (pick-wt=36): 84 [] -class_Orderings_Oord(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless__e_q(B,hAPP(C,D),E)| -c_Orderings_Oord__class_Oless(A,F,D)|c_Orderings_Oord__class_Oless(A,$f18(F,E,D,C,B,A),$f19(F,E,D,C,B,A))|c_Orderings_Oord__class_Oless(B,hAPP(C,F),E).
% 12.38/12.33 ** KEPT (pick-wt=40): 85 [] -class_Orderings_Oord(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless__e_q(B,hAPP(C,D),E)| -c_Orderings_Oord__class_Oless(A,F,D)| -c_Orderings_Oord__class_Oless(B,hAPP(C,$f18(F,E,D,C,B,A)),hAPP(C,$f19(F,E,D,C,B,A)))|c_Orderings_Oord__class_Oless(B,hAPP(C,F),E).
% 12.38/12.33 ** KEPT (pick-wt=36): 86 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless(B,hAPP(C,D),E)| -c_Orderings_Oord__class_Oless__e_q(A,F,D)|c_Orderings_Oord__class_Oless__e_q(A,$f20(F,E,D,C,B,A),$f21(F,E,D,C,B,A))|c_Orderings_Oord__class_Oless(B,hAPP(C,F),E).
% 12.38/12.33 ** KEPT (pick-wt=40): 87 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless(B,hAPP(C,D),E)| -c_Orderings_Oord__class_Oless__e_q(A,F,D)| -c_Orderings_Oord__class_Oless__e_q(B,hAPP(C,$f20(F,E,D,C,B,A)),hAPP(C,$f21(F,E,D,C,B,A)))|c_Orderings_Oord__class_Oless(B,hAPP(C,F),E).
% 12.38/12.33 ** KEPT (pick-wt=11): 88 [] A!=B|c_member(C,D,A)| -c_member(C,D,B).
% 12.38/12.33 ** KEPT (pick-wt=11): 89 [] A!=B|c_member(C,D,B)| -c_member(C,D,A).
% 12.38/12.33 ** KEPT (pick-wt=15): 90 [] -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.
% 12.38/12.33 ** KEPT (pick-wt=14): 91 [] -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).
% 12.38/12.33 ** KEPT (pick-wt=12): 92 [] -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).
% 12.38/12.33 ** KEPT (pick-wt=9): 93 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)|B!=C.
% 12.38/12.33 ** KEPT (pick-wt=15): 94 [] 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.
% 12.38/12.33 Following clause subsumed by 94 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.
% 12.38/12.33 Following clause subsumed by 92 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).
% 12.38/12.33 ** KEPT (pick-wt=9): 95 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|B!=C.
% 12.38/12.33 Following clause subsumed by 92 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).
% 12.38/12.33 ** KEPT (pick-wt=14): 96 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)| -c_member(A,D,B)|c_member(A,D,C).
% 12.38/12.33 ** KEPT (pick-wt=18): 97 [] -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).
% 12.38/12.33 ** KEPT (pick-wt=18): 98 [] -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).
% 12.38/12.33 ** KEPT (pick-wt=8): 99 [] -c_member(A,B,C)|hBOOL(hAPP(C,B)).
% 12.38/12.33 ** KEPT (pick-wt=8): 100 [] c_member(A,B,C)| -hBOOL(hAPP(C,B)).
% 12.38/12.33 ** KEPT (pick-wt=8): 101 [] -c_member(A,B,c_fe_qual(C))|B=C.
% 12.38/12.33 ** KEPT (pick-wt=8): 102 [] c_member(A,B,c_fe_qual(C))|B!=C.
% 12.38/12.33 Following clause subsumed by 89 during input processing: 0 [] A!=B| -c_member(C,D,A)|c_member(C,D,B).
% 12.38/12.33 Following clause subsumed by 88 during input processing: 0 [] A!=B|c_member(C,D,A)| -c_member(C,D,B).
% 12.38/12.33 ** KEPT (pick-wt=11): 103 [] A!=B| -c_member(C,A,D)|c_member(C,B,D).
% 12.38/12.33 ** KEPT (pick-wt=11): 104 [] A!=B|c_member(C,A,D)| -c_member(C,B,D).
% 12.38/12.33 Following clause subsumed by 104 during input processing: 0 [] A!=B| -c_member(C,B,D)|c_member(C,A,D).
% 12.38/12.33 Following clause subsumed by 95 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,B).
% 12.38/12.33 ** KEPT (pick-wt=9): 105 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),B,A).
% 12.38/12.33 ** KEPT (pick-wt=18): 106 [] -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).
% 12.38/12.33 Following clause subsumed by 91 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).
% 12.38/12.33 Following clause subsumed by 91 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).
% 12.38/12.33 ** KEPT (pick-wt=14): 107 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -hBOOL(hAPP(B,D))|hBOOL(hAPP(C,D)).
% 12.38/12.33 Following clause subsumed by 91 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).
% 12.38/12.33 Following clause subsumed by 105 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),B,A).
% 12.38/12.33 Following clause subsumed by 95 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,B).
% 12.38/12.33 Following clause subsumed by 107 during input processing: 0 [] -hBOOL(hAPP(A,B))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,D)|hBOOL(hAPP(D,B)).
% 12.38/12.33 Following clause subsumed by 95 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,B).
% 12.38/12.33 Following clause subsumed by 105 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),B,A).
% 12.38/12.33 Following clause subsumed by 90 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).
% 12.38/12.33 ** KEPT (pick-wt=18): 108 [] -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).
% 12.38/12.33 ** KEPT (pick-wt=17): 109 [] -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).
% 12.38/12.33 ** KEPT (pick-wt=15): 110 [] -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).
% 12.38/12.33 ** KEPT (pick-wt=14): 111 [] -class_Orderings_Oord(A)| -c_Lubs_OisLub(A,B,C,D)|hBOOL(hAPP(c_Lubs_OisUb(A,B,C),D)).
% 12.38/12.33 ** KEPT (pick-wt=13): 112 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Lubs_OisUb(A,B,C),D))|c_member(A,D,B).
% 12.38/12.33 ** KEPT (pick-wt=11): 113 [] -class_Orderings_Oord(A)| -c_Lubs_OisLub(A,B,C,D)|c_member(A,D,B).
% 12.38/12.33 ** KEPT (pick-wt=23): 114 [] -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,$f22(B)).
% 12.38/12.33 ** KEPT (pick-wt=23): 115 [] -c_member(tc_RealDef_Oreal,A,B)| -hBOOL(hAPP(c_Lubs_OisUb(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),B),C))|c_Lubs_OisLub(tc_RealDef_Oreal,c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_HOL_Obool)),B,$f23(B)).
% 12.38/12.33 ** KEPT (pick-wt=18): 116 [] -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).
% 12.38/12.33 ** KEPT (pick-wt=13): 118 [copy,117,flip.2] -class_Orderings_Oord(A)|c_Set_OCollect(A,c_Lubs_OisUb(A,B,C))=c_Lubs_Oubs(A,B,C).
% 12.38/12.33 ** KEPT (pick-wt=23): 119 [] -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).
% 12.38/12.33 ** KEPT (pick-wt=16): 120 [] -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).
% 12.38/12.33 ** KEPT (pick-wt=14): 121 [] -class_Orderings_Oord(A)| -c_Lubs_OisLub(A,B,C,D)|c_Lubs_OleastP(A,c_Lubs_OisUb(A,B,C),D).
% 12.38/12.33 ** KEPT (pick-wt=14): 122 [] -class_Orderings_Oord(A)| -c_Lubs_OleastP(A,c_Lubs_OisUb(A,B,C),D)|c_Lubs_OisLub(A,B,C,D).
% 12.38/12.33 Following clause subsumed by 121 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).
% 12.38/12.33 Following clause subsumed by 122 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).
% 12.38/12.33 ** KEPT (pick-wt=17): 123 [] -class_Orderings_Oord(A)| -c_Lubs_Osetle(A,B,C)| -c_member(A,C,D)|hBOOL(hAPP(c_Lubs_OisUb(A,D,B),C)).
% 12.38/12.33 ** KEPT (pick-wt=13): 124 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Lubs_OisUb(A,B,C),D))|c_Lubs_Osetle(A,C,D).
% 12.38/12.33 Following clause subsumed by 112 during input processing: 0 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Lubs_OisUb(A,B,C),D))|c_member(A,D,B).
% 12.38/12.33 Following clause subsumed by 123 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).
% 12.38/12.33 ** KEPT (pick-wt=14): 125 [] -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).
% 12.38/12.33 ** KEPT (pick-wt=10): 126 [] -class_Orderings_Oord(A)| -c_Lubs_OleastP(A,B,C)|hBOOL(hAPP(B,C)).
% 12.38/12.33 Following clause subsumed by 126 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Lubs_OleastP(A,B,C)|hBOOL(hAPP(B,C)).
% 12.38/12.33 ** KEPT (pick-wt=12): 127 [] -class_Orderings_Oord(A)| -c_Lubs_OleastP(A,B,C)|c_Lubs_Osetge(A,C,c_Set_OCollect(A,B)).
% 12.38/12.33 ** KEPT (pick-wt=16): 128 [] -class_Orderings_Oord(A)|c_Lubs_OleastP(A,B,C)| -hBOOL(hAPP(B,C))| -c_Lubs_Osetge(A,C,c_Set_OCollect(A,B)).
% 12.38/12.33 Following clause subsumed by 127 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Lubs_OleastP(A,B,C)|c_Lubs_Osetge(A,C,c_Set_OCollect(A,B)).
% 12.38/12.33 ** KEPT (pick-wt=14): 129 [] -class_Orderings_Oord(A)| -c_Lubs_OisLub(A,B,C,D)|c_Lubs_Osetge(A,D,c_Lubs_Oubs(A,B,C)).
% 12.38/12.33 ** KEPT (pick-wt=14): 130 [] -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).
% 12.38/12.33 ** KEPT (pick-wt=13): 131 [] -class_Orderings_Oord(A)|c_Lubs_Osetle(A,B,C)|c_member(A,$f24(C,B,A),B).
