TSTP Solution File: SCT159+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SCT159+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:12:36 EDT 2022
% Result : Unknown 7.99s 8.11s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SCT159+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 09:16:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 5.58/5.65 ----- Otter 3.3f, August 2004 -----
% 5.58/5.65 The process was started by sandbox on n027.cluster.edu,
% 5.58/5.65 Wed Jul 27 09:16:51 2022
% 5.58/5.65 The command was "./otter". The process ID is 26408.
% 5.58/5.65
% 5.58/5.65 set(prolog_style_variables).
% 5.58/5.65 set(auto).
% 5.58/5.65 dependent: set(auto1).
% 5.58/5.65 dependent: set(process_input).
% 5.58/5.65 dependent: clear(print_kept).
% 5.58/5.65 dependent: clear(print_new_demod).
% 5.58/5.65 dependent: clear(print_back_demod).
% 5.58/5.65 dependent: clear(print_back_sub).
% 5.58/5.65 dependent: set(control_memory).
% 5.58/5.65 dependent: assign(max_mem, 12000).
% 5.58/5.65 dependent: assign(pick_given_ratio, 4).
% 5.58/5.65 dependent: assign(stats_level, 1).
% 5.58/5.65 dependent: assign(max_seconds, 10800).
% 5.58/5.65 clear(print_given).
% 5.58/5.65
% 5.58/5.65 formula_list(usable).
% 5.58/5.65 all A (A=A).
% 5.58/5.65 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).
% 5.58/5.65 all V_A_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)->c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))=c_Finite__Set_Ocard(T_a,V_A_2)).
% 5.58/5.65 all V_B_2 V_A_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))-> (c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)=c_Set_Oimage(T_a,T_b,V_f_2,V_B_2)<->V_A_2=V_B_2)).
% 5.58/5.65 all V_x_2 T_a hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)).
% 5.58/5.65 all V_y_2 V_x_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))-> (hAPP(V_f_2,V_x_2)=hAPP(V_f_2,V_y_2)<->V_x_2=V_y_2)).
% 5.58/5.65 all V_y_2 V_x_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))-> (hAPP(V_f_2,V_x_2)=hAPP(V_f_2,V_y_2)->V_x_2=V_y_2)).
% 5.58/5.65 all V_x_2 T_b T_a (class_Orderings_Otop(T_a)->hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2)=c_Orderings_Otop__class_Otop(T_a)).
% 5.58/5.65 all V_A_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)<-> (all B_x (c_member(T_a,B_x,V_A_2)-> (all B_xa (c_member(T_a,B_xa,V_A_2)-> (hAPP(V_f_2,B_x)=hAPP(V_f_2,B_xa)->B_x=B_xa)))))).
% 5.58/5.65 all V_x_2 T_a (class_Groups_Ozero(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=V_x_2<->V_x_2=c_Groups_Ozero__class_Ozero(T_a))).
% 5.58/5.65 c_Arrow__Order__Mirabelle_OIIA(v_F).
% 5.58/5.65 c_Arrow__Order__Mirabelle_Ounanimity(v_F).
% 5.58/5.65 c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))).
% 5.58/5.65 all V_h_2 T_b V_Fa_2 T_a (c_Finite__Set_Ofinite(T_a,V_Fa_2)->c_Finite__Set_Ofinite(T_b,c_Set_Oimage(T_a,T_b,V_h_2,V_Fa_2))).
% 5.58/5.65 all V_A_2 T_a (class_Finite__Set_Ofinite(T_a)->c_Finite__Set_Ofinite(T_a,V_A_2)).
% 5.58/5.65 all T_a (c_Finite__Set_Ofinite(tc_Option_Ooption(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)))<->c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))).
% 5.58/5.65 all T_b T_a (c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)))<->c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))&c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))).
% 5.58/5.65 all V_A_2 T_a (class_Finite__Set_Ofinite(T_a)->c_Finite__Set_Ofinite(T_a,V_A_2)).
% 5.58/5.65 all T_b T_a (c_Finite__Set_Ofinite(tc_fun(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))->c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))).
% 5.58/5.65 all T_b T_a (c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))-> (c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))->c_Finite__Set_Ofinite(tc_prod(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))))).
% 5.58/5.65 all T_a (class_Finite__Set_Ofinite(T_a)->c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))).
% 5.58/5.65 all V_A_2 T_a (-c_Finite__Set_Ofinite(T_a,V_A_2)->c_Finite__Set_Ocard(T_a,V_A_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.65 all V_A_2 V_f_2 T_b T_a (c_Finite__Set_Ofinite(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))-> (c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)->c_Finite__Set_Ofinite(T_b,V_A_2))).
% 5.58/5.65 all V_A_2 T_a (c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))-> (c_Finite__Set_Ocard(T_a,V_A_2)=c_Finite__Set_Ocard(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))->V_A_2=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))).
% 5.58/5.65 all V_f_2 T_a (c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))-> (c_Set_Oimage(T_a,T_a,V_f_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))->c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))).
% 5.58/5.65 all V_f_2 T_a (c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))-> (c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))->c_Set_Oimage(T_a,T_a,V_f_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)))).
% 5.58/5.65 all V_f_2 T_b V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)-> (c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))=c_Finite__Set_Ocard(T_a,V_A_2)->c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2))).
% 5.58/5.65 all V_f_2 T_b V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)-> (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)<->c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))=c_Finite__Set_Ocard(T_a,V_A_2))).
% 5.58/5.65 all V_g_2 V_B_2 V_A_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),V_B_2)-> (c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_g_2,V_B_2),V_A_2)-> (c_Finite__Set_Ofinite(T_a,V_A_2)-> (c_Finite__Set_Ofinite(T_b,V_B_2)->c_Finite__Set_Ocard(T_a,V_A_2)=c_Finite__Set_Ocard(T_b,V_B_2))))))).
% 5.58/5.65 all T_a (c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))).
% 5.58/5.65 all V_A_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)->c_Set_Oimage(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))=V_A_2).
% 5.58/5.65 all V_A_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)->c_Fun_Oinj__on(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))).
% 5.58/5.65 all V_x_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))->hAPP(c_Fun_Othe__inv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2))=V_x_2).
% 5.58/5.65 all V_A_2 T_a (c_Finite__Set_Ocard(T_a,V_A_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))| -c_Finite__Set_Ofinite(T_a,V_A_2)).
% 5.58/5.65 all V_A_2 V_f_2 T_b T_a (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)),c_Finite__Set_Ocard(T_b,V_A_2))-> -c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)).
% 5.58/5.65 all V_B_2 V_A_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2))<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 5.58/5.65 all V_A_2 V_a_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))-> (c_member(T_b,hAPP(V_f_2,V_a_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))<->c_member(T_a,V_a_2,V_A_2))).
% 5.58/5.65 all V_b_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))-> (c_member(T_b,V_b_2,c_Set_Oimage(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))<-> (exists B_x (V_b_2=hAPP(V_f_2,B_x)& (all B_y (V_b_2=hAPP(V_f_2,B_y)->B_y=B_x)))))).
% 5.58/5.65 all V_f_2 T_b V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),c_Finite__Set_Ocard(T_a,V_A_2))).
% 5.58/5.65 all V_x T_a (class_Orderings_Opreorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x)).
% 5.58/5.65 all T_a c_Finite__Set_Ofinite(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.65 all V_f_2 T_b T_a c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.65 all V_x T_a (class_Orderings_Opreorder(T_a)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_x)).
% 5.58/5.65 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)).
% 5.58/5.65 all V_x_2 T_b T_a (class_Orderings_Obot(T_a)->hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2)=c_Orderings_Obot__class_Obot(T_a)).
% 5.58/5.65 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 5.58/5.65 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2))).
% 5.58/5.65 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (V_x_2!=V_y_2<->c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2))).
% 5.58/5.65 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|V_x_2=V_y_2)).
% 5.58/5.65 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))))).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)&V_x_2!=V_y_2)).
% 5.58/5.65 all V_y_2 V_x_2 T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)& -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 5.58/5.65 all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (V_x_2=V_y_2<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 5.58/5.65 all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2)).
% 5.58/5.65 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)).
% 5.58/5.65 all V_y_2 V_x_2 T_a (c_member(T_a,V_x_2,c_fe_qual(V_y_2))<->V_x_2=V_y_2).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 all V_x_2 V_y_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 5.58/5.65 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 all V_Q_2 T_a V_x_2 V_P_2 (hBOOL(hAPP(V_P_2,V_x_2))-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_P_2,V_Q_2)->hBOOL(hAPP(V_Q_2,V_x_2)))).
% 5.58/5.65 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)).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 5.58/5.65 all V_x_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_x_2),hAPP(V_g_2,V_x_2)))).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 all V_x_2 V_y_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 all V_x_2 V_Q_2 V_P_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_P_2,V_Q_2)-> (hBOOL(hAPP(V_P_2,V_x_2))->hBOOL(hAPP(V_Q_2,V_x_2)))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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))).
% 5.58/5.65 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)))).
% 5.58/5.65 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))).
% 5.58/5.65 all V_x_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_x_2),hAPP(V_g_2,V_x_2)))).
% 5.58/5.65 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))).
% 5.58/5.65 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)))).
% 5.58/5.65 all V_y_2 V_x_2 V_A_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)-> (hAPP(V_f_2,V_x_2)=V_y_2-> (c_member(T_a,V_x_2,V_A_2)->hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2)=V_x_2))).
% 5.58/5.65 all V_x_2 V_A_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)-> (c_member(T_a,V_x_2,V_A_2)->hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(V_f_2,V_x_2))=V_x_2)).
% 5.58/5.65 all V_B_2 V_x_2 V_A_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)-> (c_member(T_b,V_x_2,c_Set_Oimage(T_a,T_b,V_f_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,hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2),V_B_2)))).
% 5.58/5.65 all V_A_2 V_B_2 T_a (c_Finite__Set_Ofinite(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)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_B_2),c_Finite__Set_Ocard(T_a,V_A_2))->V_A_2=V_B_2))).
% 5.58/5.65 all V_A_2 V_B_2 T_a (c_Finite__Set_Ofinite(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)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_a,V_B_2)))).
% 5.58/5.65 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_Finite__Set_Ofinite(T_a,V_B_2)->c_Finite__Set_Ofinite(T_a,V_A_2))).
% 5.58/5.65 all V_A_2 V_B_2 T_a (c_Finite__Set_Ofinite(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)->c_Finite__Set_Ofinite(T_a,V_A_2))).
% 5.58/5.65 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))).
% 5.58/5.65 all T_a c_Finite__Set_Ofinite(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.65 all V_y_2 V_x_2 V_A_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)-> (V_x_2!=V_y_2-> (c_member(T_a,V_x_2,V_A_2)-> (c_member(T_a,V_y_2,V_A_2)->hAPP(V_f_2,V_x_2)!=hAPP(V_f_2,V_y_2))))).
% 5.58/5.65 all V_y_2 V_x_2 V_A_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)-> (c_member(T_a,V_x_2,V_A_2)-> (c_member(T_a,V_y_2,V_A_2)-> (hAPP(V_f_2,V_x_2)=hAPP(V_f_2,V_y_2)<->V_x_2=V_y_2)))).
% 5.58/5.65 all V_y_2 V_x_2 V_A_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)-> (hAPP(V_f_2,V_x_2)=hAPP(V_f_2,V_y_2)-> (c_member(T_a,V_x_2,V_A_2)-> (c_member(T_a,V_y_2,V_A_2)->V_x_2=V_y_2)))).
% 5.58/5.65 all V_A_2 V_B_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_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_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2))).
% 5.58/5.65 all V_y_2 V_A_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)-> (c_member(T_b,V_y_2,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))->hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2))=V_y_2)).
% 5.58/5.65 all V_A_2 T_a (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2))<->V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))&c_Finite__Set_Ofinite(T_a,V_A_2)).
% 5.58/5.65 all V_B_2 V_A_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),V_B_2)-> (c_Finite__Set_Ofinite(T_b,V_B_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_b,V_B_2))))).
% 5.58/5.65 all V_f_2 V_B_2 T_b V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),V_B_2,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))->c_Finite__Set_Ofinite(T_b,V_B_2))).
% 5.58/5.65 all T_a (c_Finite__Set_Ocard(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.65 all V_A_2 T_a (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2))->c_Finite__Set_Ofinite(T_a,V_A_2)).
% 5.58/5.65 all V_f_2 V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oimage(T_a,T_a,V_f_2,V_A_2))->c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2))).
% 5.58/5.65 all V_f_2 V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_a,T_a,V_f_2,V_A_2),V_A_2)-> (c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2)->c_Set_Oimage(T_a,T_a,V_f_2,V_A_2)=V_A_2))).
% 5.58/5.65 all V_B_2 T_b V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)-> (c_Finite__Set_Ofinite(T_b,V_B_2)-> ((exists B_f (c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)&c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,B_f,V_A_2),V_B_2)))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_b,V_B_2))))).
% 5.58/5.65 all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 5.58/5.65 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.58/5.65 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).
% 5.58/5.65 all T_a V_A_2 T_b V_x_2 V_f_2 V_b_2 (V_b_2=hAPP(V_f_2,V_x_2)-> (c_member(T_b,V_x_2,V_A_2)->c_member(T_a,V_b_2,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)))).
% 5.58/5.65 all V_x_2 T_a c_member(T_a,V_x_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.65 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))).
% 5.58/5.65 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)))).
% 5.58/5.65 all V_A_H_2 T_b T_a V_A_2 (V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))-> ((exists B_f (c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)&c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,B_f,V_A_2),V_A_H_2)))<-> (exists B_g (c_Set_Oimage(T_b,T_a,B_g,V_A_H_2)=V_A_2)))).
% 5.58/5.65 all V_P_2 V_n_2 ((exists B_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,V_n_2)&hBOOL(hAPP(V_P_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_P_2,B_x))))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 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))).
% 5.58/5.65 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)))).
% 5.58/5.65 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).
% 5.58/5.65 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).
% 5.58/5.65 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)).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 c_Orderings_Obot__class_Obot(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.65 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))).
% 5.58/5.65 all V_A_2 V_B_2 V_f_2 T_b T_a (c_Fun_Oinj__on(T_a,T_b,V_f_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_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2)))).
% 5.58/5.65 all V_A_2 V_B_2 T_a (c_Finite__Set_Ofinite(T_a,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_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_a,V_B_2)))).
% 5.58/5.65 all V_A_2 V_x_2 T_a (c_member(T_a,V_x_2,V_A_2)<->hBOOL(hAPP(V_A_2,V_x_2))).