% 12.38/12.33 ** KEPT (pick-wt=13): 132 [] -class_Orderings_Oord(A)|c_Lubs_Osetle(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,$f24(C,B,A),C).
% 12.38/12.33 Following clause subsumed by 125 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).
% 12.38/12.33 ** KEPT (pick-wt=13): 133 [] -class_Orderings_Oord(A)|c_Lubs_Osetge(A,B,C)|c_member(A,$f25(C,B,A),C).
% 12.38/12.33 ** KEPT (pick-wt=13): 134 [] -class_Orderings_Oord(A)|c_Lubs_Osetge(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,$f25(C,B,A)).
% 12.38/12.33 ** KEPT (pick-wt=11): 135 [] -class_Orderings_Oord(A)| -c_Lubs_OisLub(A,B,C,D)|c_Lubs_Osetle(A,C,D).
% 12.38/12.33 Following clause subsumed by 124 during input processing: 0 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Lubs_OisUb(A,B,C),D))|c_Lubs_Osetle(A,C,D).
% 12.38/12.33 Following clause subsumed by 130 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).
% 12.38/12.33 ** KEPT (pick-wt=19): 136 [] -class_Orderings_Oord(A)|c_member(A,$f26(B,C,A),C)|hBOOL(hAPP(c_Lubs_OisUb(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),C),B)).
% 12.38/12.33 ** KEPT (pick-wt=19): 137 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(A,$f26(B,C,A),B)|hBOOL(hAPP(c_Lubs_OisUb(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),C),B)).
% 12.38/12.33 ** KEPT (pick-wt=18): 138 [] -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)).
% 12.38/12.33 ** KEPT (pick-wt=13): 139 [] -c_member(A,$f27(B,C,A),B)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,B).
% 12.38/12.33 ** KEPT (pick-wt=13): 140 [] -class_Orderings_Oord(A)|c_member(A,$f28(B,C,A),C)|c_Lubs_Osetle(A,C,B).
% 12.38/12.33 ** KEPT (pick-wt=13): 141 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(A,$f28(B,C,A),B)|c_Lubs_Osetle(A,C,B).
% 12.38/12.33 ** KEPT (pick-wt=13): 142 [] -class_Orderings_Oord(A)|c_member(A,$f29(B,C,A),C)|c_Lubs_Osetge(A,B,C).
% 12.38/12.33 ** KEPT (pick-wt=13): 143 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,$f29(B,C,A))|c_Lubs_Osetge(A,B,C).
% 12.38/12.33 ** KEPT (pick-wt=17): 144 [] -hBOOL(hAPP(A,$f30(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)).
% 12.38/12.33 ** KEPT (pick-wt=12): 145 [] -c_member(A,$f31(B,A),B)|c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))=B.
% 12.38/12.33 ** KEPT (pick-wt=17): 146 [] -class_Orderings_Oorder(A)| -c_SEQ_Odecse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,D),hAPP(B,C)).
% 12.38/12.33 ** KEPT (pick-wt=13): 147 [] -class_Orderings_Oorder(A)|c_SEQ_Odecse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f34(B,A),$f33(B,A)).
% 12.38/12.33 ** KEPT (pick-wt=17): 148 [] -class_Orderings_Oorder(A)|c_SEQ_Odecse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f33(B,A)),hAPP(B,$f34(B,A))).
% 12.38/12.33 ** KEPT (pick-wt=17): 149 [] -class_Orderings_Oorder(A)| -c_SEQ_Oincse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,C),hAPP(B,D)).
% 12.38/12.33 ** KEPT (pick-wt=13): 150 [] -class_Orderings_Oorder(A)|c_SEQ_Oincse_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f36(B,A),$f35(B,A)).
% 12.38/12.33 ** KEPT (pick-wt=17): 151 [] -class_Orderings_Oorder(A)|c_SEQ_Oincse_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f36(B,A)),hAPP(B,$f35(B,A))).
% 12.38/12.33 ** KEPT (pick-wt=18): 152 [] -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)).
% 12.38/12.33 ** KEPT (pick-wt=20): 153 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oorder__class_Ostrict__mono(B,A,C)| -c_Orderings_Oord__class_Oless(B,D,E)|c_Orderings_Oord__class_Oless(A,hAPP(C,D),hAPP(C,E)).
% 12.38/12.33 ** KEPT (pick-wt=20): 154 [] -class_Orderings_Oorder(A)| -class_Orderings_Olinorder(B)| -c_Orderings_Oorder__class_Ostrict__mono(B,A,C)| -c_Orderings_Oord__class_Oless(A,hAPP(C,D),hAPP(C,E))|c_Orderings_Oord__class_Oless(B,D,E).
% 12.38/12.33 ** KEPT (pick-wt=20): 155 [] -class_Orderings_Oorder(A)| -class_Orderings_Olinorder(B)| -c_Orderings_Oorder__class_Ostrict__mono(B,A,C)|c_Orderings_Oord__class_Oless(A,hAPP(C,D),hAPP(C,E))| -c_Orderings_Oord__class_Oless(B,D,E).
% 12.38/12.33 ** KEPT (pick-wt=22): 156 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OatLeastAtMost(A,D,E))| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,D,B).
% 12.38/12.33 ** KEPT (pick-wt=22): 157 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OatLeastAtMost(A,D,E))| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,E).
% 12.38/12.33 ** KEPT (pick-wt=26): 158 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OatLeastAtMost(A,D,E))| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,D,B)|c_Orderings_Oord__class_Oless(A,C,E).
% 12.38/12.33 ** KEPT (pick-wt=18): 159 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OatLeastAtMost(A,D,E))|c_Orderings_Oord__class_Oless__e_q(A,D,E).
% 12.38/12.33 ** KEPT (pick-wt=22): 160 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OatLeastAtMost(A,D,E))|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E).
% 12.38/12.33 ** KEPT (pick-wt=30): 161 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OatLeastAtMost(A,D,E))| -c_Orderings_Oord__class_Oless__e_q(A,D,B)| -c_Orderings_Oord__class_Oless__e_q(A,C,E)| -c_Orderings_Oord__class_Oless(A,D,B)| -c_Orderings_Oord__class_Oless__e_q(A,D,E).
% 12.38/12.33 ** KEPT (pick-wt=30): 162 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OatLeastAtMost(A,D,E))| -c_Orderings_Oord__class_Oless__e_q(A,D,B)| -c_Orderings_Oord__class_Oless__e_q(A,C,E)| -c_Orderings_Oord__class_Oless(A,C,E)| -c_Orderings_Oord__class_Oless__e_q(A,D,E).
% 12.38/12.33 ** KEPT (pick-wt=20): 163 [] -class_Orderings_Oorder(A)| -class_Orderings_Olinorder(B)| -c_Orderings_Oorder__class_Ostrict__mono(B,A,C)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,D),hAPP(C,E))|c_Orderings_Oord__class_Oless__e_q(B,D,E).
% 12.38/12.33 ** KEPT (pick-wt=20): 164 [] -class_Orderings_Oorder(A)| -class_Orderings_Olinorder(B)| -c_Orderings_Oorder__class_Ostrict__mono(B,A,C)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,D),hAPP(C,E))| -c_Orderings_Oord__class_Oless__e_q(B,D,E).
% 12.38/12.33 ** KEPT (pick-wt=13): 165 [] -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).
% 12.38/12.33 ** KEPT (pick-wt=15): 166 [] -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).
% 12.38/12.33 ** KEPT (pick-wt=19): 167 [] 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).
% 12.38/12.33 ** KEPT (pick-wt=14): 168 [] -c_member(A,B,c_Set_Oinsert(A,C,D))|B=C|c_member(A,B,D).
% 12.38/12.33 ** KEPT (pick-wt=11): 169 [] -c_member(A,B,C)|c_member(A,B,c_Set_Oinsert(A,D,C)).
% 12.38/12.33 ** KEPT (pick-wt=10): 170 [] A!=B|c_member(C,A,c_Set_Oinsert(C,B,D)).
% 12.38/12.33 ** KEPT (pick-wt=14): 171 [] -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)).
% 12.38/12.33 ** KEPT (pick-wt=18): 172 [] -class_Orderings_Oorder(A)| -class_Orderings_Olinorder(B)| -c_Orderings_Oorder__class_Ostrict__mono(B,A,C)|hAPP(C,D)!=hAPP(C,E)|D=E.
% 12.38/12.33 ** KEPT (pick-wt=18): 173 [] -class_Orderings_Oorder(A)| -class_Orderings_Olinorder(B)| -c_Orderings_Oorder__class_Ostrict__mono(B,A,C)|hAPP(C,D)=hAPP(C,E)|D!=E.
% 12.38/12.33 ** KEPT (pick-wt=14): 174 [] -hBOOL(hAPP(c_Set_Oinsert(A,B,C),D))|B=D|hBOOL(hAPP(C,D)).
% 12.38/12.33 ** KEPT (pick-wt=10): 175 [] hBOOL(hAPP(c_Set_Oinsert(A,B,C),D))|B!=D.
% 12.38/12.33 ** KEPT (pick-wt=11): 176 [] hBOOL(hAPP(c_Set_Oinsert(A,B,C),D))| -hBOOL(hAPP(C,D)).
% 12.38/12.33 Following clause subsumed by 168 during input processing: 0 [] -c_member(A,B,c_Set_Oinsert(A,C,D))|B=C|c_member(A,B,D).
% 12.38/12.33 Following clause subsumed by 170 during input processing: 0 [] c_member(A,B,c_Set_Oinsert(A,C,D))|B!=C.
% 12.38/12.33 Following clause subsumed by 169 during input processing: 0 [] c_member(A,B,c_Set_Oinsert(A,C,D))| -c_member(A,B,D).
% 12.38/12.33 ** KEPT (pick-wt=20): 177 [] c_member(A,B,C)|c_member(A,B,D)|c_Set_Oinsert(A,B,C)!=c_Set_Oinsert(A,B,D)|C=D.
% 12.38/12.33 ** KEPT (pick-wt=20): 178 [] c_member(A,B,C)|c_member(A,B,D)|c_Set_Oinsert(A,B,C)=c_Set_Oinsert(A,B,D)|C!=D.
% 12.38/12.33 Following clause subsumed by 169 during input processing: 0 [] -c_member(A,B,C)|c_member(A,B,c_Set_Oinsert(A,D,C)).
% 12.38/12.33 ** KEPT (pick-wt=10): 179 [] -c_member(A,B,C)|c_Set_Oinsert(A,B,C)=C.
% 12.38/12.33 ** KEPT (pick-wt=18): 180 [] -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)).
% 12.38/12.33 ** KEPT (pick-wt=15): 181 [] -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)).
% 12.38/12.33 ** KEPT (pick-wt=14): 182 [] -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).
% 12.38/12.33 Following clause subsumed by 182 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).
% 12.38/12.33 Following clause subsumed by 171 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).
% 12.38/12.33 ** KEPT (pick-wt=22): 183 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OatLeastAtMost(A,D,E))| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,D,B).
% 12.38/12.33 ** KEPT (pick-wt=22): 184 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OatLeastAtMost(A,D,E))| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,E).
% 12.38/12.33 ** KEPT (pick-wt=18): 185 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OatLeastAtMost(A,D,E))|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.38/12.33 ** KEPT (pick-wt=22): 186 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OatLeastAtMost(A,D,E))| -c_Orderings_Oord__class_Oless__e_q(A,D,B)| -c_Orderings_Oord__class_Oless__e_q(A,C,E).
% 12.38/12.33 ** KEPT (pick-wt=19): 187 [] 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).
% 12.38/12.33 Following clause subsumed by 181 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).
% 12.38/12.33 ** KEPT (pick-wt=13): 188 [] -c_member(A,B,c_SetInterval_Oord_OatMost(A,C,D))|hBOOL(hAPP(hAPP(C,B),D)).
% 12.38/12.33 ** KEPT (pick-wt=13): 189 [] c_member(A,B,c_SetInterval_Oord_OatMost(A,C,D))| -hBOOL(hAPP(hAPP(C,B),D)).
% 12.38/12.33 ** KEPT (pick-wt=13): 190 [] -c_member(A,B,c_SetInterval_Oord_OatLeast(A,C,D))|hBOOL(hAPP(hAPP(C,D),B)).
% 12.38/12.33 ** KEPT (pick-wt=13): 191 [] c_member(A,B,c_SetInterval_Oord_OatLeast(A,C,D))| -hBOOL(hAPP(hAPP(C,D),B)).
% 12.38/12.33 ** KEPT (pick-wt=13): 192 [] -c_member(A,B,c_SetInterval_Oord_OlessThan(A,C,D))|hBOOL(hAPP(hAPP(C,B),D)).
% 12.38/12.33 ** KEPT (pick-wt=13): 193 [] c_member(A,B,c_SetInterval_Oord_OlessThan(A,C,D))| -hBOOL(hAPP(hAPP(C,B),D)).
% 12.38/12.33 ** KEPT (pick-wt=13): 194 [] -c_member(A,B,c_SetInterval_Oord_OgreaterThan(A,C,D))|hBOOL(hAPP(hAPP(C,D),B)).
% 12.38/12.33 ** KEPT (pick-wt=13): 195 [] c_member(A,B,c_SetInterval_Oord_OgreaterThan(A,C,D))| -hBOOL(hAPP(hAPP(C,D),B)).
% 12.38/12.33 ** KEPT (pick-wt=14): 196 [] -c_member(A,B,c_SetInterval_Oord_OatLeastAtMost(A,C,D,E))|hBOOL(hAPP(hAPP(C,D),B)).
% 12.38/12.33 ** KEPT (pick-wt=14): 197 [] -c_member(A,B,c_SetInterval_Oord_OatLeastAtMost(A,C,D,E))|hBOOL(hAPP(hAPP(C,B),E)).
% 12.38/12.33 ** KEPT (pick-wt=20): 198 [] c_member(A,B,c_SetInterval_Oord_OatLeastAtMost(A,C,D,E))| -hBOOL(hAPP(hAPP(C,D),B))| -hBOOL(hAPP(hAPP(C,B),E)).
% 12.38/12.33 ** KEPT (pick-wt=14): 199 [] -c_member(A,B,c_SetInterval_Oord_OgreaterThanLessThan(A,C,D,E))|hBOOL(hAPP(hAPP(C,D),B)).
% 12.38/12.33 ** KEPT (pick-wt=14): 200 [] -c_member(A,B,c_SetInterval_Oord_OgreaterThanLessThan(A,C,D,E))|hBOOL(hAPP(hAPP(C,B),E)).
% 12.38/12.33 ** KEPT (pick-wt=20): 201 [] c_member(A,B,c_SetInterval_Oord_OgreaterThanLessThan(A,C,D,E))| -hBOOL(hAPP(hAPP(C,D),B))| -hBOOL(hAPP(hAPP(C,B),E)).
% 12.38/12.33 ** KEPT (pick-wt=15): 202 [] -c_member(A,B,c_SetInterval_Oord_OatLeastLessThan(A,C,D,E,F))|hBOOL(hAPP(hAPP(C,E),B)).
% 12.38/12.33 ** KEPT (pick-wt=15): 203 [] -c_member(A,B,c_SetInterval_Oord_OatLeastLessThan(A,C,D,E,F))|hBOOL(hAPP(hAPP(D,B),F)).
% 12.38/12.33 ** KEPT (pick-wt=21): 204 [] c_member(A,B,c_SetInterval_Oord_OatLeastLessThan(A,C,D,E,F))| -hBOOL(hAPP(hAPP(C,E),B))| -hBOOL(hAPP(hAPP(D,B),F)).
% 12.38/12.33 ** KEPT (pick-wt=15): 205 [] -c_member(A,B,c_SetInterval_Oord_OgreaterThanAtMost(A,C,D,E,F))|hBOOL(hAPP(hAPP(D,E),B)).
% 12.38/12.33 ** KEPT (pick-wt=15): 206 [] -c_member(A,B,c_SetInterval_Oord_OgreaterThanAtMost(A,C,D,E,F))|hBOOL(hAPP(hAPP(C,B),F)).
% 12.38/12.33 ** KEPT (pick-wt=21): 207 [] c_member(A,B,c_SetInterval_Oord_OgreaterThanAtMost(A,C,D,E,F))| -hBOOL(hAPP(hAPP(D,E),B))| -hBOOL(hAPP(hAPP(C,B),F)).
% 12.38/12.33 ** KEPT (pick-wt=29): 208 [] -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)).
% 12.38/12.33 ** KEPT (pick-wt=13): 209 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f38(B,A),$f37(B,A)).
% 12.38/12.33 ** KEPT (pick-wt=17): 210 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f38(B,A)),hAPP(B,$f37(B,A))).
% 12.38/12.33 ** KEPT (pick-wt=13): 211 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f40(B,A),$f39(B,A)).
% 12.38/12.33 ** KEPT (pick-wt=17): 212 [] -class_Orderings_Oorder(A)|c_SEQ_Omonose_q(A,B)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f39(B,A)),hAPP(B,$f40(B,A))).
% 12.38/12.33 ** KEPT (pick-wt=8): 213 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 12.38/12.33 ** KEPT (pick-wt=7): 214 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 12.38/12.33 ** KEPT (pick-wt=11): 215 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B.
% 12.38/12.33 Following clause subsumed by 215 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B.
% 12.38/12.33 Following clause subsumed by 213 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.38/12.33 ** KEPT (pick-wt=7): 216 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A!=B.
% 12.38/12.33 Following clause subsumed by 213 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 12.38/12.33 Following clause subsumed by 213 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 12.38/12.33 Following clause subsumed by 215 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.38/12.33 Following clause subsumed by 213 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 12.38/12.34 Following clause subsumed by 216 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 12.38/12.34 ** KEPT (pick-wt=4): 217 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 12.38/12.34 Following clause subsumed by 214 during input processing: 0 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 12.38/12.34 ** KEPT (pick-wt=7): 218 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 12.38/12.34 Following clause subsumed by 217 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 12.38/12.34 Following clause subsumed by 218 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=A.
% 12.38/12.34 Following clause subsumed by 214 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 12.38/12.34 ** KEPT (pick-wt=8): 219 [] -class_Orderings_Oorder(A)| -c_SEQ_Oincse_q(A,B)|c_SEQ_Omonose_q(A,B).
% 12.38/12.34 ** KEPT (pick-wt=8): 220 [] -class_Orderings_Oorder(A)| -c_SEQ_Odecse_q(A,B)|c_SEQ_Omonose_q(A,B).
% 12.38/12.34 ** KEPT (pick-wt=11): 221 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,A)|A=B.
% 12.38/12.34 ** KEPT (pick-wt=12): 222 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 12.38/12.34 Following clause subsumed by 216 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 12.38/12.34 ** KEPT (pick-wt=13): 223 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f42(B,A),$f41(B,A))|c_SEQ_Omonose_q(A,B).
% 12.38/12.34 ** KEPT (pick-wt=17): 224 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f41(B,A)),hAPP(B,$f42(B,A)))|c_SEQ_Omonose_q(A,B).
% 12.38/12.34 ** KEPT (pick-wt=13): 225 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f44(B,A),$f43(B,A))|c_SEQ_Omonose_q(A,B).
% 12.38/12.34 ** KEPT (pick-wt=17): 226 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(B,$f44(B,A)),hAPP(B,$f43(B,A)))|c_SEQ_Omonose_q(A,B).
% 12.38/12.34 ** KEPT (pick-wt=16): 227 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(A,B),c_SetInterval_Oord__class_OlessThan(A,C))|c_Orderings_Oord__class_Oless(A,B,C).
% 12.38/12.34 ** KEPT (pick-wt=16): 228 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(A,B),c_SetInterval_Oord__class_OlessThan(A,C))| -c_Orderings_Oord__class_Oless(A,B,C).