% 5.58/5.65 all V_x_2 T_a V_B_2 V_A_2 (V_A_2=V_B_2-> (c_member(T_a,V_x_2,V_A_2)<->c_member(T_a,V_x_2,V_B_2))).
% 5.58/5.65 all V_A_2 T_a V_y_2 V_x_2 (V_x_2=V_y_2-> (c_member(T_a,V_x_2,V_A_2)<->c_member(T_a,V_y_2,V_A_2))).
% 5.58/5.65 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))).
% 5.58/5.65 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 5.58/5.65 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)).
% 5.58/5.65 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))).
% 5.58/5.65 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 5.58/5.65 all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)->V_m!=V_n).
% 5.58/5.65 all V_t V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)->V_s!=V_t).
% 5.58/5.65 all V_P_2 V_n_2 V_m_2 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))-> ((V_m_2=V_n_2->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))-> ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))))).
% 5.58/5.65 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)))).
% 5.58/5.65 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).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n).
% 5.58/5.65 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)).
% 5.58/5.65 all V_n V_m (V_m=V_n->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 5.58/5.65 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))).
% 5.58/5.65 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)).
% 5.58/5.65 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)))).
% 5.58/5.65 all V_A_2 V_B_2 T_a (c_Finite__Set_Ofinite(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)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_a,V_B_2))->c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)).
% 5.58/5.65 all V_x_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_x_2,V_A_2)->c_member(T_a,V_x_2,V_B_2))).
% 5.58/5.65 all V_B_2 V_A_2 V_x_2 T_a (c_member(T_a,V_x_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_x_2,V_B_2))).
% 5.58/5.65 all V_x_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_x_2,V_A_2)->c_member(T_a,V_x_2,V_B_2))).
% 5.58/5.65 all T_b V_f_2 V_b_2 V_A_2 V_x_2 T_a (c_member(T_a,V_x_2,V_A_2)-> (V_b_2=hAPP(V_f_2,V_x_2)->c_member(T_b,V_b_2,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)))).
% 5.58/5.65 all V_f_2 T_b V_A_2 V_x_2 T_a (c_member(T_a,V_x_2,V_A_2)->c_member(T_b,hAPP(V_f_2,V_x_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))).
% 5.58/5.65 all V_A_2 V_f_2 T_b V_z_2 T_a (c_member(T_a,V_z_2,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))<-> (exists B_x (c_member(T_b,B_x,V_A_2)&V_z_2=hAPP(V_f_2,B_x)))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 all V_A_2 V_f_2 T_a T_b (c_Set_Oimage(T_b,T_a,V_f_2,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_b,tc_HOL_Obool))).
% 5.58/5.65 all V_f_2 T_a T_b (c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.65 all V_A_2 V_f_2 T_b T_a (c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))=c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)<->V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.58/5.65 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)).
% 5.58/5.65 all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.58/5.65 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))).
% 5.58/5.65 all V_f_2 T_b 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_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2))).
% 5.58/5.65 all V_A_2 V_f_2 T_b V_B_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))<-> (exists B_AA (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),B_AA,V_A_2)&V_B_2=c_Set_Oimage(T_b,T_a,V_f_2,B_AA)))).
% 5.58/5.65 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)).
% 5.58/5.65 all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 5.58/5.65 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).
% 5.58/5.65 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).
% 5.58/5.65 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)).
% 5.58/5.65 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))).
% 5.58/5.65 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)).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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))).
% 5.58/5.65 all T_b T_a V_x_2 V_f_2 V_b_2 (V_b_2=hAPP(V_f_2,V_x_2)->c_member(T_a,V_b_2,c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))).
% 5.58/5.65 all T_b V_x_2 V_f_2 T_a c_member(T_a,hAPP(V_f_2,V_x_2),c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 all V_P_2 V_n_2 ((all B_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,V_n_2)->hBOOL(hAPP(V_P_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_P_2,B_x))))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 -c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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)).
% 5.58/5.65 all V_x_2 T_a c_member(T_a,V_x_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.65 all T_b T_a (c_Finite__Set_Ofinite(tc_fun(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))-> (c_Finite__Set_Ocard(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))->c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))).
% 5.58/5.65 all V_B_2 V_A_2 V_Fa_2 V_f_2 T_a (c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)-> (c_Finite__Set_Ofinite(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(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)->hAPP(hAPP(V_f_2,hAPP(V_Fa_2,V_B_2)),hAPP(V_Fa_2,V_A_2))=hAPP(V_Fa_2,V_A_2))))).
% 5.58/5.65 all V_B_2 V_A_2 V_Fa_2 V_g_2 V_z_2 V_f_2 T_b T_a (c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)-> (c_Finite__Set_Ofinite(T_b,V_A_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),V_B_2,V_A_2)->hAPP(hAPP(V_f_2,hAPP(V_Fa_2,V_B_2)),hAPP(V_Fa_2,V_A_2))=hAPP(V_Fa_2,V_A_2)))).
% 5.58/5.65 all V_x_2 V_A_2 V_Fa_2 V_g_2 V_z_2 V_f_2 T_b T_a (c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)-> (c_Finite__Set_Ofinite(T_b,V_A_2)-> (c_member(T_b,V_x_2,V_A_2)->hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_2,V_A_2))=hAPP(V_Fa_2,V_A_2)))).
% 5.58/5.65 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),hAPP(c_Nat_OSuc,V_n))).
% 5.58/5.65 all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(c_Nat_OSuc,V_n)).
% 5.58/5.65 all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)).
% 5.58/5.65 all V_n (V_n!=hAPP(c_Nat_OSuc,V_n)).
% 5.58/5.65 all V_n (hAPP(c_Nat_OSuc,V_n)!=V_n).
% 5.58/5.65 all V_nat_H_2 V_nat_2 (hAPP(c_Nat_OSuc,V_nat_2)=hAPP(c_Nat_OSuc,V_nat_H_2)<->V_nat_2=V_nat_H_2).
% 5.58/5.65 all V_y V_x (hAPP(c_Nat_OSuc,V_x)=hAPP(c_Nat_OSuc,V_y)->V_x=V_y).
% 5.58/5.65 all V_N_2 c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2).
% 5.58/5.65 all V_x_2 V_Fa_2 V_f_2 T_a (c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)->hAPP(hAPP(V_f_2,V_x_2),V_x_2)=V_x_2).
% 5.58/5.65 all V_x_2 V_Fa_2 V_g_2 V_z_2 V_f_2 T_b T_a (c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)->hAPP(hAPP(V_f_2,V_x_2),V_x_2)=V_x_2).
% 5.58/5.65 all V_j_2 V_i_2 (c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2,V_j_2))=c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2))).
% 5.58/5.65 all V_n (-c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n),V_n)).
% 5.58/5.65 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,hAPP(c_Nat_OSuc,V_n_2),V_m_2)).
% 5.58/5.65 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,hAPP(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=hAPP(c_Nat_OSuc,V_n_2)).
% 5.58/5.65 all V_m_2 V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2)).
% 5.58/5.65 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,hAPP(c_Nat_OSuc,V_n))).
% 5.58/5.65 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n))-> (-c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->V_m=hAPP(c_Nat_OSuc,V_n))).
% 5.58/5.65 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 5.58/5.65 all V_n_2 V_m_2 (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,V_m_2))).
% 5.58/5.65 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2).
% 5.58/5.65 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 5.58/5.65 all V_m_2 V_n_2 (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,V_m_2))<->V_n_2=V_m_2)).
% 5.58/5.65 all V_m V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(c_Nat_OSuc,V_m))->V_m=V_n)).
% 5.58/5.65 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n))).
% 5.58/5.65 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)-> (hAPP(c_Nat_OSuc,V_m)!=V_n->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n))).
% 5.58/5.65 all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i),V_k))).
% 5.58/5.65 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n))-> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->V_m=V_n)).
% 5.58/5.65 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)).
% 5.58/5.65 all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),hAPP(c_Nat_OSuc,V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)).
% 5.58/5.65 all V_m (hAPP(c_Nat_OSuc,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.65 all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_m)).
% 5.58/5.65 all V_nat_H_1 (hAPP(c_Nat_OSuc,V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.65 all V_m (hAPP(c_Nat_OSuc,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.65 all V_nat_H (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_nat_H)).
% 5.58/5.65 all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_m)).
% 5.58/5.65 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)<-> (exists B_m (V_n_2=hAPP(c_Nat_OSuc,B_m)))).
% 5.58/5.65 all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.65 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| (exists B_j (V_m_2=hAPP(c_Nat_OSuc,B_j)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)))).
% 5.58/5.65 all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)).
% 5.58/5.65 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,hAPP(c_Nat_OSuc,V_m_2))<->V_n_2=V_m_2)).
% 5.58/5.65 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,hAPP(c_Nat_OSuc,V_m),V_n)).
% 5.58/5.65 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,hAPP(c_Nat_OSuc,V_n))).
% 5.58/5.65 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 5.58/5.65 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)).
% 5.58/5.65 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,hAPP(c_Nat_OSuc,V_n_2),V_m_2)).
% 5.58/5.65 all V_x_2 V_A_2 V_Fa_2 V_f_2 T_a (c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)-> (c_Finite__Set_Ofinite(T_a,V_A_2)-> (c_member(T_a,V_x_2,V_A_2)->hAPP(hAPP(V_f_2,V_x_2),hAPP(V_Fa_2,V_A_2))=hAPP(V_Fa_2,V_A_2)))).
% 5.58/5.65 all V_N_2 V_h_2 V_Fa_2 V_f_2 T_a (c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)-> ((all B_x B_y (hAPP(V_h_2,hAPP(hAPP(V_f_2,B_x),B_y))=hAPP(hAPP(V_f_2,hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))))-> (c_Finite__Set_Ofinite(T_a,V_N_2)-> (V_N_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))->hAPP(V_h_2,hAPP(V_Fa_2,V_N_2))=hAPP(V_Fa_2,c_Set_Oimage(T_a,T_a,V_h_2,V_N_2)))))).
% 5.58/5.65 c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))).
% 5.58/5.65 all V_B_2 V_A_2 T_b T_a (c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))->c_Finite__Set_Ofinite(T_b,V_B_2)).
% 5.58/5.65 all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (c_SetInterval_Oord__class_OgreaterThan(T_a,V_x_2)=c_SetInterval_Oord__class_OgreaterThan(T_a,V_y_2)<->V_x_2=V_y_2)).
% 5.58/5.65 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))).
% 5.58/5.65 all V_y_2 V_x_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_x_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_y_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 5.58/5.65 all V_B_2 V_A_2 T_b T_a (c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))<->c_Finite__Set_Ofinite(T_a,V_A_2)&c_Finite__Set_Ofinite(T_b,V_B_2)).
% 5.58/5.65 all V_B_2 T_b V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)-> (c_Finite__Set_Ofinite(T_b,V_B_2)->c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)))).
% 5.58/5.65 all V_B_2 V_A_2 T_b T_a (c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))->c_Finite__Set_Ofinite(T_a,V_A_2)).
% 5.58/5.65 all T_b T_a (c_Sum__Type_OPlus(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool))).
% 5.58/5.65 all V_B_2 V_A_2 T_b T_a (c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_a,T_b),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_b,tc_HOL_Obool))).
% 5.58/5.65 all V_B_2 T_b V_A_2 T_a ((c_Finite__Set_Ofinite(T_a,V_A_2)&c_Finite__Set_Ofinite(T_b,V_B_2)->c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_b,V_B_2)))& (-(c_Finite__Set_Ofinite(T_a,V_A_2)&c_Finite__Set_Ofinite(T_b,V_B_2))->c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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)).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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).
% 5.58/5.65 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).
% 5.58/5.65 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))).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 all V_k_2 V_A_2 (c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_Nat_Onat,tc_HOL_Obool),V_A_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,c_Finite__Set_Ocard(tc_Nat_Onat,V_A_2))))->V_A_2=c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,c_Finite__Set_Ocard(tc_Nat_Onat,V_A_2)))).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 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)))).
% 5.58/5.65 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)).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 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))).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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)))).
% 5.58/5.65 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))).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 all V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 5.58/5.65 all V_n (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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))))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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).
% 5.58/5.65 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).
% 5.58/5.65 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))).
% 5.58/5.65 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).
% 5.58/5.65 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).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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))))).
% 5.58/5.65 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)))).
% 5.58/5.65 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)))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n))).
% 5.58/5.65 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)=hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))).
% 5.58/5.65 all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n))=hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))).
% 5.58/5.65 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))))).
% 5.58/5.65 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))))).
% 5.58/5.65 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))))).
% 5.58/5.65 all V_y_2 V_x_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_x_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)-> (c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))))).
% 5.58/5.65 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))))).
% 5.58/5.65 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)))).
% 5.58/5.65 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))).
% 5.58/5.65 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))))).
% 5.58/5.65 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))))).
% 5.58/5.65 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))))).
% 5.58/5.65 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))))).
% 5.58/5.65 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)))).
% 5.58/5.65 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))).
% 5.58/5.65 all V_n_2 V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.58/5.65 all V_n_2 V_m_2 (hAPP(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=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.58/5.65 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)).
% 5.58/5.65 all V_m V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))).
% 5.58/5.65 all V_m V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))).
% 5.58/5.65 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)<-> (exists B_k (V_n_2=hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k))))).
% 5.58/5.65 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))))).
% 5.58/5.65 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))))).
% 5.58/5.65 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))))).
% 5.58/5.65 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))))).
% 5.58/5.65 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))))).
% 5.58/5.65 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))))).
% 5.58/5.65 all V_B_2 T_b V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)-> (c_Finite__Set_Ofinite(T_b,V_B_2)->c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_b,V_B_2)))).
% 5.58/5.65 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))))).
% 5.58/5.65 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)))).
% 5.58/5.65 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))).
% 5.58/5.65 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)))).
% 5.58/5.65 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).
% 5.58/5.65 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).
% 5.58/5.65 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))).
% 5.58/5.65 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)).
% 5.58/5.65 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))).
% 5.58/5.65 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)).
% 5.58/5.65 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))).
% 5.58/5.65 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)).
% 5.58/5.65 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))).
% 5.58/5.65 all V_nat (c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(V_nat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 5.58/5.65 all V_f_2 V_m_2 V_n_2 T_a (class_Groups_Ocomm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)->c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)))=c_Groups_Ozero__class_Ozero(T_a))& (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)->c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)))=c_Groups_Oplus__class_Oplus(T_a,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_n_2)),hAPP(V_f_2,V_n_2)))).