% 12.38/12.34 ** KEPT (pick-wt=16): 229 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(A,B),c_SetInterval_Oord__class_OgreaterThan(A,C))|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.34 ** KEPT (pick-wt=16): 230 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(A,B),c_SetInterval_Oord__class_OgreaterThan(A,C))| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.38/12.34 ** KEPT (pick-wt=18): 231 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)|c_Orderings_Oord__class_Oless(B,$f46(C,B,A),$f45(C,B,A))|c_Orderings_Oorder__class_Ostrict__mono(B,A,C).
% 12.38/12.34 ** KEPT (pick-wt=22): 232 [] -class_Orderings_Oorder(A)| -class_Orderings_Oorder(B)| -c_Orderings_Oord__class_Oless(A,hAPP(C,$f46(C,B,A)),hAPP(C,$f45(C,B,A)))|c_Orderings_Oorder__class_Ostrict__mono(B,A,C).
% 12.38/12.34 ** KEPT (pick-wt=12): 233 [] -class_Orderings_Oord(A)| -c_member(A,B,c_SetInterval_Oord__class_OgreaterThan(A,C))|c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.34 ** KEPT (pick-wt=12): 234 [] -class_Orderings_Oord(A)|c_member(A,B,c_SetInterval_Oord__class_OgreaterThan(A,C))| -c_Orderings_Oord__class_Oless(A,C,B).
% 12.38/12.34 ** KEPT (pick-wt=16): 235 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(A,B),c_SetInterval_Oord__class_OlessThan(A,C))|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.38/12.34 ** KEPT (pick-wt=16): 236 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(A,B),c_SetInterval_Oord__class_OlessThan(A,C))| -c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=12): 237 [] -class_Orderings_Olinorder(A)|c_SetInterval_Oord__class_OlessThan(A,B)!=c_SetInterval_Oord__class_OlessThan(A,C)|B=C.
% 12.43/12.34 ** KEPT (pick-wt=12): 238 [] -class_Orderings_Olinorder(A)|c_SetInterval_Oord__class_OlessThan(A,B)=c_SetInterval_Oord__class_OlessThan(A,C)|B!=C.
% 12.43/12.34 ** KEPT (pick-wt=12): 239 [] -class_Orderings_Olinorder(A)|c_SetInterval_Oord__class_OgreaterThan(A,B)!=c_SetInterval_Oord__class_OgreaterThan(A,C)|B=C.
% 12.43/12.34 ** KEPT (pick-wt=12): 240 [] -class_Orderings_Olinorder(A)|c_SetInterval_Oord__class_OgreaterThan(A,B)=c_SetInterval_Oord__class_OgreaterThan(A,C)|B!=C.
% 12.43/12.34 ** KEPT (pick-wt=12): 241 [] -class_Orderings_Oord(A)| -c_member(A,B,c_SetInterval_Oord__class_OlessThan(A,C))|c_Orderings_Oord__class_Oless(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=12): 242 [] -class_Orderings_Oord(A)|c_member(A,B,c_SetInterval_Oord__class_OlessThan(A,C))| -c_Orderings_Oord__class_Oless(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=16): 243 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(A,B),c_SetInterval_Oord__class_OatMost(A,C))|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=16): 244 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(A,B),c_SetInterval_Oord__class_OatMost(A,C))| -c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=16): 245 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeast(A,B),c_SetInterval_Oord__class_OatLeast(A,C))|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.43/12.34 ** KEPT (pick-wt=16): 246 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeast(A,B),c_SetInterval_Oord__class_OatLeast(A,C))| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.43/12.34 ** KEPT (pick-wt=12): 247 [] -class_Orderings_Oord(A)| -c_member(A,B,c_SetInterval_Oord__class_OatMost(A,C))|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=12): 248 [] -class_Orderings_Oord(A)|c_member(A,B,c_SetInterval_Oord__class_OatMost(A,C))| -c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=12): 249 [] -class_Orderings_Oord(A)| -c_member(A,B,c_SetInterval_Oord__class_OatLeast(A,C))|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.43/12.34 ** KEPT (pick-wt=12): 250 [] -class_Orderings_Oord(A)|c_member(A,B,c_SetInterval_Oord__class_OatLeast(A,C))| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 12.43/12.34 ** KEPT (pick-wt=10): 251 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),c_RComplete_Onatceiling(B)).
% 12.43/12.34 ** KEPT (pick-wt=22): 252 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f48(A,B,C),$f47(A,B,C))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(C,B),hAPP(C,A)).
% 12.43/12.34 ** KEPT (pick-wt=26): 253 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,$f48(B,C,A)),hAPP(A,$f47(B,C,A)))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(A,C),hAPP(A,B)).
% 12.43/12.34 ** KEPT (pick-wt=13): 255 [copy,254,flip.2] -c_member(A,B,C)|c_Set_Oinsert(A,B,$f49(C,B,A))=C.
% 12.43/12.34 ** KEPT (pick-wt=11): 256 [] -c_member(A,B,C)| -c_member(A,B,$f49(C,B,A)).
% 12.43/12.34 ** KEPT (pick-wt=12): 257 [] -class_Orderings_Olinorder(A)|c_SetInterval_Oord__class_OatLeast(A,B)!=c_SetInterval_Oord__class_OatLeast(A,C)|B=C.
% 12.43/12.34 ** KEPT (pick-wt=12): 258 [] -class_Orderings_Olinorder(A)|c_SetInterval_Oord__class_OatLeast(A,B)=c_SetInterval_Oord__class_OatLeast(A,C)|B!=C.
% 12.43/12.34 ** KEPT (pick-wt=12): 259 [] -class_Orderings_Olinorder(A)|c_SetInterval_Oord__class_OatMost(A,B)!=c_SetInterval_Oord__class_OatMost(A,C)|B=C.
% 12.43/12.34 ** KEPT (pick-wt=12): 260 [] -class_Orderings_Olinorder(A)|c_SetInterval_Oord__class_OatMost(A,B)=c_SetInterval_Oord__class_OatMost(A,C)|B!=C.
% 12.43/12.34 ** KEPT (pick-wt=21): 261 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThan(A,C))=c_SetInterval_Oord__class_OatLeast(A,B).
% 12.43/12.34 ** KEPT (pick-wt=21): 262 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(A,B),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C))=c_SetInterval_Oord__class_OatMost(A,C).
% 12.43/12.34 ** KEPT (pick-wt=11): 263 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_RealDef_Oreal(tc_Nat_Onat,B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatceiling(A),B).
% 12.43/12.34 ** KEPT (pick-wt=13): 265 [copy,264,flip.2] -c_member(A,B,C)|c_Set_Oinsert(A,B,$f50(C,B,A))=C.
% 12.43/12.34 ** KEPT (pick-wt=11): 266 [] -c_member(A,B,C)| -c_member(A,B,$f50(C,B,A)).
% 12.43/12.34 ** KEPT (pick-wt=8): 267 [] -c_SEQ_Osubse_q(A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,hAPP(A,B)).
% 12.43/12.34 ** KEPT (pick-wt=10): 268 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_RComplete_Onatfloor(A),c_RComplete_Onatfloor(B)).
% 12.43/12.34 ** KEPT (pick-wt=17): 269 [] -hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),B,C),D))|hBOOL(hAPP(B,D))|hBOOL(hAPP(C,D)).
% 12.43/12.34 ** KEPT (pick-wt=13): 270 [] -hBOOL(hAPP(A,B))|hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(C,tc_HOL_Obool),D,A),B)).
% 12.43/12.34 ** KEPT (pick-wt=13): 271 [] -hBOOL(hAPP(A,B))|hBOOL(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(C,tc_HOL_Obool),A,D),B)).
% 12.43/12.34 ** KEPT (pick-wt=13): 272 [] -c_member(A,B,C)|c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),D,C)).
% 12.43/12.34 ** KEPT (pick-wt=13): 273 [] -c_member(A,B,C)|c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D)).
% 12.43/12.34 ** KEPT (pick-wt=17): 274 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))|c_member(A,B,C)|c_member(A,B,D).
% 12.43/12.34 ** KEPT (pick-wt=5): 275 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.43/12.34 ** KEPT (pick-wt=29): 276 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))| -hBOOL(hAPP(E,B))|c_member(A,$f51(E,D,C,A),C)|c_member(A,$f52(E,D,C,A),D).
% 12.43/12.34 ** KEPT (pick-wt=29): 277 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))| -hBOOL(hAPP(E,B))|c_member(A,$f51(E,D,C,A),C)|hBOOL(hAPP(E,$f52(E,D,C,A))).
% 12.43/12.34 ** KEPT (pick-wt=29): 278 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))| -hBOOL(hAPP(E,B))|hBOOL(hAPP(E,$f51(E,D,C,A)))|c_member(A,$f52(E,D,C,A),D).
% 12.43/12.34 ** KEPT (pick-wt=29): 279 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))| -hBOOL(hAPP(E,B))|hBOOL(hAPP(E,$f51(E,D,C,A)))|hBOOL(hAPP(E,$f52(E,D,C,A))).
% 12.43/12.34 ** KEPT (pick-wt=21): 280 [] c_member(A,$f53(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)).
% 12.43/12.34 ** KEPT (pick-wt=21): 281 [] c_member(A,$f53(B,C,D,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),D,C))| -c_member(A,E,C)| -hBOOL(hAPP(B,E)).
% 12.43/12.34 ** KEPT (pick-wt=16): 282 [] hBOOL(hAPP(A,$f53(A,B,C,D)))| -c_member(D,E,C)| -hBOOL(hAPP(A,E)).
% 12.43/12.34 ** KEPT (pick-wt=16): 283 [] hBOOL(hAPP(A,$f53(A,B,C,D)))| -c_member(D,E,B)| -hBOOL(hAPP(A,E)).
% 12.43/12.34 ** KEPT (pick-wt=21): 284 [] c_member(A,$f54(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)).
% 12.43/12.34 ** KEPT (pick-wt=21): 285 [] c_member(A,$f54(B,C,D,A),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),D,C))| -c_member(A,E,C)|hBOOL(hAPP(B,E)).
% 12.43/12.34 ** KEPT (pick-wt=16): 286 [] -hBOOL(hAPP(A,$f54(A,B,C,D)))| -c_member(D,E,C)|hBOOL(hAPP(A,E)).
% 12.43/12.34 ** KEPT (pick-wt=16): 287 [] -hBOOL(hAPP(A,$f54(A,B,C,D)))| -c_member(D,E,B)|hBOOL(hAPP(A,E)).
% 12.43/12.34 ** KEPT (pick-wt=29): 288 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))|hBOOL(hAPP(E,B))|c_member(A,$f55(E,D,C,A),C)|c_member(A,$f56(E,D,C,A),D).
% 12.43/12.34 ** KEPT (pick-wt=29): 289 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))|hBOOL(hAPP(E,B))|c_member(A,$f55(E,D,C,A),C)| -hBOOL(hAPP(E,$f56(E,D,C,A))).
% 12.43/12.34 ** KEPT (pick-wt=29): 290 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))|hBOOL(hAPP(E,B))| -hBOOL(hAPP(E,$f55(E,D,C,A)))|c_member(A,$f56(E,D,C,A),D).
% 12.43/12.34 ** KEPT (pick-wt=29): 291 [] -c_member(A,B,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),C,D))|hBOOL(hAPP(E,B))| -hBOOL(hAPP(E,$f55(E,D,C,A)))| -hBOOL(hAPP(E,$f56(E,D,C,A))).
% 12.43/12.34 Following clause subsumed by 271 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)).
% 12.43/12.34 Following clause subsumed by 270 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)).
% 12.43/12.34 ** KEPT (pick-wt=10): 292 [] c_RealDef_Oreal(tc_Nat_Onat,A)!=c_RealDef_Oreal(tc_Nat_Onat,B)|A=B.
% 12.43/12.34 ** KEPT (pick-wt=10): 293 [] c_RealDef_Oreal(tc_Nat_Onat,A)=c_RealDef_Oreal(tc_Nat_Onat,B)|A!=B.
% 12.43/12.34 ** KEPT (pick-wt=11): 294 [] -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)).
% 12.43/12.34 Following clause subsumed by 272 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)).
% 12.43/12.34 Following clause subsumed by 273 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)).
% 12.43/12.34 Following clause subsumed by 274 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).
% 12.43/12.34 Following clause subsumed by 273 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).
% 12.43/12.34 Following clause subsumed by 272 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).
% 12.43/12.34 ** KEPT (pick-wt=14): 295 [] -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.
% 12.43/12.34 ** KEPT (pick-wt=14): 296 [] 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.
% 12.43/12.34 Following clause subsumed by 295 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.
% 12.43/12.34 ** KEPT (pick-wt=14): 297 [] -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.
% 12.43/12.34 ** KEPT (pick-wt=23): 298 [] -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).
% 12.43/12.34 ** KEPT (pick-wt=28): 299 [] -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)).
% 12.43/12.34 ** KEPT (pick-wt=8): 300 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.43/12.34 Following clause subsumed by 275 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.43/12.34 Following clause subsumed by 218 during input processing: 0 [] A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 12.43/12.34 Following clause subsumed by 275 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 12.43/12.34 ** KEPT (pick-wt=9): 301 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.43/12.34 Following clause subsumed by 216 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.43/12.34 ** KEPT (pick-wt=12): 302 [] -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).
% 12.43/12.34 ** KEPT (pick-wt=12): 303 [] 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).
% 12.43/12.34 ** KEPT (pick-wt=12): 304 [] -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).
% 12.43/12.34 ** KEPT (pick-wt=12): 305 [] 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).
% 12.43/12.34 ** KEPT (pick-wt=14): 306 [] -c_SEQ_Osubse_q(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,B),hAPP(A,C)).
% 12.43/12.34 ** KEPT (pick-wt=12): 307 [] c_SEQ_Osubse_q(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(A,$f58(A)),hAPP(A,$f57(A))).
% 12.43/12.34 ** KEPT (pick-wt=19): 308 [] -class_Lattices_Olattice(A)|hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(B,A),C,D),E)=c_Lattices_Osemilattice__sup__class_Osup(A,hAPP(C,E),hAPP(D,E)).
% 12.43/12.34 ** KEPT (pick-wt=10): 309 [] -class_Lattices_Obounded__lattice__top(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Orderings_Otop__class_Otop(A))=c_Orderings_Otop__class_Otop(A).
% 12.43/12.34 ** KEPT (pick-wt=10): 310 [] -class_Lattices_Obounded__lattice__top(A)|c_Lattices_Osemilattice__sup__class_Osup(A,c_Orderings_Otop__class_Otop(A),B)=c_Orderings_Otop__class_Otop(A).
% 12.43/12.34 ** KEPT (pick-wt=18): 311 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f59(A,B),B)| -c_member(tc_Nat_Onat,C,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B))|hBOOL(hAPP(A,C)).
% 12.43/12.34 ** KEPT (pick-wt=18): 312 [] -hBOOL(hAPP(A,$f59(A,B)))| -c_member(tc_Nat_Onat,C,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B))|hBOOL(hAPP(A,C)).
% 12.43/12.34 ** KEPT (pick-wt=18): 313 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|hBOOL(hAPP(C,A))|c_member(tc_Nat_Onat,$f60(C,B),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)).
% 12.43/12.34 ** KEPT (pick-wt=14): 314 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|hBOOL(hAPP(C,A))| -hBOOL(hAPP(C,$f60(C,B))).
% 12.43/12.34 ** KEPT (pick-wt=18): 315 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -hBOOL(hAPP(C,A))|c_member(tc_Nat_Onat,$f61(C,B),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)).
% 12.43/12.34 ** KEPT (pick-wt=14): 316 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -hBOOL(hAPP(C,A))|hBOOL(hAPP(C,$f61(C,B))).
% 12.43/12.34 ** KEPT (pick-wt=18): 317 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f62(A,B),B)| -c_member(tc_Nat_Onat,C,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B))| -hBOOL(hAPP(A,C)).
% 12.43/12.34 ** KEPT (pick-wt=18): 318 [] hBOOL(hAPP(A,$f62(A,B)))| -c_member(tc_Nat_Onat,C,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B))| -hBOOL(hAPP(A,C)).
% 12.43/12.34 ** KEPT (pick-wt=13): 319 [] -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)).
% 12.43/12.34 ** KEPT (pick-wt=13): 320 [] -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)).
% 12.43/12.34 ** KEPT (pick-wt=8): 321 [] -class_Lattices_Osemilattice__sup(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,B)=B.
% 12.43/12.34 Following clause subsumed by 321 during input processing: 0 [] -class_Lattices_Osemilattice__sup(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,B)=B.
% 12.43/12.34 ** KEPT (pick-wt=11): 322 [] -class_Lattices_Osemilattice__sup(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,C)=c_Lattices_Osemilattice__sup__class_Osup(A,C,B).
% 12.43/12.34 ** KEPT (pick-wt=11): 323 [] -class_Lattices_Olattice(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,C)=c_Lattices_Osemilattice__sup__class_Osup(A,C,B).
% 12.43/12.34 Following clause subsumed by 322 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).
% 12.43/12.34 ** KEPT (pick-wt=14): 324 [] -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).
% 12.43/12.34 ** KEPT (pick-wt=14): 325 [] -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).
% 12.43/12.34 Following clause subsumed by 324 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).
% 12.43/12.34 ** KEPT (pick-wt=17): 326 [] -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)).
% 12.43/12.34 ** KEPT (pick-wt=17): 327 [] -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)).
% 12.43/12.34 Following clause subsumed by 326 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)).
% 12.43/12.34 ** KEPT (pick-wt=17): 328 [] -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)).
% 12.43/12.34 ** KEPT (pick-wt=17): 329 [] -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)).
% 12.43/12.34 Following clause subsumed by 328 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)).
% 12.43/12.34 ** KEPT (pick-wt=13): 330 [] -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).
% 12.43/12.34 ** KEPT (pick-wt=13): 331 [] -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).
% 12.43/12.34 ** KEPT (pick-wt=20): 332 [] -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)).
% 12.43/12.34 ** KEPT (pick-wt=17): 333 [] -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).
% 12.43/12.34 Following clause subsumed by 333 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).
% 12.43/12.34 ** KEPT (pick-wt=12): 334 [] -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.
% 12.43/12.34 ** KEPT (pick-wt=12): 335 [] -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.
% 12.43/12.34 ** KEPT (pick-wt=13): 336 [] -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)).
% 12.43/12.34 ** KEPT (pick-wt=13): 337 [] -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)).
% 12.43/12.34 Following clause subsumed by 330 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).
% 12.43/12.34 Following clause subsumed by 331 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).
% 12.43/12.34 Following clause subsumed by 333 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).
% 12.43/12.34 Following clause subsumed by 335 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.
% 12.43/12.34 ** KEPT (pick-wt=12): 338 [] -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.
% 12.43/12.34 ** KEPT (pick-wt=9): 339 [] -class_Lattices_Osemilattice__sup(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,B)).
% 12.43/12.34 ** KEPT (pick-wt=9): 340 [] -class_Lattices_Olattice(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,C,B)).
% 12.43/12.34 ** KEPT (pick-wt=9): 341 [] -class_Lattices_Osemilattice__sup(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C)).
% 12.43/12.34 ** KEPT (pick-wt=9): 342 [] -class_Lattices_Olattice(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C)).
% 12.43/12.34 ** KEPT (pick-wt=21): 343 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C),c_SetInterval_Oord__class_OatLeast(A,C))=c_SetInterval_Oord__class_OgreaterThan(A,B).
% 12.43/12.34 ** KEPT (pick-wt=21): 344 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(A,B),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C))=c_SetInterval_Oord__class_OlessThan(A,C).
% 12.43/12.34 ** KEPT (pick-wt=16): 345 [] -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).
% 12.43/12.34 ** KEPT (pick-wt=20): 346 [] -class_Orderings_Olinorder(A)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(A,B))=c_SetInterval_Oord__class_OatLeast(A,B).
% 12.43/12.34 ** KEPT (pick-wt=16): 347 [] -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)).
% 12.43/12.34 Following clause subsumed by 263 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)).