% 5.58/5.65 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.65 all V_f_2 V_p_2 V_n_2 V_m_2 T_a (class_Groups_Ocomm__monoid__add(T_a)-> (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,V_n_2,V_p_2)->c_Groups_Oplus__class_Oplus(T_a,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_n_2)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2,V_p_2)))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_p_2))))).
% 5.58/5.65 all V_k_2 V_f_2 T_a (class_Groups_Ocomm__monoid__add(T_a)-> (hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(T_a)->c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)))).
% 5.58/5.65 all V_f_2 V_n_2 V_m_2 T_a (class_Groups_Ocomm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)->c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_n_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(V_f_2,V_m_2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))))).
% 5.58/5.65 all V_g_2 V_A_2 T_a T_b (class_Groups_Ocomm__monoid__add(T_b)-> (-c_Finite__Set_Ofinite(T_a,V_A_2)->c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,V_A_2)=c_Groups_Ozero__class_Ozero(T_b))).
% 5.58/5.65 all V_f_2 V_A_2 T_a T_b (class_Groups_Ocomm__monoid__add(T_b)-> (-c_Finite__Set_Ofinite(T_a,V_A_2)->c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,V_A_2)=c_Groups_Ozero__class_Ozero(T_b))).
% 5.58/5.65 all V_f_2 V_Fa_2 T_a (c_Finite__Set_Ofinite(T_a,V_Fa_2)-> (c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_Fa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<-> (all B_x (c_member(T_a,B_x,V_Fa_2)->hAPP(V_f_2,B_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))).
% 5.58/5.65 all V_f_2 V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)-> (c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<-> (exists B_x (c_member(T_a,B_x,V_A_2)&hAPP(V_f_2,B_x)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (all B_xa (c_member(T_a,B_xa,V_A_2)-> (B_x!=B_xa->hAPP(V_f_2,B_xa)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))).
% 5.58/5.65 all V_f_2 T_b T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(T_a)).
% 5.58/5.65 all V_g_2 T_b T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(T_a)).
% 5.58/5.65 all V_nat (c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_nat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,V_nat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 5.58/5.65 all V_g_2 V_f_2 V_A_2 T_a T_b (class_Groups_Ocomm__monoid__add(T_b)&class_Groups_Oordered__cancel__ab__semigroup__add(T_b)-> (c_Finite__Set_Ofinite(T_a,V_A_2)-> (V_A_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)->c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x))))->c_Orderings_Oord__class_Oless(T_b,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,V_A_2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,V_A_2)))))).
% 5.58/5.65 all V_n (c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n)=V_n).
% 5.58/5.65 c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.65 all V_n_2 V_A_2 V_f_2 T_a (c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2)=hAPP(c_Nat_OSuc,V_n_2)-> (exists B_x (c_member(T_a,B_x,V_A_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(V_f_2,B_x))))).
% 5.58/5.65 all V_h_2 V_g_2 V_B_2 V_A_2 V_f_2 T_b T_a T_c (class_Groups_Ocomm__monoid__add(T_c)-> (c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)-> (V_B_2=c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)-> ((all B_a (c_member(T_a,B_a,V_A_2)->hAPP(V_g_2,B_a)=hAPP(V_h_2,hAPP(V_f_2,B_a))))->c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c,V_h_2,V_B_2)=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c,V_g_2,V_A_2))))).
% 5.58/5.65 all V_g_2 V_f_2 V_d_2 V_b_2 V_c_2 V_a_2 T_a T_b (class_Groups_Ocomm__monoid__add(T_b)&class_Orderings_Oord(T_a)-> (V_a_2=V_c_2-> (V_b_2=V_d_2-> ((all B_x (c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,B_x)-> (c_Orderings_Oord__class_Oless(T_a,B_x,V_d_2)->hAPP(V_f_2,B_x)=hAPP(V_g_2,B_x))))->c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2)))))).
% 5.58/5.65 all V_f_2 V_m_2 V_n_2 T_a (class_Groups_Ocomm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),V_m_2)->c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)))=c_Groups_Ozero__class_Ozero(T_a))& (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),V_m_2)->c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)))=c_Groups_Oplus__class_Oplus(T_a,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))))).
% 5.58/5.65 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)).
% 5.58/5.65 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))).
% 5.58/5.65 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)))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 all V_u_2 V_l_2 (c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2,hAPP(c_Nat_OSuc,V_u_2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)).
% 5.58/5.65 all V_P_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_P_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_P_2,B_x))))).
% 5.58/5.65 all V_P_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_P_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_P_2,B_x))))).
% 5.58/5.65 all V_j_2 V_i_2 (c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2))).
% 5.58/5.65 all V_k_2 V_f_2 (hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2))).
% 5.58/5.65 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))).
% 5.58/5.65 all V_f_2 V_n_2 V_m_2 T_a (class_Groups_Ocomm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)->c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(V_f_2,V_m_2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))))).
% 5.58/5.65 all V_p_2 V_f_2 V_n_2 V_m_2 T_a (class_Groups_Ocomm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))->c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_p_2)))=c_Groups_Oplus__class_Oplus(T_a,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_p_2)))))).
% 5.58/5.65 c_HOL_Obool_Obool__size(c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.65 c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 5.58/5.65 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)))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.65 all V_n (hAPP(c_Nat_OSuc,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)).
% 5.58/5.65 all V_n (hAPP(c_Nat_OSuc,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 5.58/5.65 all V_x_2 T_a (class_Groups_Oone(T_a)-> (c_Groups_Oone__class_Oone(T_a)=V_x_2<->V_x_2=c_Groups_Oone__class_Oone(T_a))).
% 5.58/5.65 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)))).
% 5.58/5.65 all V_f_2 V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)-> (c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)<-> (exists B_x (c_member(T_a,B_x,V_A_2)&hAPP(V_f_2,B_x)=c_Groups_Oone__class_Oone(tc_Nat_Onat)& (all B_xa (c_member(T_a,B_xa,V_A_2)-> (B_x!=B_xa->hAPP(V_f_2,B_xa)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))))).
% 5.58/5.65 c_HOL_Obool_Obool__size(c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.65 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))))).
% 5.58/5.65 all V_n_2 V_P_2 (-hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))-> (hBOOL(hAPP(V_P_2,V_n_2))-> (exists B_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2)& (all B_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i,B_k)-> -hBOOL(hAPP(V_P_2,B_i))))&hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))).
% 5.58/5.65 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))).
% 5.58/5.65 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))))).
% 5.58/5.65 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))).
% 5.58/5.65 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)))).
% 5.58/5.65 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))).
% 5.58/5.65 all V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)-> (((exists B_x c_member(T_a,B_x,V_A_2))->c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))->c_Finite__Set_Ocard(T_a,V_A_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.58/5.65 all V_x_2 V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)-> (-c_member(T_a,V_x_2,V_A_2)->c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2)))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 all V_a_2 V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)->c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_a_2,V_A_2))).
% 5.58/5.65 all V_x_2 V_A_2 V_Fa_2 V_g_2 V_z_2 V_f_2 T_b T_a (c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)-> (c_Finite__Set_Ofinite(T_b,V_A_2)->hAPP(V_Fa_2,c_Set_Oinsert(T_b,V_x_2,V_A_2))=hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_2,V_A_2)))).
% 5.58/5.65 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))).
% 5.58/5.65 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))).
% 5.58/5.65 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)).
% 5.58/5.65 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).
% 5.58/5.65 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).
% 5.58/5.65 all V_B_2 V_A_2 V_x_2 T_a (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2),V_B_2)<->c_member(T_a,V_x_2,V_B_2)&c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)).
% 5.58/5.65 all V_B_2 V_A_2 V_x_2 T_a (-c_member(T_a,V_x_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_x_2,V_B_2))<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2))).
% 5.58/5.65 all V_f_2 T_b V_A_2 V_x_2 T_a (c_member(T_a,V_x_2,V_A_2)->c_Set_Oinsert(T_b,hAPP(V_f_2,V_x_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))=c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)).
% 5.58/5.65 all V_x_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_x_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_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))).
% 5.58/5.65 all V_B_2 V_a_2 V_f_2 T_a T_b (c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oinsert(T_b,V_a_2,V_B_2))=c_Set_Oinsert(T_a,hAPP(V_f_2,V_a_2),c_Set_Oimage(T_b,T_a,V_f_2,V_B_2))).
% 5.58/5.65 all V_A_2 V_x_2 T_a (c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_x_2,V_A_2))=c_Set_Oinsert(T_a,V_x_2,V_A_2)).
% 5.58/5.65 all V_A_2 V_y_2 V_x_2 T_a (c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_y_2,V_A_2))=c_Set_Oinsert(T_a,V_y_2,c_Set_Oinsert(T_a,V_x_2,V_A_2))).
% 5.58/5.65 all V_x_2 V_A_2 V_y_2 T_a (hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2))<->V_y_2=V_x_2|hBOOL(hAPP(V_A_2,V_x_2))).
% 5.58/5.65 all V_A_2 V_a_2 T_a (c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_a_2,V_A_2))<->c_Finite__Set_Ofinite(T_a,V_A_2)).
% 5.58/5.65 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)).
% 5.58/5.65 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)).
% 5.58/5.65 all V_B_2 V_A_2 V_x_2 T_a (-c_member(T_a,V_x_2,V_A_2)-> (-c_member(T_a,V_x_2,V_B_2)-> (c_Set_Oinsert(T_a,V_x_2,V_A_2)=c_Set_Oinsert(T_a,V_x_2,V_B_2)<->V_A_2=V_B_2))).
% 5.58/5.65 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))).
% 5.58/5.65 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).
% 5.58/5.65 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).
% 5.58/5.65 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).
% 5.58/5.65 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))).
% 5.58/5.65 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)).
% 5.58/5.65 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))))).
% 5.58/5.65 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)).
% 5.58/5.65 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)))).
% 5.58/5.65 all V_x_2 V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)))).
% 5.58/5.65 all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))->c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))=c_Set_Oinsert(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))).
% 5.58/5.65 all V_m_2 (c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,hAPP(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)))).
% 5.58/5.65 all V_x_2 V_A_2 V_Fa_2 V_f_2 T_a (c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)-> (c_Finite__Set_Ofinite(T_a,V_A_2)-> (V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))->hAPP(V_Fa_2,c_Set_Oinsert(T_a,V_x_2,V_A_2))=hAPP(hAPP(V_f_2,V_x_2),hAPP(V_Fa_2,V_A_2))))).
% 5.58/5.65 all V_g_2 V_x_2 V_A_2 T_a T_b (class_Groups_Ocomm__monoid__add(T_b)-> (c_Finite__Set_Ofinite(T_a,V_A_2)-> (-c_member(T_a,V_x_2,V_A_2)->c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,c_Set_Oinsert(T_a,V_x_2,V_A_2))=c_Groups_Oplus__class_Oplus(T_b,hAPP(V_g_2,V_x_2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,V_A_2))))).
% 5.58/5.66 all V_f_2 V_a_2 V_Fa_2 T_a T_b (class_Groups_Ocomm__monoid__add(T_b)-> (c_Finite__Set_Ofinite(T_a,V_Fa_2)-> (-c_member(T_a,V_a_2,V_Fa_2)->c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,c_Set_Oinsert(T_a,V_a_2,V_Fa_2))=c_Groups_Oplus__class_Oplus(T_b,hAPP(V_f_2,V_a_2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,V_Fa_2))))).
% 5.58/5.66 all V_x_2 V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)-> (-c_member(T_a,V_x_2,V_A_2)->c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2))=hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(T_a,V_A_2)))).
% 5.58/5.66 all V_x_2 V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)-> (c_member(T_a,V_x_2,V_A_2)->c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2))=c_Finite__Set_Ocard(T_a,V_A_2))& (-c_member(T_a,V_x_2,V_A_2)->c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2))=hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(T_a,V_A_2)))).
% 5.58/5.66 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,hAPP(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,hAPP(c_Nat_OSuc,V_n_2))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))).
% 5.58/5.66 all V_x_2 T_a (c_Set_Othe__elem(T_a,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=V_x_2).
% 5.58/5.66 all V_k_2 V_A_2 T_a (c_Finite__Set_Ocard(T_a,V_A_2)=hAPP(c_Nat_OSuc,V_k_2)<-> (exists B_b B_B (V_A_2=c_Set_Oinsert(T_a,B_b,B_B)& -c_member(T_a,B_b,B_B)&c_Finite__Set_Ocard(T_a,B_B)=V_k_2& (V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->B_B=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))).
% 5.58/5.66 all V_x_2 V_A_2 V_Fa_2 V_f_2 T_a (c_Finite__Set_Ofolding__one(T_a,V_f_2,V_Fa_2)-> (c_Finite__Set_Ofinite(T_a,V_A_2)-> (-c_member(T_a,V_x_2,V_A_2)-> (V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))->hAPP(V_Fa_2,c_Set_Oinsert(T_a,V_x_2,V_A_2))=hAPP(hAPP(V_f_2,V_x_2),hAPP(V_Fa_2,V_A_2)))))).
% 5.58/5.66 all V_x_2 V_A_2 T_a (c_Finite__Set_Ofinite(T_a,V_A_2)-> (c_member(T_a,V_x_2,V_A_2)->c_Finite__Set_Ocard(T_a,V_A_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))))).
% 5.58/5.66 all T_2 T_1 (class_Orderings_Opreorder(T_1)->class_Orderings_Opreorder(tc_fun(T_2,T_1))).
% 5.58/5.66 all T_1 T_2 (class_Finite__Set_Ofinite(T_2)&class_Finite__Set_Ofinite(T_1)->class_Finite__Set_Ofinite(tc_fun(T_2,T_1))).
% 5.58/5.66 all T_2 T_1 (class_Orderings_Oorder(T_1)->class_Orderings_Oorder(tc_fun(T_2,T_1))).
% 5.58/5.66 all T_2 T_1 (class_Orderings_Otop(T_1)->class_Orderings_Otop(tc_fun(T_2,T_1))).
% 5.58/5.66 all T_2 T_1 (class_Orderings_Oord(T_1)->class_Orderings_Oord(tc_fun(T_2,T_1))).
% 5.58/5.66 all T_2 T_1 (class_Orderings_Obot(T_1)->class_Orderings_Obot(tc_fun(T_2,T_1))).