% 12.43/12.34 ** KEPT (pick-wt=16): 348 [] -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).
% 12.43/12.34 Following clause subsumed by 294 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,B,c_RComplete_Onatfloor(A))| -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B),A).
% 12.43/12.34 ** KEPT (pick-wt=7): 349 [] -c_member(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 12.43/12.34 ** KEPT (pick-wt=15): 350 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_SetInterval_Oord__class_OgreaterThanLessThan(A,C,B)=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.43/12.34 ** KEPT (pick-wt=11): 351 [] -class_Orderings_Obot(A)|hAPP(c_Orderings_Obot__class_Obot(tc_fun(B,A)),C)=c_Orderings_Obot__class_Obot(A).
% 12.43/12.34 ** KEPT (pick-wt=10): 352 [] A!=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))| -c_member(B,C,A).
% 12.43/12.34 Following clause subsumed by 349 during input processing: 0 [] -c_member(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 12.43/12.34 Following clause subsumed by 352 during input processing: 0 [] -c_member(A,B,C)|C!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.43/12.34 Following clause subsumed by 352 during input processing: 0 [] -c_member(A,B,C)|C!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.43/12.34 ** KEPT (pick-wt=9): 353 [] c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))!=c_Set_Oinsert(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=9): 354 [] c_Set_Oinsert(A,B,C)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.43/12.34 ** KEPT (pick-wt=27): 355 [] 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.
% 12.43/12.34 ** KEPT (pick-wt=27): 356 [] 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.
% 12.43/12.34 ** KEPT (pick-wt=27): 357 [] 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.
% 12.43/12.34 ** KEPT (pick-wt=27): 358 [] 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.
% 12.43/12.34 ** KEPT (pick-wt=27): 359 [] 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.
% 12.43/12.34 ** KEPT (pick-wt=27): 360 [] 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.
% 12.43/12.34 ** KEPT (pick-wt=18): 361 [] 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.
% 12.43/12.34 ** KEPT (pick-wt=12): 362 [] c_Set_OCollect(A,B)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))| -hBOOL(hAPP(B,C)).
% 12.43/12.34 ** KEPT (pick-wt=12): 363 [] c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))!=c_Set_OCollect(A,B)| -hBOOL(hAPP(B,C)).
% 12.43/12.34 ** KEPT (pick-wt=9): 364 [] c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.43/12.34 ** KEPT (pick-wt=15): 365 [] -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)).
% 12.43/12.34 Following clause subsumed by 95 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)).
% 12.43/12.34 ** KEPT (pick-wt=17): 366 [] 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)).
% 12.43/12.34 ** KEPT (pick-wt=17): 367 [] 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)).
% 12.43/12.34 ** KEPT (pick-wt=23): 368 [] 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)).
% 12.43/12.34 ** KEPT (pick-wt=10): 369 [] c_Set_OPow(A,B)!=c_Orderings_Obot__class_Obot(tc_fun(tc_fun(A,tc_HOL_Obool),tc_HOL_Obool)).
% 12.43/12.34 ** KEPT (pick-wt=9): 370 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 12.43/12.34 ** KEPT (pick-wt=7): 371 [] -class_Orderings_Obot(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Orderings_Obot__class_Obot(A),B).
% 12.43/12.34 ** KEPT (pick-wt=9): 372 [] -class_Lattices_Obounded__lattice__bot(A)|c_Lattices_Osemilattice__sup__class_Osup(A,c_Orderings_Obot__class_Obot(A),B)=B.
% 12.43/12.34 ** KEPT (pick-wt=9): 373 [] -class_Lattices_Obounded__lattice__bot(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Orderings_Obot__class_Obot(A))=B.
% 12.43/12.34 ** KEPT (pick-wt=13): 374 [] -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).
% 12.43/12.34 ** KEPT (pick-wt=13): 375 [] -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).
% 12.43/12.34 ** KEPT (pick-wt=17): 376 [] -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).
% 12.43/12.34 ** KEPT (pick-wt=13): 377 [] -c_member(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B=C.
% 12.43/12.34 Following clause subsumed by 377 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.
% 12.43/12.34 Following clause subsumed by 170 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.
% 12.43/12.34 ** KEPT (pick-wt=27): 378 [] -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))).
% 12.43/12.34 ** KEPT (pick-wt=15): 379 [] -class_Orderings_Oorder(A)|c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))!=c_SetInterval_Oord__class_OatLeastAtMost(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=15): 380 [] -class_Orderings_Oorder(A)|c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastAtMost(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=15): 381 [] -class_Orderings_Oorder(A)|c_SetInterval_Oord__class_OatLeastAtMost(A,B,C)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))| -c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=15): 382 [] -class_Orderings_Oorder(A)|c_SetInterval_Oord__class_OatLeastAtMost(A,B,C)=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=15): 383 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_SetInterval_Oord__class_OatLeastAtMost(A,C,B)=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.43/12.34 ** KEPT (pick-wt=17): 384 [] -class_Orderings_Oorder(A)|B!=C|c_SetInterval_Oord__class_OatLeastAtMost(A,B,C)=c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 12.43/12.34 ** KEPT (pick-wt=17): 385 [] -class_Orderings_Oorder(A)|c_SetInterval_Oord__class_OatLeastAtMost(A,B,C)!=c_Set_Oinsert(A,D,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))|B=C.
% 12.43/12.34 ** KEPT (pick-wt=17): 386 [] -class_Orderings_Oorder(A)|c_SetInterval_Oord__class_OatLeastAtMost(A,B,C)!=c_Set_Oinsert(A,D,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))|C=D.
% 12.43/12.34 ** KEPT (pick-wt=20): 387 [] -class_Orderings_Oorder(A)|c_SetInterval_Oord__class_OatLeastAtMost(A,B,C)=c_Set_Oinsert(A,D,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))|B!=C|C!=D.
% 12.43/12.34 ** KEPT (pick-wt=14): 389 [copy,388,flip.2] -class_Orderings_Oorder(A)|c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))=c_SetInterval_Oord__class_OatLeastAtMost(A,B,B).
% 12.43/12.34 ** KEPT (pick-wt=10): 390 [] c_RealDef_Oreal(tc_Nat_Onat,A)!=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.43/12.34 ** KEPT (pick-wt=10): 391 [] c_RealDef_Oreal(tc_Nat_Onat,A)=c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.43/12.34 ** KEPT (pick-wt=7): 392 [] -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)).
% 12.43/12.34 ** KEPT (pick-wt=11): 393 [] -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).
% 12.43/12.34 ** KEPT (pick-wt=11): 394 [] 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).
% 12.43/12.34 ** KEPT (pick-wt=10): 395 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatfloor(A)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.43/12.34 ** KEPT (pick-wt=10): 396 [] -c_Orderings_Oord__class_Oless__e_q(tc_RealDef_Oreal,A,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))|c_RComplete_Onatceiling(A)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 12.43/12.34 ** KEPT (pick-wt=12): 397 [] -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).
% 12.43/12.34 ** KEPT (pick-wt=12): 398 [] -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).
% 12.43/12.34 ** KEPT (pick-wt=12): 399 [] 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).
% 12.43/12.34 ** KEPT (pick-wt=20): 400 [] -class_Orderings_Olinorder(A)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(A,B),c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))=c_SetInterval_Oord__class_OatMost(A,B).
% 12.43/12.34 ** KEPT (pick-wt=27): 401 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C),c_SetInterval_Oord__class_OatLeastAtMost(A,C,D))=c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,D).
% 12.43/12.34 ** KEPT (pick-wt=26): 402 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C),c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))=c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=26): 403 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C))=c_SetInterval_Oord__class_OatLeastAtMost(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=27): 404 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThanLessThan(A,C,D))=c_SetInterval_Oord__class_OatLeastLessThan(A,B,D).
% 12.43/12.34 ** KEPT (pick-wt=22): 405 [] -class_Orderings_Olinorder(A)|c_SetInterval_Oord__class_OatLeastLessThan(A,B,C)!=c_SetInterval_Oord__class_OatLeastLessThan(A,D,E)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|C=E.
% 12.43/12.34 ** KEPT (pick-wt=22): 406 [] -class_Orderings_Olinorder(A)|c_SetInterval_Oord__class_OatLeastLessThan(A,B,C)!=c_SetInterval_Oord__class_OatLeastLessThan(A,D,E)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|B=D.
% 12.43/12.34 Following clause subsumed by 406 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|c_SetInterval_Oord__class_OatLeastLessThan(A,B,C)!=c_SetInterval_Oord__class_OatLeastLessThan(A,D,E)|B=D.
% 12.43/12.34 Following clause subsumed by 405 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|c_SetInterval_Oord__class_OatLeastLessThan(A,B,C)!=c_SetInterval_Oord__class_OatLeastLessThan(A,D,E)|C=E.
% 12.43/12.34 ** KEPT (pick-wt=25): 407 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|c_SetInterval_Oord__class_OatLeastLessThan(A,B,C)=c_SetInterval_Oord__class_OatLeastLessThan(A,D,E)|B!=D|C!=E.
% 12.43/12.34 ** KEPT (pick-wt=18): 408 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f67(A,B),B)| -c_member(tc_Nat_Onat,C,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B))|hBOOL(hAPP(A,C)).
% 12.43/12.34 ** KEPT (pick-wt=18): 409 [] -hBOOL(hAPP(A,$f67(A,B)))| -c_member(tc_Nat_Onat,C,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B))|hBOOL(hAPP(A,C)).
% 12.43/12.34 ** KEPT (pick-wt=18): 410 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|hBOOL(hAPP(C,A))|c_member(tc_Nat_Onat,$f68(C,B),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)).
% 12.43/12.34 ** KEPT (pick-wt=14): 411 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|hBOOL(hAPP(C,A))| -hBOOL(hAPP(C,$f68(C,B))).
% 12.43/12.34 ** KEPT (pick-wt=18): 412 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -hBOOL(hAPP(C,A))|c_member(tc_Nat_Onat,$f69(C,B),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)).
% 12.43/12.34 ** KEPT (pick-wt=14): 413 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -hBOOL(hAPP(C,A))|hBOOL(hAPP(C,$f69(C,B))).
% 12.43/12.34 ** KEPT (pick-wt=18): 414 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f70(A,B),B)| -c_member(tc_Nat_Onat,C,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B))| -hBOOL(hAPP(A,C)).
% 12.43/12.34 ** KEPT (pick-wt=18): 415 [] hBOOL(hAPP(A,$f70(A,B)))| -c_member(tc_Nat_Onat,C,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B))| -hBOOL(hAPP(A,C)).
% 12.43/12.34 ** KEPT (pick-wt=15): 416 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_SetInterval_Oord__class_OatLeastLessThan(A,C,B)=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.43/12.34 ** KEPT (pick-wt=15): 417 [] -class_Orderings_Oorder(A)|c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))!=c_SetInterval_Oord__class_OatLeastLessThan(A,B,C)| -c_Orderings_Oord__class_Oless(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=15): 418 [] -class_Orderings_Oorder(A)|c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastLessThan(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=15): 419 [] -class_Orderings_Oorder(A)|c_SetInterval_Oord__class_OatLeastLessThan(A,B,C)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))| -c_Orderings_Oord__class_Oless(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=15): 420 [] -class_Orderings_Oorder(A)|c_SetInterval_Oord__class_OatLeastLessThan(A,B,C)=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|c_Orderings_Oord__class_Oless(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=22): 421 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C),c_SetInterval_Oord__class_OatLeastLessThan(A,D,E))|c_Orderings_Oord__class_Oless__e_q(A,C,B)|c_Orderings_Oord__class_Oless__e_q(A,D,B).
% 12.43/12.34 ** KEPT (pick-wt=22): 422 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C),c_SetInterval_Oord__class_OatLeastLessThan(A,D,E))|c_Orderings_Oord__class_Oless__e_q(A,C,B)|c_Orderings_Oord__class_Oless__e_q(A,C,E).
% 12.43/12.34 ** KEPT (pick-wt=27): 423 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C),c_SetInterval_Oord__class_OatLeastLessThan(A,C,D))=c_SetInterval_Oord__class_OatLeastLessThan(A,B,D).
% 12.43/12.34 ** KEPT (pick-wt=15): 424 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_SetInterval_Oord__class_OgreaterThanAtMost(A,C,B)=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.43/12.34 ** KEPT (pick-wt=15): 425 [] -class_Orderings_Oorder(A)|c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))!=c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C)| -c_Orderings_Oord__class_Oless(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=15): 426 [] -class_Orderings_Oorder(A)|c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))=c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=15): 427 [] -class_Orderings_Oorder(A)|c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))| -c_Orderings_Oord__class_Oless(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=15): 428 [] -class_Orderings_Oorder(A)|c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C)=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|c_Orderings_Oord__class_Oless(A,B,C).
% 12.43/12.34 ** KEPT (pick-wt=27): 429 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThanAtMost(A,C,D))=c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,D).
% 12.43/12.34 ** KEPT (pick-wt=27): 430 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C),c_SetInterval_Oord__class_OatLeastAtMost(A,C,D))=c_SetInterval_Oord__class_OatLeastAtMost(A,B,D).
% 12.43/12.34 ** KEPT (pick-wt=21): 431 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(A,B),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C))=c_SetInterval_Oord__class_OlessThan(A,C).
% 12.43/12.34 ** KEPT (pick-wt=21): 432 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C),c_SetInterval_Oord__class_OatLeast(A,C))=c_SetInterval_Oord__class_OatLeast(A,B).
% 12.43/12.34 ** KEPT (pick-wt=27): 433 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThanAtMost(A,C,D))=c_SetInterval_Oord__class_OatLeastAtMost(A,B,D).
% 12.43/12.34 ** KEPT (pick-wt=21): 434 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(A,B),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C))=c_SetInterval_Oord__class_OatMost(A,C).
% 12.43/12.34 ** KEPT (pick-wt=21): 435 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThan(A,C))=c_SetInterval_Oord__class_OgreaterThan(A,B).
% 12.45/12.35 ** KEPT (pick-wt=27): 436 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C),c_SetInterval_Oord__class_OatLeastLessThan(A,C,D))=c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,D).
% 12.45/12.35 ** KEPT (pick-wt=27): 437 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThanLessThan(A,C,D))=c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,D).
% 12.45/12.35 ** KEPT (pick-wt=26): 438 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C),c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))=c_SetInterval_Oord__class_OatLeastAtMost(A,B,C).
% 12.45/12.35 ** KEPT (pick-wt=26): 439 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Lattices_Osemilattice__sup__class_Osup(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C))=c_SetInterval_Oord__class_OatLeastLessThan(A,B,C).
% 12.45/12.35 ** KEPT (pick-wt=19): 440 [] -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).
% 12.45/12.35 ** KEPT (pick-wt=34): 441 [] -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).
% 12.45/12.35 ** KEPT (pick-wt=23): 442 [] -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).
% 12.45/12.35 ** KEPT (pick-wt=23): 443 [] 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).
% 12.45/12.35 ** KEPT (pick-wt=34): 444 [] 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).
% 12.45/12.35 ** KEPT (pick-wt=36): 445 [] 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).
% 12.45/12.35 ** KEPT (pick-wt=19): 446 [] 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).
% 12.45/12.35 ** KEPT (pick-wt=25): 447 [] 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).
% 12.45/12.35 ** KEPT (pick-wt=36): 448 [] 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).
% 12.45/12.35 ** KEPT (pick-wt=38): 449 [] 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).
% 12.45/12.35 ** KEPT (pick-wt=20): 450 [] -class_Orderings_Oorder(A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(A,B),c_SetInterval_Oord__class_OatLeast(A,B))=c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 12.45/12.35 ** KEPT (pick-wt=11): 451 [] -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).
% 12.45/12.35 ** KEPT (pick-wt=30): 452 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=17): 453 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=13): 454 [] -hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,C),D))|hBOOL(hAPP(B,D)).
% 12.45/12.35 ** KEPT (pick-wt=13): 455 [] -hBOOL(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),B,C),D))|hBOOL(hAPP(C,D)).
% 12.45/12.35 ** KEPT (pick-wt=13): 456 [] -c_member(A,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,D))|c_member(A,B,C).
% 12.45/12.35 ** KEPT (pick-wt=13): 457 [] -c_member(A,B,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),C,D))|c_member(A,B,D).
% 12.45/12.35 ** KEPT (pick-wt=17): 458 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=13): 459 [] -c_member(A,B,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),C,D))|c_member(A,B,C).
% 12.45/12.35 ** KEPT (pick-wt=13): 460 [] -c_member(A,B,c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),C,D))| -c_member(A,B,D).
% 12.45/12.35 ** KEPT (pick-wt=17): 461 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=19): 462 [] 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.
% 12.45/12.35 ** KEPT (pick-wt=10): 463 [] -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).
% 12.45/12.35 ** KEPT (pick-wt=10): 464 [] -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).
% 12.45/12.35 ** KEPT (pick-wt=20): 465 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=20): 467 [copy,466,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).
% 12.45/12.35 ** KEPT (pick-wt=20): 468 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=20): 470 [copy,469,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)).
% 12.45/12.35 ** KEPT (pick-wt=11): 471 [] -class_Lattices_Olattice(A)|c_Lattices_Osemilattice__sup__class_Osup(A,B,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C))=B.
% 12.45/12.35 ** KEPT (pick-wt=11): 472 [] -class_Lattices_Olattice(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Lattices_Osemilattice__sup__class_Osup(A,B,C))=B.
% 12.45/12.35 ** KEPT (pick-wt=9): 473 [] -class_Lattices_Obounded__lattice__top(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,c_Orderings_Otop__class_Otop(A),B)=B.
% 12.45/12.35 ** KEPT (pick-wt=9): 474 [] -class_Lattices_Obounded__lattice__top(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,c_Orderings_Otop__class_Otop(A))=B.
% 12.45/12.35 ** KEPT (pick-wt=13): 475 [] -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).
% 12.45/12.35 ** KEPT (pick-wt=13): 476 [] -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).
% 12.45/12.35 ** KEPT (pick-wt=17): 477 [] -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).
% 12.45/12.35 Following clause subsumed by 456 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).
% 12.45/12.35 Following clause subsumed by 457 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).
% 12.45/12.35 Following clause subsumed by 458 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).
% 12.45/12.35 Following clause subsumed by 456 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).
% 12.45/12.35 Following clause subsumed by 457 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).
% 12.45/12.35 Following clause subsumed by 459 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).
% 12.45/12.35 Following clause subsumed by 460 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).
% 12.45/12.35 Following clause subsumed by 461 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).
% 12.45/12.35 Following clause subsumed by 459 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).
% 12.45/12.35 Following clause subsumed by 460 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).
% 12.45/12.35 ** KEPT (pick-wt=22): 478 [] 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.
% 12.45/12.35 ** KEPT (pick-wt=28): 479 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=23): 480 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=14): 481 [] -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.
% 12.45/12.35 ** KEPT (pick-wt=14): 482 [] -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.
% 12.45/12.35 ** KEPT (pick-wt=25): 483 [] -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.
% 12.45/12.35 ** KEPT (pick-wt=28): 484 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=8): 485 [] -class_Lattices_Osemilattice__inf(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,B)=B.
% 12.45/12.35 Following clause subsumed by 485 during input processing: 0 [] -class_Lattices_Osemilattice__inf(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,B)=B.
% 12.45/12.35 ** KEPT (pick-wt=11): 486 [] -class_Lattices_Osemilattice__inf(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)=c_Lattices_Osemilattice__inf__class_Oinf(A,C,B).
% 12.45/12.35 ** KEPT (pick-wt=11): 487 [] -class_Lattices_Olattice(A)|c_Lattices_Osemilattice__inf__class_Oinf(A,B,C)=c_Lattices_Osemilattice__inf__class_Oinf(A,C,B).
% 12.45/12.35 Following clause subsumed by 486 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).
% 12.45/12.35 ** KEPT (pick-wt=14): 488 [] -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).