% 5.58/5.66 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 5.58/5.66 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 5.58/5.66 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 5.58/5.66 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 5.58/5.66 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 5.58/5.66 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 5.58/5.66 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 5.58/5.66 class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 5.58/5.66 class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 5.58/5.66 class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 5.58/5.66 class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 5.58/5.66 class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 5.58/5.66 class_Orderings_Opreorder(tc_Nat_Onat).
% 5.58/5.66 class_Orderings_Olinorder(tc_Nat_Onat).
% 5.58/5.66 class_Groups_Omonoid__add(tc_Nat_Onat).
% 5.58/5.66 class_Orderings_Oorder(tc_Nat_Onat).
% 5.58/5.66 class_Orderings_Oord(tc_Nat_Onat).
% 5.58/5.66 class_Orderings_Obot(tc_Nat_Onat).
% 5.58/5.66 class_Groups_Ozero(tc_Nat_Onat).
% 5.58/5.66 class_Groups_Oone(tc_Nat_Onat).
% 5.58/5.66 class_Orderings_Opreorder(tc_HOL_Obool).
% 5.58/5.66 class_Finite__Set_Ofinite(tc_HOL_Obool).
% 5.58/5.66 class_Orderings_Oorder(tc_HOL_Obool).
% 5.58/5.66 class_Orderings_Otop(tc_HOL_Obool).
% 5.58/5.66 class_Orderings_Oord(tc_HOL_Obool).
% 5.58/5.66 class_Orderings_Obot(tc_HOL_Obool).
% 5.58/5.66 all T_1 T_2 (class_Finite__Set_Ofinite(T_2)&class_Finite__Set_Ofinite(T_1)->class_Finite__Set_Ofinite(tc_sum(T_2,T_1))).
% 5.58/5.66 all T_1 (class_Finite__Set_Ofinite(T_1)->class_Finite__Set_Ofinite(tc_Option_Ooption(T_1))).
% 5.58/5.66 all T_1 T_2 (class_Finite__Set_Ofinite(T_2)&class_Finite__Set_Ofinite(T_1)->class_Finite__Set_Ofinite(tc_prod(T_2,T_1))).
% 5.58/5.66 class_Finite__Set_Ofinite(tc_Product__Type_Ounit).
% 5.58/5.66 all V_y_2 V_x_2 (-hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2))|V_x_2=V_y_2).
% 5.58/5.66 all V_y_2 V_x_2 (V_x_2!=V_y_2|hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2))).
% 5.58/5.66 -hBOOL(c_fFalse).
% 5.58/5.66 hBOOL(c_fTrue).
% 5.58/5.66 all B_h (c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))-> (c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))=c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))->v_thesis____)).
% 5.58/5.66 -v_thesis____.
% 5.58/5.66 end_of_list.
% 5.58/5.66
% 5.58/5.66 -------> usable clausifies to:
% 5.58/5.66
% 5.58/5.66 list(usable).
% 5.58/5.66 0 [] A=A.
% 5.58/5.66 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.
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)|c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))=c_Finite__Set_Ocard(T_a,V_A_2).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))|c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)!=c_Set_Oimage(T_a,T_b,V_f_2,V_B_2)|V_A_2=V_B_2.
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))|c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)=c_Set_Oimage(T_a,T_b,V_f_2,V_B_2)|V_A_2!=V_B_2.
% 5.58/5.66 0 [] hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))|hAPP(V_f_2,V_x_2)!=hAPP(V_f_2,V_y_2)|V_x_2=V_y_2.
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))|hAPP(V_f_2,V_x_2)=hAPP(V_f_2,V_y_2)|V_x_2!=V_y_2.
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))|hAPP(V_f_2,V_x_2)!=hAPP(V_f_2,V_y_2)|V_x_2=V_y_2.
% 5.58/5.66 0 [] -class_Orderings_Otop(T_a)|hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2)=c_Orderings_Otop__class_Otop(T_a).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)| -c_member(T_a,B_x,V_A_2)| -c_member(T_a,B_xa,V_A_2)|hAPP(V_f_2,B_x)!=hAPP(V_f_2,B_xa)|B_x=B_xa.
% 5.58/5.66 0 [] c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)|c_member(T_a,$f3(V_A_2,V_f_2,T_b,T_a),V_A_2).
% 5.58/5.66 0 [] c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)|c_member(T_a,$f2(V_A_2,V_f_2,T_b,T_a),V_A_2).
% 5.58/5.66 0 [] c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)|hAPP(V_f_2,$f3(V_A_2,V_f_2,T_b,T_a))=hAPP(V_f_2,$f2(V_A_2,V_f_2,T_b,T_a)).
% 5.58/5.66 0 [] c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)|$f3(V_A_2,V_f_2,T_b,T_a)!=$f2(V_A_2,V_f_2,T_b,T_a).
% 5.58/5.66 0 [] -class_Groups_Ozero(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=V_x_2|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 5.58/5.66 0 [] -class_Groups_Ozero(T_a)|c_Groups_Ozero__class_Ozero(T_a)=V_x_2|V_x_2!=c_Groups_Ozero__class_Ozero(T_a).
% 5.58/5.66 0 [] c_Arrow__Order__Mirabelle_OIIA(v_F).
% 5.58/5.66 0 [] c_Arrow__Order__Mirabelle_Ounanimity(v_F).
% 5.58/5.66 0 [] c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,V_Fa_2)|c_Finite__Set_Ofinite(T_b,c_Set_Oimage(T_a,T_b,V_h_2,V_Fa_2)).
% 5.58/5.66 0 [] -class_Finite__Set_Ofinite(T_a)|c_Finite__Set_Ofinite(T_a,V_A_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(tc_Option_Ooption(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)))|c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.66 0 [] c_Finite__Set_Ofinite(tc_Option_Ooption(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)))| -c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)))|c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)))|c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))).
% 5.58/5.66 0 [] c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)))| -c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))| -c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))).
% 5.58/5.66 0 [] -class_Finite__Set_Ofinite(T_a)|c_Finite__Set_Ofinite(T_a,V_A_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(tc_fun(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))|c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))| -c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))|c_Finite__Set_Ofinite(tc_prod(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))).
% 5.58/5.66 0 [] -class_Finite__Set_Ofinite(T_a)|c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.66 0 [] c_Finite__Set_Ofinite(T_a,V_A_2)|c_Finite__Set_Ocard(T_a,V_A_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))| -c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)|c_Finite__Set_Ofinite(T_b,V_A_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))|c_Finite__Set_Ocard(T_a,V_A_2)!=c_Finite__Set_Ocard(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))|V_A_2=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))|c_Set_Oimage(T_a,T_a,V_f_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))|c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))| -c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))|c_Set_Oimage(T_a,T_a,V_f_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)).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))!=c_Finite__Set_Ocard(T_a,V_A_2)|c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)| -c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)|c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))=c_Finite__Set_Ocard(T_a,V_A_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)|c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))!=c_Finite__Set_Ocard(T_a,V_A_2).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),V_B_2)| -c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_g_2,V_B_2),V_A_2)| -c_Finite__Set_Ofinite(T_a,V_A_2)| -c_Finite__Set_Ofinite(T_b,V_B_2)|c_Finite__Set_Ocard(T_a,V_A_2)=c_Finite__Set_Ocard(T_b,V_B_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)|c_Set_Oimage(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))=V_A_2.
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)|c_Fun_Oinj__on(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))|hAPP(c_Fun_Othe__inv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2))=V_x_2.
% 5.58/5.66 0 [] c_Finite__Set_Ocard(T_a,V_A_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))| -c_Finite__Set_Ofinite(T_a,V_A_2).
% 5.58/5.66 0 [] c_Finite__Set_Ocard(T_a,V_A_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 5.58/5.66 0 [] c_Finite__Set_Ocard(T_a,V_A_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Finite__Set_Ofinite(T_a,V_A_2).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)),c_Finite__Set_Ocard(T_b,V_A_2))| -c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))| -c_member(T_b,hAPP(V_f_2,V_a_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))|c_member(T_a,V_a_2,V_A_2).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))|c_member(T_b,hAPP(V_f_2,V_a_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))| -c_member(T_a,V_a_2,V_A_2).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))| -c_member(T_b,V_b_2,c_Set_Oimage(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))|V_b_2=hAPP(V_f_2,$f4(V_b_2,V_f_2,T_b,T_a)).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))| -c_member(T_b,V_b_2,c_Set_Oimage(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))|V_b_2!=hAPP(V_f_2,B_y)|B_y=$f4(V_b_2,V_f_2,T_b,T_a).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))|c_member(T_b,V_b_2,c_Set_Oimage(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))|V_b_2!=hAPP(V_f_2,B_x)|V_b_2=hAPP(V_f_2,$f5(V_b_2,V_f_2,T_b,T_a,B_x)).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))|c_member(T_b,V_b_2,c_Set_Oimage(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))|V_b_2!=hAPP(V_f_2,B_x)|$f5(V_b_2,V_f_2,T_b,T_a,B_x)!=B_x.
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),c_Finite__Set_Ocard(T_a,V_A_2)).
% 5.58/5.66 0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x).
% 5.58/5.66 0 [] c_Finite__Set_Ofinite(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.66 0 [] c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.66 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_x).
% 5.58/5.66 0 [] -class_Orderings_Obot(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Orderings_Obot__class_Obot(T_a),V_x).
% 5.58/5.66 0 [] -class_Orderings_Obot(T_a)|hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2)=c_Orderings_Obot__class_Obot(T_a).
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)|V_x_2=V_y_2|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)|V_x_2!=V_y_2| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2).
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)|V_x_2!=V_y_2| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|V_x_2=V_y_2.
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 5.58/5.66 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)).
% 5.58/5.66 0 [] -class_Orderings_Oord(T_b)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,$f6(V_g_2,V_f_2,T_a,T_b)),hAPP(V_g_2,$f6(V_g_2,V_f_2,T_a,T_b))).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2).
% 5.58/5.66 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 5.58/5.66 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 5.58/5.66 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2).
% 5.58/5.66 0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 5.58/5.66 0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 5.58/5.66 0 [] -class_Orderings_Oorder(T_a)|V_x_2!=V_y_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2).
% 5.58/5.66 0 [] -class_Orderings_Oorder(T_a)|V_x_2!=V_y_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 5.58/5.66 0 [] -class_Orderings_Oorder(T_a)|V_x_2=V_y_2| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 5.58/5.66 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 5.58/5.66 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2).
% 5.58/5.66 0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 5.58/5.66 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).
% 5.58/5.66 0 [] -c_member(T_a,V_x_2,c_fe_qual(V_y_2))|V_x_2=V_y_2.
% 5.58/5.66 0 [] c_member(T_a,V_x_2,c_fe_qual(V_y_2))|V_x_2!=V_y_2.
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 0 [] -hBOOL(hAPP(V_P_2,V_x_2))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_P_2,V_Q_2)|hBOOL(hAPP(V_Q_2,V_x_2)).
% 5.58/5.66 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 0 [] -class_Orderings_Opreorder(T_a)|V_x!=V_y|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 5.58/5.66 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_x_2),hAPP(V_g_2,V_x_2)).
% 5.58/5.66 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 5.58/5.66 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_y!=V_x.
% 5.58/5.66 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.
% 5.58/5.66 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 5.58/5.66 0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_P_2,V_Q_2)| -hBOOL(hAPP(V_P_2,V_x_2))|hBOOL(hAPP(V_Q_2,V_x_2)).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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.
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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.
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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_x_2),hAPP(V_g_2,V_x_2)).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)|hAPP(V_f_2,V_x_2)!=V_y_2| -c_member(T_a,V_x_2,V_A_2)|hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2)=V_x_2.
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)| -c_member(T_a,V_x_2,V_A_2)|hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(V_f_2,V_x_2))=V_x_2.
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)| -c_member(T_b,V_x_2,c_Set_Oimage(T_a,T_b,V_f_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,hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2),V_B_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(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)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_B_2),c_Finite__Set_Ocard(T_a,V_A_2))|V_A_2=V_B_2.
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(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)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_a,V_B_2)).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Finite__Set_Ofinite(T_a,V_B_2)|c_Finite__Set_Ofinite(T_a,V_A_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(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)|c_Finite__Set_Ofinite(T_a,V_A_2).
% 5.58/5.66 0 [] -class_Orderings_Otop(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Orderings_Otop__class_Otop(T_a)).
% 5.58/5.66 0 [] c_Finite__Set_Ofinite(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)|V_x_2=V_y_2| -c_member(T_a,V_x_2,V_A_2)| -c_member(T_a,V_y_2,V_A_2)|hAPP(V_f_2,V_x_2)!=hAPP(V_f_2,V_y_2).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)| -c_member(T_a,V_x_2,V_A_2)| -c_member(T_a,V_y_2,V_A_2)|hAPP(V_f_2,V_x_2)!=hAPP(V_f_2,V_y_2)|V_x_2=V_y_2.
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)| -c_member(T_a,V_x_2,V_A_2)| -c_member(T_a,V_y_2,V_A_2)|hAPP(V_f_2,V_x_2)=hAPP(V_f_2,V_y_2)|V_x_2!=V_y_2.
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)|hAPP(V_f_2,V_x_2)!=hAPP(V_f_2,V_y_2)| -c_member(T_a,V_x_2,V_A_2)| -c_member(T_a,V_y_2,V_A_2)|V_x_2=V_y_2.
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_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_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)| -c_member(T_b,V_y_2,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))|hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2))=V_y_2.
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2))|V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2))|c_Finite__Set_Ofinite(T_a,V_A_2).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2))|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))| -c_Finite__Set_Ofinite(T_a,V_A_2).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),V_B_2)| -c_Finite__Set_Ofinite(T_b,V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_b,V_B_2)).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),V_B_2,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))|c_Finite__Set_Ofinite(T_b,V_B_2).
% 5.58/5.66 0 [] c_Finite__Set_Ocard(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2))|c_Finite__Set_Ofinite(T_a,V_A_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oimage(T_a,T_a,V_f_2,V_A_2))|c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_a,T_a,V_f_2,V_A_2),V_A_2)| -c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2)|c_Set_Oimage(T_a,T_a,V_f_2,V_A_2)=V_A_2.
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)| -c_Finite__Set_Ofinite(T_b,V_B_2)| -c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,B_f,V_A_2),V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_b,V_B_2)).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)| -c_Finite__Set_Ofinite(T_b,V_B_2)|c_Fun_Oinj__on(T_a,T_b,$f7(V_B_2,T_b,V_A_2,T_a),V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_b,V_B_2)).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)| -c_Finite__Set_Ofinite(T_b,V_B_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,$f7(V_B_2,T_b,V_A_2,T_a),V_A_2),V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_b,V_B_2)).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.66 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).
% 5.58/5.66 0 [] V_b_2!=hAPP(V_f_2,V_x_2)| -c_member(T_b,V_x_2,V_A_2)|c_member(T_a,V_b_2,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)).
% 5.58/5.66 0 [] c_member(T_a,V_x_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.66 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).
% 5.58/5.66 0 [] -c_member(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.66 0 [] V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))| -c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,B_f,V_A_2),V_A_H_2)|c_Set_Oimage(T_b,T_a,$f8(V_A_H_2,T_b,T_a,V_A_2),V_A_H_2)=V_A_2.
% 5.58/5.66 0 [] V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|c_Fun_Oinj__on(T_a,T_b,$f9(V_A_H_2,T_b,T_a,V_A_2),V_A_2)|c_Set_Oimage(T_b,T_a,B_g,V_A_H_2)!=V_A_2.
% 5.58/5.66 0 [] V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,$f9(V_A_H_2,T_b,T_a,V_A_2),V_A_2),V_A_H_2)|c_Set_Oimage(T_b,T_a,B_g,V_A_H_2)!=V_A_2.
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,V_n_2)| -hBOOL(hAPP(V_P_2,B_m))|c_member(tc_Nat_Onat,$f10(V_P_2,V_n_2),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,V_n_2)| -hBOOL(hAPP(V_P_2,B_m))|hBOOL(hAPP(V_P_2,$f10(V_P_2,V_n_2))).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f11(V_P_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_P_2,B_x)).
% 5.58/5.66 0 [] hBOOL(hAPP(V_P_2,$f11(V_P_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_P_2,B_x)).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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.
% 5.58/5.66 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2,V_u_2)).
% 5.58/5.66 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).
% 5.58/5.66 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))).
% 5.58/5.66 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).
% 5.58/5.66 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.
% 5.58/5.66 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.
% 5.58/5.66 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.
% 5.58/5.66 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).
% 5.58/5.66 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.
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 0 [] c_Orderings_Obot__class_Obot(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 0 [] -c_Fun_Oinj__on(T_a,T_b,V_f_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_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2)).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,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_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_a,V_B_2)).
% 5.58/5.66 0 [] -c_member(T_a,V_x_2,V_A_2)|hBOOL(hAPP(V_A_2,V_x_2)).
% 5.58/5.66 0 [] c_member(T_a,V_x_2,V_A_2)| -hBOOL(hAPP(V_A_2,V_x_2)).
% 5.58/5.66 0 [] V_A_2!=V_B_2| -c_member(T_a,V_x_2,V_A_2)|c_member(T_a,V_x_2,V_B_2).
% 5.58/5.66 0 [] V_A_2!=V_B_2|c_member(T_a,V_x_2,V_A_2)| -c_member(T_a,V_x_2,V_B_2).
% 5.58/5.66 0 [] V_x_2!=V_y_2| -c_member(T_a,V_x_2,V_A_2)|c_member(T_a,V_y_2,V_A_2).
% 5.58/5.66 0 [] V_x_2!=V_y_2|c_member(T_a,V_x_2,V_A_2)| -c_member(T_a,V_y_2,V_A_2).
% 5.58/5.66 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).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 5.58/5.66 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).
% 5.58/5.66 0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 5.58/5.66 0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 5.58/5.66 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).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)|V_m!=V_n.
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)|V_s!=V_t.
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)|hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)).
% 5.58/5.66 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,$f12(V_N_2)).
% 5.58/5.66 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)|c_member(tc_Nat_Onat,$f13(V_N_2,B_m),V_N_2).
% 5.58/5.66 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f13(V_N_2,B_m),B_m).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n).
% 5.58/5.66 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).
% 5.58/5.66 0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 5.58/5.66 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).
% 5.58/5.66 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.
% 5.58/5.66 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,$f14(V_N_2)).
% 5.58/5.66 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)|c_member(tc_Nat_Onat,$f15(V_N_2,B_m),V_N_2).
% 5.58/5.66 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f15(V_N_2,B_m),B_m).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_a,V_B_2))|c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 5.58/5.66 0 [] c_member(T_a,$f16(V_A_2,T_a),V_A_2)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 0 [] c_member(T_a,$f17(V_A_2,T_a),V_A_2)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 5.58/5.66 0 [] -c_member(T_a,V_c_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.66 0 [] V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))| -c_member(T_a,V_a_2,V_A_2).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_member(T_a,V_x_2,V_A_2)|c_member(T_a,V_x_2,V_B_2).
% 5.58/5.66 0 [] -c_member(T_a,V_x_2,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)|c_member(T_a,V_x_2,V_B_2).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)| -c_member(T_a,V_x_2,V_A_2)|c_member(T_a,V_x_2,V_B_2).
% 5.58/5.66 0 [] -c_member(T_a,V_x_2,V_A_2)|V_b_2!=hAPP(V_f_2,V_x_2)|c_member(T_b,V_b_2,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)).
% 5.58/5.66 0 [] -c_member(T_a,V_x_2,V_A_2)|c_member(T_b,hAPP(V_f_2,V_x_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)).
% 5.58/5.66 0 [] -c_member(T_a,V_z_2,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))|c_member(T_b,$f18(V_A_2,V_f_2,T_b,V_z_2,T_a),V_A_2).
% 5.58/5.66 0 [] -c_member(T_a,V_z_2,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))|V_z_2=hAPP(V_f_2,$f18(V_A_2,V_f_2,T_b,V_z_2,T_a)).
% 5.58/5.66 0 [] c_member(T_a,V_z_2,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))| -c_member(T_b,B_x,V_A_2)|V_z_2!=hAPP(V_f_2,B_x).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 0 [] c_Set_Oimage(T_b,T_a,V_f_2,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_b,tc_HOL_Obool)).
% 5.58/5.66 0 [] c_Set_Oimage(T_b,T_a,V_f_2,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_b,tc_HOL_Obool)).
% 5.58/5.66 0 [] c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 5.58/5.66 0 [] c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))!=c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)).
% 5.58/5.66 0 [] c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))=c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)|V_A_2!=c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)).
% 5.58/5.66 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).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.66 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))).
% 5.58/5.66 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_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2)).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),$f19(V_A_2,V_f_2,T_b,V_B_2,T_a),V_A_2).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))|V_B_2=c_Set_Oimage(T_b,T_a,V_f_2,$f19(V_A_2,V_f_2,T_b,V_B_2,T_a)).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),B_AA,V_A_2)|V_B_2!=c_Set_Oimage(T_b,T_a,V_f_2,B_AA).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 5.58/5.66 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).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=V_n_2.
% 5.58/5.66 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.
% 5.58/5.66 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.
% 5.58/5.66 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).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=V_n_2.
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 5.58/5.66 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.
% 5.58/5.66 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.
% 5.58/5.66 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.
% 5.58/5.66 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.
% 5.58/5.66 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.
% 5.58/5.66 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)).
% 5.58/5.66 0 [] V_b_2!=hAPP(V_f_2,V_x_2)|c_member(T_a,V_b_2,c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))).
% 5.58/5.66 0 [] c_member(T_a,hAPP(V_f_2,V_x_2),c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))).
% 5.58/5.66 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)).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f20(V_P_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_P_2,B_x)).
% 5.58/5.66 0 [] -hBOOL(hAPP(V_P_2,$f20(V_P_2,V_n_2)))| -c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))|hBOOL(hAPP(V_P_2,B_x)).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,V_n_2)|hBOOL(hAPP(V_P_2,B_m))|c_member(tc_Nat_Onat,$f21(V_P_2,V_n_2),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,V_n_2)|hBOOL(hAPP(V_P_2,B_m))| -hBOOL(hAPP(V_P_2,$f21(V_P_2,V_n_2))).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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).
% 5.58/5.66 0 [] c_member(T_a,V_x_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(tc_fun(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))|c_Finite__Set_Ocard(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.66 0 [] -c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)| -c_Finite__Set_Ofinite(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(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)|hAPP(hAPP(V_f_2,hAPP(V_Fa_2,V_B_2)),hAPP(V_Fa_2,V_A_2))=hAPP(V_Fa_2,V_A_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)| -c_Finite__Set_Ofinite(T_b,V_A_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_b,tc_HOL_Obool),V_B_2,V_A_2)|hAPP(hAPP(V_f_2,hAPP(V_Fa_2,V_B_2)),hAPP(V_Fa_2,V_A_2))=hAPP(V_Fa_2,V_A_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)| -c_Finite__Set_Ofinite(T_b,V_A_2)| -c_member(T_b,V_x_2,V_A_2)|hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_2,V_A_2))=hAPP(V_Fa_2,V_A_2).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),hAPP(c_Nat_OSuc,V_n)).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(c_Nat_OSuc,V_n)).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)).
% 5.58/5.66 0 [] V_n!=hAPP(c_Nat_OSuc,V_n).
% 5.58/5.66 0 [] hAPP(c_Nat_OSuc,V_n)!=V_n.
% 5.58/5.66 0 [] hAPP(c_Nat_OSuc,V_nat_2)!=hAPP(c_Nat_OSuc,V_nat_H_2)|V_nat_2=V_nat_H_2.
% 5.58/5.66 0 [] hAPP(c_Nat_OSuc,V_nat_2)=hAPP(c_Nat_OSuc,V_nat_H_2)|V_nat_2!=V_nat_H_2.
% 5.58/5.66 0 [] hAPP(c_Nat_OSuc,V_x)!=hAPP(c_Nat_OSuc,V_y)|V_x=V_y.
% 5.58/5.66 0 [] c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)|hAPP(hAPP(V_f_2,V_x_2),V_x_2)=V_x_2.
% 5.58/5.66 0 [] -c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)|hAPP(hAPP(V_f_2,V_x_2),V_x_2)=V_x_2.
% 5.58/5.66 0 [] c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2,V_j_2))=c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n),V_n).
% 5.58/5.66 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,hAPP(c_Nat_OSuc,V_n_2),V_m_2).
% 5.58/5.66 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,hAPP(c_Nat_OSuc,V_n_2),V_m_2).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,hAPP(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=hAPP(c_Nat_OSuc,V_n_2).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))|V_m_2!=hAPP(c_Nat_OSuc,V_n_2).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2).
% 5.58/5.66 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,hAPP(c_Nat_OSuc,V_n)).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|V_m=hAPP(c_Nat_OSuc,V_n).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,V_m_2)).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,V_m_2)).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2.
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))|V_m_2!=V_n_2.
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,V_m_2))|V_n_2=V_m_2.
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,V_m_2))|V_n_2!=V_m_2.
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(c_Nat_OSuc,V_m))|V_m=V_n.
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n)).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|hAPP(c_Nat_OSuc,V_m)=V_n|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i),V_k).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_m=V_n.
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),hAPP(c_Nat_OSuc,V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 5.58/5.66 0 [] hAPP(c_Nat_OSuc,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.66 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_m).
% 5.58/5.66 0 [] hAPP(c_Nat_OSuc,V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.66 0 [] hAPP(c_Nat_OSuc,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.66 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_nat_H).
% 5.58/5.66 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_m).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)|V_n_2=hAPP(c_Nat_OSuc,$f22(V_n_2)).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)|V_n_2!=hAPP(c_Nat_OSuc,B_m).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=hAPP(c_Nat_OSuc,$f23(V_n_2,V_m_2)).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f23(V_n_2,V_m_2),V_n_2).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))|V_m_2!=hAPP(c_Nat_OSuc,B_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 5.58/5.66 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,hAPP(c_Nat_OSuc,V_m_2))|V_n_2=V_m_2.
% 5.58/5.66 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,hAPP(c_Nat_OSuc,V_m_2))|V_n_2!=V_m_2.
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n).
% 5.58/5.66 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,hAPP(c_Nat_OSuc,V_n)).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 5.58/5.66 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 5.58/5.66 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 5.58/5.66 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,hAPP(c_Nat_OSuc,V_n_2),V_m_2).
% 5.58/5.66 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,hAPP(c_Nat_OSuc,V_n_2),V_m_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)| -c_Finite__Set_Ofinite(T_a,V_A_2)| -c_member(T_a,V_x_2,V_A_2)|hAPP(hAPP(V_f_2,V_x_2),hAPP(V_Fa_2,V_A_2))=hAPP(V_Fa_2,V_A_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)|hAPP(V_h_2,hAPP(hAPP(V_f_2,$f25(V_N_2,V_h_2,V_Fa_2,V_f_2,T_a)),$f24(V_N_2,V_h_2,V_Fa_2,V_f_2,T_a)))!=hAPP(hAPP(V_f_2,hAPP(V_h_2,$f25(V_N_2,V_h_2,V_Fa_2,V_f_2,T_a))),hAPP(V_h_2,$f24(V_N_2,V_h_2,V_Fa_2,V_f_2,T_a)))| -c_Finite__Set_Ofinite(T_a,V_N_2)|V_N_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|hAPP(V_h_2,hAPP(V_Fa_2,V_N_2))=hAPP(V_Fa_2,c_Set_Oimage(T_a,T_a,V_h_2,V_N_2)).
% 5.58/5.66 0 [] c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))|c_Finite__Set_Ofinite(T_b,V_B_2).
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)|c_SetInterval_Oord__class_OgreaterThan(T_a,V_x_2)!=c_SetInterval_Oord__class_OgreaterThan(T_a,V_y_2)|V_x_2=V_y_2.
% 5.58/5.66 0 [] -class_Orderings_Olinorder(T_a)|c_SetInterval_Oord__class_OgreaterThan(T_a,V_x_2)=c_SetInterval_Oord__class_OgreaterThan(T_a,V_y_2)|V_x_2!=V_y_2.
% 5.58/5.66 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).
% 5.58/5.66 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).
% 5.58/5.66 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_x_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_y_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 5.58/5.66 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_x_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_y_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))|c_Finite__Set_Ofinite(T_a,V_A_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))|c_Finite__Set_Ofinite(T_b,V_B_2).
% 5.58/5.66 0 [] c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))| -c_Finite__Set_Ofinite(T_a,V_A_2)| -c_Finite__Set_Ofinite(T_b,V_B_2).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)| -c_Finite__Set_Ofinite(T_b,V_B_2)|c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))|c_Finite__Set_Ofinite(T_a,V_A_2).
% 5.58/5.66 0 [] c_Sum__Type_OPlus(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)).
% 5.58/5.66 0 [] c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)!=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool))|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 5.58/5.66 0 [] c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)!=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool))|V_B_2=c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)).