% 12.45/12.35 ** KEPT (pick-wt=14): 489 [] -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).
% 12.45/12.35 Following clause subsumed by 488 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).
% 12.45/12.35 ** KEPT (pick-wt=17): 490 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=17): 491 [] -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)).
% 12.45/12.35 Following clause subsumed by 490 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)).
% 12.45/12.35 ** KEPT (pick-wt=17): 492 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=17): 493 [] -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)).
% 12.45/12.35 Following clause subsumed by 492 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)).
% 12.45/12.35 ** KEPT (pick-wt=19): 494 [] -class_Groups_Ominus(A)|hAPP(c_Groups_Ominus__class_Ominus(tc_fun(B,A),C,D),E)=c_Groups_Ominus__class_Ominus(A,hAPP(C,E),hAPP(D,E)).
% 12.45/12.35 ** KEPT (pick-wt=19): 495 [] -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)).
% 12.45/12.35 Following clause subsumed by 454 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)).
% 12.45/12.35 Following clause subsumed by 455 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)).
% 12.45/12.35 ** KEPT (pick-wt=13): 496 [] -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).
% 12.45/12.35 ** KEPT (pick-wt=13): 497 [] -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).
% 12.45/12.35 ** KEPT (pick-wt=13): 498 [] -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).
% 12.45/12.35 ** KEPT (pick-wt=13): 499 [] -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).
% 12.45/12.35 ** KEPT (pick-wt=20): 500 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=17): 501 [] -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)).
% 12.45/12.35 Following clause subsumed by 501 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)).
% 12.45/12.35 ** KEPT (pick-wt=12): 502 [] -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.
% 12.45/12.35 ** KEPT (pick-wt=12): 503 [] -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.
% 12.45/12.35 ** KEPT (pick-wt=13): 504 [] -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).
% 12.45/12.35 ** KEPT (pick-wt=13): 505 [] -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).
% 12.45/12.35 Following clause subsumed by 498 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).
% 12.45/12.35 Following clause subsumed by 499 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).
% 12.45/12.35 Following clause subsumed by 501 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).
% 12.45/12.35 Following clause subsumed by 503 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.
% 12.45/12.35 ** KEPT (pick-wt=12): 506 [] -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.
% 12.45/12.35 ** KEPT (pick-wt=9): 507 [] -class_Lattices_Osemilattice__inf(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),C).
% 12.45/12.35 ** KEPT (pick-wt=9): 508 [] -class_Lattices_Olattice(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),C).
% 12.45/12.35 ** KEPT (pick-wt=9): 509 [] -class_Lattices_Osemilattice__inf(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),B).
% 12.45/12.35 ** KEPT (pick-wt=9): 510 [] -class_Lattices_Olattice(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Lattices_Osemilattice__inf__class_Oinf(A,B,C),B).
% 12.45/12.35 ** KEPT (pick-wt=21): 511 [] -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))).
% 12.45/12.35 ** KEPT (pick-wt=21): 512 [] -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))).
% 12.45/12.35 ** KEPT (pick-wt=23): 514 [copy,513,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).
% 12.45/12.35 ** KEPT (pick-wt=23): 516 [copy,515,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)).
% 12.45/12.35 Following clause subsumed by 514 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).
% 12.45/12.35 Following clause subsumed by 516 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)).
% 12.45/12.35 ** KEPT (pick-wt=20): 517 [] -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).
% 12.45/12.35 Following clause subsumed by 517 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).
% 12.45/12.35 ** KEPT (pick-wt=23): 518 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(A,B,D),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C))=c_SetInterval_Oord__class_OatLeastLessThan(A,C,D).
% 12.45/12.35 ** KEPT (pick-wt=29): 519 [] 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).
% 12.45/12.35 ** KEPT (pick-wt=29): 520 [] 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).
% 12.45/12.35 ** KEPT (pick-wt=19): 521 [] -class_Orderings_Oorder(A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C),c_SetInterval_Oord__class_OatLeastLessThan(A,C,D))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.45/12.35 ** KEPT (pick-wt=19): 522 [] -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.
% 12.45/12.35 ** KEPT (pick-wt=22): 523 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=22): 524 [] 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)).
% 12.45/12.35 ** KEPT (pick-wt=19): 525 [] -class_Orderings_Oorder(A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThanAtMost(A,C,D))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.45/12.35 ** KEPT (pick-wt=21): 526 [] -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.
% 12.45/12.35 ** KEPT (pick-wt=19): 527 [] -class_Orderings_Oorder(A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C),c_SetInterval_Oord__class_OatLeastAtMost(A,C,D))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.45/12.35 ** KEPT (pick-wt=24): 528 [] -class_Orderings_Oorder(A)|c_Groups_Ominus__class_Ominus(tc_fun(A,tc_HOL_Obool),c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(A,B))=c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 12.45/12.35 ** KEPT (pick-wt=18): 529 [] -class_Orderings_Oorder(A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(A,B),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.45/12.35 ** KEPT (pick-wt=18): 530 [] -class_Orderings_Oorder(A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OlessThan(A,B),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.45/12.35 ** KEPT (pick-wt=19): 531 [] -class_Orderings_Oorder(A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C),c_SetInterval_Oord__class_OatLeastLessThan(A,C,D))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.45/12.35 ** KEPT (pick-wt=19): 532 [] -class_Orderings_Oorder(A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C),c_SetInterval_Oord__class_OatLeastAtMost(A,C,D))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.45/12.35 ** KEPT (pick-wt=19): 533 [] -class_Orderings_Oorder(A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThanLessThan(A,C,D))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.45/12.35 ** KEPT (pick-wt=19): 534 [] -class_Orderings_Oorder(A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThanAtMost(A,C,D))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.45/12.35 ** KEPT (pick-wt=18): 535 [] -class_Orderings_Oorder(A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(A,B,C),c_SetInterval_Oord__class_OatLeast(A,C))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.45/12.35 ** KEPT (pick-wt=18): 536 [] -class_Orderings_Oorder(A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThan(A,C))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.45/12.35 ** KEPT (pick-wt=18): 537 [] -class_Orderings_Oorder(A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(A,B),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.45/12.35 ** KEPT (pick-wt=18): 538 [] -class_Orderings_Oorder(A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OatMost(A,B),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.45/12.35 ** KEPT (pick-wt=19): 539 [] -class_Orderings_Oorder(A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThanLessThan(A,C,D))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.45/12.35 ** KEPT (pick-wt=18): 540 [] -class_Orderings_Oorder(A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,C),c_SetInterval_Oord__class_OatLeast(A,C))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.45/12.35 ** KEPT (pick-wt=18): 541 [] -class_Orderings_Oorder(A)|c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(A,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,C),c_SetInterval_Oord__class_OgreaterThan(A,C))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 12.45/12.35 ** KEPT (pick-wt=8): 542 [] -class_Rings_Osemiring__1(A)|c_member(A,c_Groups_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_ONats(A)).
% 12.45/12.35 ** KEPT (pick-wt=30): 543 [] -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).
% 12.45/12.35 Following clause subsumed by 187 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).
% 12.45/12.35 Following clause subsumed by 181 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).
% 12.45/12.35 Following clause subsumed by 452 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_member(A,C,B).
% 12.45/12.35 Following clause subsumed by 181 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).
% 12.45/12.35 ** KEPT (pick-wt=14): 544 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=14): 545 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=14): 546 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=14): 547 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=19): 548 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,D,E).
% 12.45/12.35 ** KEPT (pick-wt=19): 549 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E).
% 12.45/12.35 ** KEPT (pick-wt=19): 550 [] -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).
% 12.45/12.35 ** KEPT (pick-wt=19): 551 [] -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).
% 12.45/12.35 ** KEPT (pick-wt=12): 552 [] -class_Groups_Ogroup__add(A)|c_Groups_Om
% 12.45/12.35 Search stopped in tp_alloc by max_mem option.
% 12.45/12.35 inus__class_Ominus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|B=C.
% 12.45/12.35 ** KEPT (pick-wt=12): 553 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)=c_Groups_Ozero__class_Ozero(A)|B!=C.
% 12.45/12.35 ** KEPT (pick-wt=17): 554 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=B.
% 12.45/12.35 ** KEPT (pick-wt=11): 555 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),B).
% 12.45/12.35 ** KEPT (pick-wt=18): 556 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)).
% 12.45/12.35 ** KEPT (pick-wt=14): 557 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=14): 558 [] -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)).
% 12.45/12.35 ** KEPT (pick-wt=13): 559 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=A.
% 12.45/12.35 ** KEPT (pick-wt=20): 560 [] -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.
% 12.45/12.35 ** KEPT (pick-wt=20): 561 [] -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.
% 12.45/12.35 ** KEPT (pick-wt=23): 562 [] -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).
% 12.45/12.35 ** KEPT (pick-wt=22): 563 [] -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).
% 12.45/12.35 Following clause subsumed by 558 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).
% 12.45/12.35 ** KEPT (pick-wt=19): 564 [] -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)).
% 12.45/12.35
% 12.45/12.35 Search stopped in tp_alloc by max_mem option.
% 12.45/12.35
% 12.45/12.35 ============ end of search ============
% 12.45/12.35
% 12.45/12.35 -------------- statistics -------------
% 12.45/12.35 clauses given 0
% 12.45/12.35 clauses generated 0
% 12.45/12.35 clauses kept 556
% 12.45/12.35 clauses forward subsumed 143
% 12.45/12.35 clauses back subsumed 0
% 12.45/12.35 Kbytes malloced 11718
% 12.45/12.35
% 12.45/12.35 ----------- times (seconds) -----------
% 12.45/12.35 user CPU time 0.15 (0 hr, 0 min, 0 sec)
% 12.45/12.35 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 12.45/12.35 wall-clock time 12 (0 hr, 0 min, 12 sec)
% 12.45/12.35
% 12.45/12.35 Process 32166 finished Wed Jul 27 02:54:04 2022
% 12.45/12.35 Otter interrupted
% 12.45/12.35 PROOF NOT FOUND
%------------------------------------------------------------------------------