% 5.58/5.66 0 [] c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_a,T_b),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_b,tc_HOL_Obool)).
% 5.58/5.66 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)| -c_Finite__Set_Ofinite(T_b,V_B_2)|c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_b,V_B_2)).
% 5.58/5.66 0 [] c_Finite__Set_Ofinite(T_a,V_A_2)|c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.66 0 [] c_Finite__Set_Ofinite(T_b,V_B_2)|c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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).
% 5.58/5.66 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)).
% 5.58/5.66 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)).
% 5.58/5.66 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.
% 5.58/5.66 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.
% 5.58/5.66 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.
% 5.58/5.66 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.
% 5.58/5.66 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)).
% 5.58/5.66 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.
% 5.58/5.66 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.
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_Nat_Onat,tc_HOL_Obool),V_A_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,c_Finite__Set_Ocard(tc_Nat_Onat,V_A_2))))|V_A_2=c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,c_Finite__Set_Ocard(tc_Nat_Onat,V_A_2))).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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,$f26(V_n_2,V_m_2)).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i).
% 5.58/5.67 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 5.58/5.67 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n.
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n)).
% 5.58/5.67 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)=hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 5.58/5.67 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n))=hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 5.58/5.67 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_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 5.58/5.67 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_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_a)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.67 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.67 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.67 0 [] hAPP(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=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] hAPP(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=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.67 0 [] hAPP(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).
% 5.58/5.67 0 [] hAPP(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=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.67 0 [] hAPP(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!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] hAPP(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!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))).
% 5.58/5.67 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))).
% 5.58/5.67 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2=hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,$f27(V_n_2,V_m_2))).
% 5.58/5.67 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2!=hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)| -c_Finite__Set_Ofinite(T_b,V_B_2)|c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_b,V_B_2)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 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)).
% 5.58/5.67 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).
% 5.58/5.67 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)).
% 5.58/5.67 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).
% 5.58/5.67 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)).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 0 [] c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(V_nat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)))=c_Groups_Ozero__class_Ozero(T_a).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)))=c_Groups_Oplus__class_Oplus(T_a,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_n_2)),hAPP(V_f_2,V_n_2)).
% 5.58/5.67 0 [] c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_a)| -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,V_n_2,V_p_2)|c_Groups_Oplus__class_Oplus(T_a,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_n_2)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2,V_p_2)))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_p_2)).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(T_a)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_n_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(V_f_2,V_m_2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_b)|c_Finite__Set_Ofinite(T_a,V_A_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,V_A_2)=c_Groups_Ozero__class_Ozero(T_b).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_b)|c_Finite__Set_Ofinite(T_a,V_A_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,V_A_2)=c_Groups_Ozero__class_Ozero(T_b).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_Fa_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_Fa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_member(T_a,B_x,V_Fa_2)|hAPP(V_f_2,B_x)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_Fa_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_Fa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_member(T_a,$f28(V_f_2,V_Fa_2,T_a),V_Fa_2).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_Fa_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_Fa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(V_f_2,$f28(V_f_2,V_Fa_2,T_a))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_member(T_a,$f29(V_f_2,V_A_2,T_a),V_A_2).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(V_f_2,$f29(V_f_2,V_A_2,T_a))=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))| -c_member(T_a,B_xa,V_A_2)|$f29(V_f_2,V_A_2,T_a)=B_xa|hAPP(V_f_2,B_xa)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))| -c_member(T_a,B_x,V_A_2)|hAPP(V_f_2,B_x)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_member(T_a,$f30(V_f_2,V_A_2,T_a,B_x),V_A_2).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))| -c_member(T_a,B_x,V_A_2)|hAPP(V_f_2,B_x)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B_x!=$f30(V_f_2,V_A_2,T_a,B_x).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))| -c_member(T_a,B_x,V_A_2)|hAPP(V_f_2,B_x)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(V_f_2,$f30(V_f_2,V_A_2,T_a,B_x))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(T_a).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(T_a).
% 5.58/5.67 0 [] c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_nat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,V_nat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_b)| -class_Groups_Oordered__cancel__ab__semigroup__add(T_b)| -c_Finite__Set_Ofinite(T_a,V_A_2)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|c_member(T_a,$f31(V_g_2,V_f_2,V_A_2,T_a,T_b),V_A_2)|c_Orderings_Oord__class_Oless(T_b,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,V_A_2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,V_A_2)).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_b)| -class_Groups_Oordered__cancel__ab__semigroup__add(T_b)| -c_Finite__Set_Ofinite(T_a,V_A_2)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))| -c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,$f31(V_g_2,V_f_2,V_A_2,T_a,T_b)),hAPP(V_g_2,$f31(V_g_2,V_f_2,V_A_2,T_a,T_b)))|c_Orderings_Oord__class_Oless(T_b,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,V_A_2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,V_A_2)).
% 5.58/5.67 0 [] c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n)=V_n.
% 5.58/5.67 0 [] c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2)!=hAPP(c_Nat_OSuc,V_n_2)|c_member(T_a,$f32(V_n_2,V_A_2,V_f_2,T_a),V_A_2).
% 5.58/5.67 0 [] c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2)!=hAPP(c_Nat_OSuc,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(V_f_2,$f32(V_n_2,V_A_2,V_f_2,T_a))).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_c)| -c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)|V_B_2!=c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)|c_member(T_a,$f33(V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c),V_A_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c,V_h_2,V_B_2)=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c,V_g_2,V_A_2).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_c)| -c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)|V_B_2!=c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)|hAPP(V_g_2,$f33(V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c))!=hAPP(V_h_2,hAPP(V_f_2,$f33(V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c)))|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c,V_h_2,V_B_2)=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c,V_g_2,V_A_2).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_b)| -class_Orderings_Oord(T_a)|V_a_2!=V_c_2|V_b_2!=V_d_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,$f34(V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_a,T_b))|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2)).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_b)| -class_Orderings_Oord(T_a)|V_a_2!=V_c_2|V_b_2!=V_d_2|c_Orderings_Oord__class_Oless(T_a,$f34(V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_a,T_b),V_d_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2)).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_b)| -class_Orderings_Oord(T_a)|V_a_2!=V_c_2|V_b_2!=V_d_2|hAPP(V_f_2,$f34(V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_a,T_b))!=hAPP(V_g_2,$f34(V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_a,T_b))|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2)).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),V_m_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)))=c_Groups_Ozero__class_Ozero(T_a).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),V_m_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)))=c_Groups_Oplus__class_Oplus(T_a,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))).
% 5.58/5.67 0 [] c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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)).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 0 [] c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2,hAPP(c_Nat_OSuc,V_u_2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2).
% 5.58/5.67 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,V_n_2)| -hBOOL(hAPP(V_P_2,B_m))|c_member(tc_Nat_Onat,$f35(V_P_2,V_n_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 5.58/5.67 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,V_n_2)| -hBOOL(hAPP(V_P_2,B_m))|hBOOL(hAPP(V_P_2,$f35(V_P_2,V_n_2))).
% 5.58/5.67 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f36(V_P_2,V_n_2),V_n_2)| -c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))| -hBOOL(hAPP(V_P_2,B_x)).
% 5.58/5.67 0 [] hBOOL(hAPP(V_P_2,$f36(V_P_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_P_2,B_x)).
% 5.58/5.67 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f37(V_P_2,V_n_2),V_n_2)| -c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))|hBOOL(hAPP(V_P_2,B_x)).
% 5.58/5.67 0 [] -hBOOL(hAPP(V_P_2,$f37(V_P_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_P_2,B_x)).
% 5.58/5.67 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,V_n_2)|hBOOL(hAPP(V_P_2,B_m))|c_member(tc_Nat_Onat,$f38(V_P_2,V_n_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 5.58/5.67 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_m,V_n_2)|hBOOL(hAPP(V_P_2,B_m))| -hBOOL(hAPP(V_P_2,$f38(V_P_2,V_n_2))).
% 5.58/5.67 0 [] c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)).
% 5.58/5.67 0 [] hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 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).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))=c_Groups_Oplus__class_Oplus(T_a,hAPP(V_f_2,V_m_2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_p_2)))=c_Groups_Oplus__class_Oplus(T_a,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_p_2)))).
% 5.58/5.67 0 [] c_HOL_Obool_Obool__size(c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 5.58/5.67 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))).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a).
% 5.58/5.67 0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a).
% 5.58/5.67 0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.67 0 [] hAPP(c_Nat_OSuc,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n).
% 5.58/5.67 0 [] hAPP(c_Nat_OSuc,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 5.58/5.67 0 [] -class_Groups_Oone(T_a)|c_Groups_Oone__class_Oone(T_a)!=V_x_2|V_x_2=c_Groups_Oone__class_Oone(T_a).
% 5.58/5.67 0 [] -class_Groups_Oone(T_a)|c_Groups_Oone__class_Oone(T_a)=V_x_2|V_x_2!=c_Groups_Oone__class_Oone(T_a).
% 5.58/5.67 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))).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_member(T_a,$f39(V_f_2,V_A_2,T_a),V_A_2).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(V_f_2,$f39(V_f_2,V_A_2,T_a))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)| -c_member(T_a,B_xa,V_A_2)|$f39(V_f_2,V_A_2,T_a)=B_xa|hAPP(V_f_2,B_xa)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)| -c_member(T_a,B_x,V_A_2)|hAPP(V_f_2,B_x)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_member(T_a,$f40(V_f_2,V_A_2,T_a,B_x),V_A_2).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)| -c_member(T_a,B_x,V_A_2)|hAPP(V_f_2,B_x)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B_x!=$f40(V_f_2,V_A_2,T_a,B_x).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)| -c_member(T_a,B_x,V_A_2)|hAPP(V_f_2,B_x)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(V_f_2,$f40(V_f_2,V_A_2,T_a,B_x))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] c_HOL_Obool_Obool__size(c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f41(V_n_2,V_P_2),V_n_2).
% 5.58/5.67 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i,$f41(V_n_2,V_P_2))| -hBOOL(hAPP(V_P_2,B_i)).
% 5.58/5.67 0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))|hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,$f41(V_n_2,V_P_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 5.58/5.67 0 [] -class_Rings_Oring__1(T_a)|c_member(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Oring__1__class_OInts(T_a)).
% 5.58/5.67 0 [] -class_Rings_Oring__1(T_a)| -c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))| -c_member(T_a,V_b_2,c_Int_Oring__1__class_OInts(T_a))|c_member(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2),c_Int_Oring__1__class_OInts(T_a)).
% 5.58/5.67 0 [] -class_Rings_Oring__1(T_a)|c_member(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Oring__1__class_OInts(T_a)).
% 5.58/5.67 0 [] -class_Int_Oring__char__0(T_a)| -c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_a_2=c_Groups_Ozero__class_Ozero(T_a).
% 5.58/5.67 0 [] -class_Int_Oring__char__0(T_a)| -c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))|c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)=c_Groups_Ozero__class_Ozero(T_a)|V_a_2!=c_Groups_Ozero__class_Ozero(T_a).
% 5.58/5.67 0 [] -class_Int_Oring__char__0(T_a)| -c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2),V_a_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_member(T_a,$f42(V_A_2,T_a),V_A_2)|c_Finite__Set_Ocard(T_a,V_A_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Finite__Set_Ocard(T_a,V_A_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_member(T_a,V_x_2,V_A_2)|c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2)).
% 5.58/5.67 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).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_a_2,V_A_2)).
% 5.58/5.67 0 [] -c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)| -c_Finite__Set_Ofinite(T_b,V_A_2)|hAPP(V_Fa_2,c_Set_Oinsert(T_b,V_x_2,V_A_2))=hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_2,V_A_2)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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)).
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2),V_B_2)|c_member(T_a,V_x_2,V_B_2).
% 5.58/5.67 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_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).
% 5.58/5.67 0 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2),V_B_2)| -c_member(T_a,V_x_2,V_B_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 5.58/5.67 0 [] c_member(T_a,V_x_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_x_2,V_B_2))|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 5.58/5.67 0 [] c_member(T_a,V_x_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_x_2,V_B_2))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2).
% 5.58/5.67 0 [] -c_member(T_a,V_x_2,V_A_2)|c_Set_Oinsert(T_b,hAPP(V_f_2,V_x_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))=c_Set_Oimage(T_a,T_b,V_f_2,V_A_2).
% 5.58/5.67 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_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_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))).
% 5.58/5.67 0 [] c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oinsert(T_b,V_a_2,V_B_2))=c_Set_Oinsert(T_a,hAPP(V_f_2,V_a_2),c_Set_Oimage(T_b,T_a,V_f_2,V_B_2)).
% 5.58/5.67 0 [] c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_x_2,V_A_2))=c_Set_Oinsert(T_a,V_x_2,V_A_2).
% 5.58/5.67 0 [] c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_y_2,V_A_2))=c_Set_Oinsert(T_a,V_y_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)).
% 5.58/5.67 0 [] -hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2))|V_y_2=V_x_2|hBOOL(hAPP(V_A_2,V_x_2)).
% 5.58/5.67 0 [] hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2))|V_y_2!=V_x_2.
% 5.58/5.67 0 [] hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2))| -hBOOL(hAPP(V_A_2,V_x_2)).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_a_2,V_A_2))|c_Finite__Set_Ofinite(T_a,V_A_2).
% 5.58/5.67 0 [] c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_a_2,V_A_2))| -c_Finite__Set_Ofinite(T_a,V_A_2).
% 5.58/5.67 0 [] c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)).
% 5.58/5.67 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).
% 5.58/5.67 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.
% 5.58/5.67 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).
% 5.58/5.67 0 [] c_member(T_a,V_x_2,V_A_2)|c_member(T_a,V_x_2,V_B_2)|c_Set_Oinsert(T_a,V_x_2,V_A_2)!=c_Set_Oinsert(T_a,V_x_2,V_B_2)|V_A_2=V_B_2.
% 5.58/5.67 0 [] c_member(T_a,V_x_2,V_A_2)|c_member(T_a,V_x_2,V_B_2)|c_Set_Oinsert(T_a,V_x_2,V_A_2)=c_Set_Oinsert(T_a,V_x_2,V_B_2)|V_A_2!=V_B_2.
% 5.58/5.67 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)).
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 0 [] c_Set_Oinsert(T_a,V_a_2,V_A_2)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 5.58/5.67 0 [] c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))!=c_Set_Oinsert(T_a,V_a_2,V_A_2).
% 5.58/5.67 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))).
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 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.
% 5.58/5.67 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))).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2))).
% 5.58/5.67 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))|c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))=c_Set_Oinsert(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)).
% 5.58/5.67 0 [] c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,hAPP(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))).
% 5.58/5.67 0 [] -c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)| -c_Finite__Set_Ofinite(T_a,V_A_2)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|hAPP(V_Fa_2,c_Set_Oinsert(T_a,V_x_2,V_A_2))=hAPP(hAPP(V_f_2,V_x_2),hAPP(V_Fa_2,V_A_2)).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_b)| -c_Finite__Set_Ofinite(T_a,V_A_2)|c_member(T_a,V_x_2,V_A_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,c_Set_Oinsert(T_a,V_x_2,V_A_2))=c_Groups_Oplus__class_Oplus(T_b,hAPP(V_g_2,V_x_2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,V_A_2)).
% 5.58/5.67 0 [] -class_Groups_Ocomm__monoid__add(T_b)| -c_Finite__Set_Ofinite(T_a,V_Fa_2)|c_member(T_a,V_a_2,V_Fa_2)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,c_Set_Oinsert(T_a,V_a_2,V_Fa_2))=c_Groups_Oplus__class_Oplus(T_b,hAPP(V_f_2,V_a_2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,V_Fa_2)).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_member(T_a,V_x_2,V_A_2)|c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2))=hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(T_a,V_A_2)).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)| -c_member(T_a,V_x_2,V_A_2)|c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2))=c_Finite__Set_Ocard(T_a,V_A_2).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)|c_member(T_a,V_x_2,V_A_2)|c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2))=hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(T_a,V_A_2)).
% 5.58/5.67 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,hAPP(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)).
% 5.58/5.67 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,hAPP(c_Nat_OSuc,V_n_2))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)).
% 5.58/5.67 0 [] c_Set_Othe__elem(T_a,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))=V_x_2.
% 5.58/5.67 0 [] c_Finite__Set_Ocard(T_a,V_A_2)!=hAPP(c_Nat_OSuc,V_k_2)|V_A_2=c_Set_Oinsert(T_a,$f44(V_k_2,V_A_2,T_a),$f43(V_k_2,V_A_2,T_a)).
% 5.58/5.67 0 [] c_Finite__Set_Ocard(T_a,V_A_2)!=hAPP(c_Nat_OSuc,V_k_2)| -c_member(T_a,$f44(V_k_2,V_A_2,T_a),$f43(V_k_2,V_A_2,T_a)).
% 5.58/5.67 0 [] c_Finite__Set_Ocard(T_a,V_A_2)!=hAPP(c_Nat_OSuc,V_k_2)|c_Finite__Set_Ocard(T_a,$f43(V_k_2,V_A_2,T_a))=V_k_2.
% 5.58/5.67 0 [] c_Finite__Set_Ocard(T_a,V_A_2)!=hAPP(c_Nat_OSuc,V_k_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|$f43(V_k_2,V_A_2,T_a)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 5.58/5.67 0 [] c_Finite__Set_Ocard(T_a,V_A_2)=hAPP(c_Nat_OSuc,V_k_2)|V_A_2!=c_Set_Oinsert(T_a,B_b,B_B)|c_member(T_a,B_b,B_B)|c_Finite__Set_Ocard(T_a,B_B)!=V_k_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] c_Finite__Set_Ocard(T_a,V_A_2)=hAPP(c_Nat_OSuc,V_k_2)|V_A_2!=c_Set_Oinsert(T_a,B_b,B_B)|c_member(T_a,B_b,B_B)|c_Finite__Set_Ocard(T_a,B_B)!=V_k_2|B_B!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)).
% 5.58/5.67 0 [] -c_Finite__Set_Ofolding__one(T_a,V_f_2,V_Fa_2)| -c_Finite__Set_Ofinite(T_a,V_A_2)|c_member(T_a,V_x_2,V_A_2)|V_A_2=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))|hAPP(V_Fa_2,c_Set_Oinsert(T_a,V_x_2,V_A_2))=hAPP(hAPP(V_f_2,V_x_2),hAPP(V_Fa_2,V_A_2)).
% 5.58/5.67 0 [] -c_Finite__Set_Ofinite(T_a,V_A_2)| -c_member(T_a,V_x_2,V_A_2)|c_Finite__Set_Ocard(T_a,V_A_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))).
% 5.58/5.67 0 [] -class_Orderings_Opreorder(T_1)|class_Orderings_Opreorder(tc_fun(T_2,T_1)).
% 5.58/5.67 0 [] -class_Finite__Set_Ofinite(T_2)| -class_Finite__Set_Ofinite(T_1)|class_Finite__Set_Ofinite(tc_fun(T_2,T_1)).
% 5.58/5.67 0 [] -class_Orderings_Oorder(T_1)|class_Orderings_Oorder(tc_fun(T_2,T_1)).
% 5.58/5.67 0 [] -class_Orderings_Otop(T_1)|class_Orderings_Otop(tc_fun(T_2,T_1)).
% 5.58/5.67 0 [] -class_Orderings_Oord(T_1)|class_Orderings_Oord(tc_fun(T_2,T_1)).
% 5.58/5.67 0 [] -class_Orderings_Obot(T_1)|class_Orderings_Obot(tc_fun(T_2,T_1)).
% 5.58/5.67 0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Orderings_Opreorder(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Orderings_Olinorder(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Groups_Omonoid__add(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Orderings_Oorder(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Orderings_Oord(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Orderings_Obot(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Groups_Ozero(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Groups_Oone(tc_Nat_Onat).
% 5.58/5.67 0 [] class_Orderings_Opreorder(tc_HOL_Obool).
% 5.58/5.67 0 [] class_Finite__Set_Ofinite(tc_HOL_Obool).
% 5.58/5.67 0 [] class_Orderings_Oorder(tc_HOL_Obool).
% 5.58/5.67 0 [] class_Orderings_Otop(tc_HOL_Obool).
% 5.58/5.67 0 [] class_Orderings_Oord(tc_HOL_Obool).
% 5.58/5.67 0 [] class_Orderings_Obot(tc_HOL_Obool).
% 5.58/5.67 0 [] -class_Finite__Set_Ofinite(T_2)| -class_Finite__Set_Ofinite(T_1)|class_Finite__Set_Ofinite(tc_sum(T_2,T_1)).
% 5.58/5.67 0 [] -class_Finite__Set_Ofinite(T_1)|class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)).
% 5.58/5.67 0 [] -class_Finite__Set_Ofinite(T_2)| -class_Finite__Set_Ofinite(T_1)|class_Finite__Set_Ofinite(tc_prod(T_2,T_1)).
% 5.58/5.67 0 [] class_Finite__Set_Ofinite(tc_Product__Type_Ounit).
% 5.58/5.67 0 [] -hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2))|V_x_2=V_y_2.
% 5.58/5.67 0 [] V_x_2!=V_y_2|hBOOL(hAPP(c_fe_qual(V_x_2),V_y_2)).
% 5.58/5.67 0 [] -hBOOL(c_fFalse).
% 5.58/5.67 0 [] hBOOL(c_fTrue).
% 5.58/5.67 0 [] -c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))|c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))!=c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))|v_thesis____.
% 5.58/5.67 0 [] -v_thesis____.
% 5.58/5.67 end_of_list.
% 5.58/5.67
% 5.58/5.67 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 5.58/5.67
% 5.58/5.67 This ia a non-Horn set with equality. The strategy will be
% 5.58/5.67 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 5.58/5.67 deletion, with positive clauses in sos and nonpositive
% 5.58/5.67 clauses in usable.
% 5.58/5.67
% 5.58/5.67 dependent: set(knuth_bendix).
% 5.58/5.67 dependent: set(anl_eq).
% 5.58/5.67 dependent: set(para_from).
% 5.58/5.67 dependent: set(para_into).
% 5.58/5.67 dependent: clear(para_from_right).
% 5.58/5.67 dependent: clear(para_into_right).
% 5.58/5.67 dependent: set(para_from_vars).
% 5.58/5.67 dependent: set(eq_units_both_ways).
% 5.58/5.67 dependent: set(dynamic_demod_all).
% 5.58/5.67 dependent: set(dynamic_demod).
% 5.58/5.67 dependent: set(order_eq).
% 5.58/5.67 dependent: set(back_demod).
% 5.58/5.67 dependent: set(lrpo).
% 5.58/5.67 dependent: set(hyper_res).
% 5.58/5.67 dependent: set(unit_deletion).
% 5.58/5.67 dependent: set(factor).
% 5.58/5.67
% 5.58/5.67 ------------> process usable:
% 5.58/5.67 ** KEPT (pick-wt=14): 1 [] hAPP(A,$f1(B,A))!=hAPP(B,$f1(B,A))|A=B.
% 5.58/5.67 ** KEPT (pick-wt=16): 2 [] -c_Fun_Oinj__on(A,B,C,D)|c_Finite__Set_Ocard(B,c_Set_Oimage(A,B,C,D))=c_Finite__Set_Ocard(A,D).
% 5.58/5.67 ** KEPT (pick-wt=22): 3 [] -c_Fun_Oinj__on(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))|c_Set_Oimage(A,B,C,D)!=c_Set_Oimage(A,B,C,E)|D=E.
% 5.58/5.67 ** KEPT (pick-wt=22): 4 [] -c_Fun_Oinj__on(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))|c_Set_Oimage(A,B,C,D)=c_Set_Oimage(A,B,C,E)|D!=E.
% 5.58/5.67 ** KEPT (pick-wt=18): 5 [] -c_Fun_Oinj__on(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))|hAPP(C,D)!=hAPP(C,E)|D=E.
% 5.58/5.67 ** KEPT (pick-wt=18): 6 [] -c_Fun_Oinj__on(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))|hAPP(C,D)=hAPP(C,E)|D!=E.
% 5.58/5.67 Following clause subsumed by 5 during input processing: 0 [] -c_Fun_Oinj__on(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))|hAPP(C,D)!=hAPP(C,E)|D=E.
% 5.58/5.67 ** KEPT (pick-wt=11): 7 [] -class_Orderings_Otop(A)|hAPP(c_Orderings_Otop__class_Otop(tc_fun(B,A)),C)=c_Orderings_Otop__class_Otop(A).
% 5.58/5.67 ** KEPT (pick-wt=23): 8 [] -c_Fun_Oinj__on(A,B,C,D)| -c_member(A,E,D)| -c_member(A,F,D)|hAPP(C,E)!=hAPP(C,F)|E=F.
% 5.58/5.67 ** KEPT (pick-wt=16): 9 [] c_Fun_Oinj__on(A,B,C,D)|$f3(D,C,B,A)!=$f2(D,C,B,A).
% 5.58/5.67 ** KEPT (pick-wt=10): 10 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 5.58/5.67 ** KEPT (pick-wt=10): 11 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 5.58/5.67 ** KEPT (pick-wt=10): 12 [] -c_Finite__Set_Ofinite(A,B)|c_Finite__Set_Ofinite(C,c_Set_Oimage(A,C,D,B)).
% 5.58/5.67 ** KEPT (pick-wt=5): 13 [] -class_Finite__Set_Ofinite(A)|c_Finite__Set_Ofinite(A,B).
% 5.58/5.67 ** KEPT (pick-wt=14): 14 [] -c_Finite__Set_Ofinite(tc_Option_Ooption(A),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(A),tc_HOL_Obool)))|c_Finite__Set_Ofinite(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))).
% 5.58/5.67 ** KEPT (pick-wt=14): 15 [] c_Finite__Set_Ofinite(tc_Option_Ooption(A),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(A),tc_HOL_Obool)))| -c_Finite__Set_Ofinite(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))).
% 5.58/5.67 ** KEPT (pick-wt=16): 16 [] -c_Finite__Set_Ofinite(tc_sum(A,B),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(A,B),tc_HOL_Obool)))|c_Finite__Set_Ofinite(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))).
% 5.58/5.67 ** KEPT (pick-wt=16): 17 [] -c_Finite__Set_Ofinite(tc_sum(A,B),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(A,B),tc_HOL_Obool)))|c_Finite__Set_Ofinite(B,c_Orderings_Otop__class_Otop(tc_fun(B,tc_HOL_Obool))).
% 5.58/5.67 ** KEPT (pick-wt=22): 18 [] c_Finite__Set_Ofinite(tc_sum(A,B),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(A,B),tc_HOL_Obool)))| -c_Finite__Set_Ofinite(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))| -c_Finite__Set_Ofinite(B,c_Orderings_Otop__class_Otop(tc_fun(B,tc_HOL_Obool))).
% 5.58/5.67 Following clause subsumed by 13 during input processing: 0 [] -class_Finite__Set_Ofinite(A)|c_Finite__Set_Ofinite(A,B).
% 5.58/5.67 ** KEPT (pick-wt=16): 19 [] -c_Finite__Set_Ofinite(tc_fun(A,B),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(A,B),tc_HOL_Obool)))|c_Finite__Set_Ofinite(B,c_Orderings_Otop__class_Otop(tc_fun(B,tc_HOL_Obool))).
% 5.58/5.67 ** KEPT (pick-wt=22): 20 [] -c_Finite__Set_Ofinite(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))| -c_Finite__Set_Ofinite(B,c_Orderings_Otop__class_Otop(tc_fun(B,tc_HOL_Obool)))|c_Finite__Set_Ofinite(tc_prod(A,B),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(A,B),tc_HOL_Obool))).
% 5.58/5.67 Following clause subsumed by 13 during input processing: 0 [] -class_Finite__Set_Ofinite(A)|c_Finite__Set_Ofinite(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))).
% 5.58/5.67 ** KEPT (pick-wt=15): 21 [] -c_Finite__Set_Ofinite(A,c_Set_Oimage(B,A,C,D))| -c_Fun_Oinj__on(B,A,C,D)|c_Finite__Set_Ofinite(B,D).
% 5.58/5.67 ** KEPT (pick-wt=22): 22 [] -c_Finite__Set_Ofinite(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))|c_Finite__Set_Ocard(A,B)!=c_Finite__Set_Ocard(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))|B=c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)).
% 5.58/5.67 ** KEPT (pick-wt=27): 23 [] -c_Finite__Set_Ofinite(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))|c_Set_Oimage(A,A,B,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))!=c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))|c_Fun_Oinj__on(A,A,B,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))).
% 5.58/5.67 ** KEPT (pick-wt=27): 24 [] -c_Finite__Set_Ofinite(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))| -c_Fun_Oinj__on(A,A,B,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))|c_Set_Oimage(A,A,B,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))=c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)).
% 5.58/5.67 ** KEPT (pick-wt=19): 25 [] -c_Finite__Set_Ofinite(A,B)|c_Finite__Set_Ocard(C,c_Set_Oimage(A,C,D,B))!=c_Finite__Set_Ocard(A,B)|c_Fun_Oinj__on(A,C,D,B).
% 5.58/5.67 Following clause subsumed by 2 during input processing: 0 [] -c_Finite__Set_Ofinite(A,B)| -c_Fun_Oinj__on(A,C,D,B)|c_Finite__Set_Ocard(C,c_Set_Oimage(A,C,D,B))=c_Finite__Set_Ocard(A,B).
% 5.58/5.67 Following clause subsumed by 25 during input processing: 0 [] -c_Finite__Set_Ofinite(A,B)|c_Fun_Oinj__on(A,C,D,B)|c_Finite__Set_Ocard(C,c_Set_Oimage(A,C,D,B))!=c_Finite__Set_Ocard(A,B).
% 5.58/5.67 ** KEPT (pick-wt=43): 26 [] -c_Fun_Oinj__on(A,B,C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,tc_HOL_Obool),c_Set_Oimage(A,B,C,D),E)| -c_Fun_Oinj__on(B,A,F,E)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Set_Oimage(B,A,F,E),D)| -c_Finite__Set_Ofinite(A,D)| -c_Finite__Set_Ofinite(B,E)|c_Finite__Set_Ocard(A,D)=c_Finite__Set_Ocard(B,E).
% 5.58/5.67 ** KEPT (pick-wt=16): 27 [] -c_Finite__Set_Ofinite(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))).
% 5.58/5.67 ** KEPT (pick-wt=20): 28 [] -c_Fun_Oinj__on(A,B,C,D)|c_Set_Oimage(B,A,c_Fun_Othe__inv__into(A,B,D,C),c_Set_Oimage(A,B,C,D))=D.
% 5.58/5.67 ** KEPT (pick-wt=18): 29 [] -c_Fun_Oinj__on(A,B,C,D)|c_Fun_Oinj__on(B,A,c_Fun_Othe__inv__into(A,B,D,C),c_Set_Oimage(A,B,C,D)).
% 5.58/5.67 ** KEPT (pick-wt=22): 30 [] -c_Fun_Oinj__on(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))|hAPP(c_Fun_Othe__inv__into(A,B,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),C),hAPP(C,D))=D.
% 5.58/5.67 ** KEPT (pick-wt=15): 31 [] c_Finite__Set_Ocard(A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))| -c_Finite__Set_Ofinite(A,B).
% 5.58/5.67 ** KEPT (pick-wt=12): 32 [] c_Finite__Set_Ocard(A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 5.58/5.67 ** KEPT (pick-wt=17): 33 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(A,c_Set_Oimage(B,A,C,D)),c_Finite__Set_Ocard(B,D))| -c_Fun_Oinj__on(B,A,C,D).
% 5.58/5.67 ** KEPT (pick-wt=28): 34 [] -c_Fun_Oinj__on(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,tc_HOL_Obool),c_Set_Oimage(A,B,C,D),c_Set_Oimage(A,B,C,E))|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),D,E).
% 5.58/5.67 ** KEPT (pick-wt=28): 35 [] -c_Fun_Oinj__on(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,tc_HOL_Obool),c_Set_Oimage(A,B,C,D),c_Set_Oimage(A,B,C,E))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),D,E).
% 5.58/5.67 ** KEPT (pick-wt=22): 36 [] -c_Fun_Oinj__on(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))| -c_member(B,hAPP(C,D),c_Set_Oimage(A,B,C,E))|c_member(A,D,E).
% 5.58/5.68 ** KEPT (pick-wt=22): 37 [] -c_Fun_Oinj__on(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))|c_member(B,hAPP(C,D),c_Set_Oimage(A,B,C,E))| -c_member(A,D,E).
% 5.58/5.68 ** KEPT (pick-wt=28): 39 [copy,38,flip.3] -c_Fun_Oinj__on(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))| -c_member(B,D,c_Set_Oimage(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))))|hAPP(C,$f4(D,C,B,A))=D.
% 5.58/5.68 ** KEPT (pick-wt=31): 40 [] -c_Fun_Oinj__on(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))| -c_member(B,D,c_Set_Oimage(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))))|D!=hAPP(C,E)|E=$f4(D,C,B,A).
% 5.58/5.68 ** KEPT (pick-wt=34): 42 [copy,41,flip.4] -c_Fun_Oinj__on(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))|c_member(B,D,c_Set_Oimage(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))))|D!=hAPP(C,E)|hAPP(C,$f5(D,C,B,A,E))=D.
% 5.58/5.68 ** KEPT (pick-wt=32): 43 [] -c_Fun_Oinj__on(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)))|c_member(B,D,c_Set_Oimage(A,B,C,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))))|D!=hAPP(C,E)|$f5(D,C,B,A,E)!=E.
% 5.58/5.68 ** KEPT (pick-wt=15): 44 [] -c_Finite__Set_Ofinite(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(C,c_Set_Oimage(A,C,D,B)),c_Finite__Set_Ocard(A,B)).
% 5.58/5.68 ** KEPT (pick-wt=6): 45 [] -class_Orderings_Opreorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,B).
% 5.58/5.68 ** KEPT (pick-wt=6): 46 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,B).
% 5.58/5.68 ** KEPT (pick-wt=7): 47 [] -class_Orderings_Obot(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Orderings_Obot__class_Obot(A),B).
% 5.58/5.68 ** KEPT (pick-wt=11): 48 [] -class_Orderings_Obot(A)|hAPP(c_Orderings_Obot__class_Obot(tc_fun(B,A)),C)=c_Orderings_Obot__class_Obot(A).
% 5.58/5.68 ** KEPT (pick-wt=10): 49 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 5.58/5.68 ** KEPT (pick-wt=10): 50 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 5.58/5.68 Following clause subsumed by 49 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).
% 5.58/5.68 Following clause subsumed by 50 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).
% 5.58/5.68 ** KEPT (pick-wt=13): 51 [] -class_Orderings_Olinorder(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 5.58/5.68 ** KEPT (pick-wt=9): 52 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,B,C).
% 5.58/5.68 ** KEPT (pick-wt=9): 53 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,B).
% 5.58/5.68 Following clause subsumed by 51 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.
% 5.58/5.68 ** KEPT (pick-wt=10): 54 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 5.58/5.68 Following clause subsumed by 52 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 5.58/5.68 ** KEPT (pick-wt=16): 55 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 5.58/5.68 ** KEPT (pick-wt=24): 56 [] -class_Orderings_Oord(A)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,$f6(D,C,B,A)),hAPP(D,$f6(D,C,B,A))).
% 5.58/5.68 Following clause subsumed by 49 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).
% 5.58/5.68 ** KEPT (pick-wt=10): 57 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 5.58/5.68 ** KEPT (pick-wt=10): 58 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 5.58/5.68 ** KEPT (pick-wt=9): 59 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 5.58/5.68 ** KEPT (pick-wt=13): 60 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C.
% 5.58/5.68 ** KEPT (pick-wt=10): 61 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 5.58/5.68 ** KEPT (pick-wt=10): 62 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 5.58/5.68 ** KEPT (pick-wt=14): 63 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=9): 64 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 5.58/5.68 ** KEPT (pick-wt=9): 65 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 5.58/5.68 ** KEPT (pick-wt=13): 66 [] -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).
% 5.58/5.68 Following clause subsumed by 60 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 5.58/5.68 Following clause subsumed by 58 during input processing: 0 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,B,C).
% 5.58/5.68 Following clause subsumed by 64 during input processing: 0 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C.
% 5.58/5.68 Following clause subsumed by 51 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).
% 5.58/5.68 ** KEPT (pick-wt=8): 67 [] -c_member(A,B,c_fe_qual(C))|B=C.
% 5.58/5.68 ** KEPT (pick-wt=8): 68 [] c_member(A,B,c_fe_qual(C))|B!=C.
% 5.58/5.68 Following clause subsumed by 49 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).
% 5.58/5.68 Following clause subsumed by 49 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).
% 5.58/5.68 Following clause subsumed by 51 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.
% 5.58/5.68 Following clause subsumed by 52 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.
% 5.58/5.68 ** KEPT (pick-wt=13): 69 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C.
% 5.58/5.68 ** KEPT (pick-wt=13): 70 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C.
% 5.58/5.68 Following clause subsumed by 60 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).
% 5.58/5.68 ** KEPT (pick-wt=13): 71 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|c_Orderings_Oord__class_Oless(A,C,B).
% 5.58/5.68 Following clause subsumed by 51 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).
% 5.58/5.68 ** KEPT (pick-wt=14): 72 [] -hBOOL(hAPP(A,B))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,D)|hBOOL(hAPP(D,B)).
% 5.58/5.68 Following clause subsumed by 59 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 5.58/5.68 ** KEPT (pick-wt=10): 73 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 5.58/5.68 Following clause subsumed by 50 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).
% 5.58/5.68 ** KEPT (pick-wt=9): 74 [] -class_Orderings_Opreorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 5.58/5.68 Following clause subsumed by 61 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).
% 5.58/5.68 Following clause subsumed by 73 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 5.58/5.68 Following clause subsumed by 69 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.
% 5.58/5.68 Following clause subsumed by 52 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.
% 5.58/5.68 Following clause subsumed by 55 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 5.58/5.68 Following clause subsumed by 59 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 5.58/5.68 ** KEPT (pick-wt=9): 75 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=B.
% 5.58/5.68 Following clause subsumed by 60 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 5.58/5.68 Following clause subsumed by 66 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.
% 5.58/5.68 Following clause subsumed by 64 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.
% 5.58/5.68 Following clause subsumed by 60 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,B,C).
% 5.58/5.68 Following clause subsumed by 71 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|C=B|c_Orderings_Oord__class_Oless(A,B,C).
% 5.58/5.68 Following clause subsumed by 72 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -hBOOL(hAPP(B,D))|hBOOL(hAPP(C,D)).
% 5.58/5.68 Following clause subsumed by 73 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 5.58/5.68 ** KEPT (pick-wt=10): 76 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 5.58/5.68 ** KEPT (pick-wt=13): 77 [] -class_Orderings_Oord(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 5.58/5.68 ** KEPT (pick-wt=13): 78 [] -class_Orderings_Oorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,D,C)|c_Orderings_Oord__class_Oless(A,D,B).
% 5.58/5.68 ** KEPT (pick-wt=13): 79 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=13): 80 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=13): 81 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=D|c_Orderings_Oord__class_Oless(A,B,D).
% 5.58/5.68 ** KEPT (pick-wt=13): 82 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=D|c_Orderings_Oord__class_Oless(A,D,C).
% 5.58/5.68 ** KEPT (pick-wt=14): 83 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=14): 84 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=14): 85 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=14): 86 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=13): 87 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=13): 88 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=14): 89 [] -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).
% 5.58/5.68 Following clause subsumed by 66 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.
% 5.58/5.68 ** KEPT (pick-wt=14): 90 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=14): 91 [] -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).
% 5.58/5.68 Following clause subsumed by 66 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.
% 5.58/5.68 ** KEPT (pick-wt=14): 92 [] -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).
% 5.58/5.68 Following clause subsumed by 73 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 5.58/5.68 Following clause subsumed by 55 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 5.58/5.68 Following clause subsumed by 57 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 5.58/5.68 Following clause subsumed by 51 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).
% 5.58/5.68 ** KEPT (pick-wt=23): 93 [] -c_Fun_Oinj__on(A,B,C,D)|hAPP(C,E)!=F| -c_member(A,E,D)|hAPP(c_Fun_Othe__inv__into(A,B,D,C),F)=E.
% 5.58/5.68 ** KEPT (pick-wt=20): 94 [] -c_Fun_Oinj__on(A,B,C,D)| -c_member(A,E,D)|hAPP(c_Fun_Othe__inv__into(A,B,D,C),hAPP(C,E))=E.
% 5.58/5.68 ** KEPT (pick-wt=29): 95 [] -c_Fun_Oinj__on(A,B,C,D)| -c_member(B,E,c_Set_Oimage(A,B,C,D))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),D,F)|c_member(A,hAPP(c_Fun_Othe__inv__into(A,B,D,C),E),F).
% 5.58/5.68 ** KEPT (pick-wt=20): 96 [] -c_Finite__Set_Ofinite(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(A,B),c_Finite__Set_Ocard(A,C))|C=B.
% 5.58/5.68 ** KEPT (pick-wt=17): 97 [] -c_Finite__Set_Ofinite(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(A,C),c_Finite__Set_Ocard(A,B)).
% 5.58/5.68 ** KEPT (pick-wt=12): 98 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Finite__Set_Ofinite(A,C)|c_Finite__Set_Ofinite(A,B).
% 5.58/5.68 Following clause subsumed by 98 during input processing: 0 [] -c_Finite__Set_Ofinite(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,B)|c_Finite__Set_Ofinite(A,C).
% 5.58/5.68 ** KEPT (pick-wt=7): 99 [] -class_Orderings_Otop(A)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Orderings_Otop__class_Otop(A)).
% 5.58/5.68 Following clause subsumed by 8 during input processing: 0 [] -c_Fun_Oinj__on(A,B,C,D)|E=F| -c_member(A,E,D)| -c_member(A,F,D)|hAPP(C,E)!=hAPP(C,F).
% 5.58/5.68 Following clause subsumed by 8 during input processing: 0 [] -c_Fun_Oinj__on(A,B,C,D)| -c_member(A,E,D)| -c_member(A,F,D)|hAPP(C,E)!=hAPP(C,F)|E=F.
% 5.58/5.68 ** KEPT (pick-wt=23): 100 [] -c_Fun_Oinj__on(A,B,C,D)| -c_member(A,E,D)| -c_member(A,F,D)|hAPP(C,E)=hAPP(C,F)|E!=F.
% 5.58/5.68 Following clause subsumed by 8 during input processing: 0 [] -c_Fun_Oinj__on(A,B,C,D)|hAPP(C,E)!=hAPP(C,F)| -c_member(A,E,D)| -c_member(A,F,D)|E=F.
% 5.58/5.68 ** KEPT (pick-wt=16): 101 [] -c_Fun_Oinj__on(A,B,C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),E,D)|c_Fun_Oinj__on(A,B,C,E).
% 5.58/5.68 ** KEPT (pick-wt=24): 102 [] -c_Fun_Oinj__on(A,B,C,D)| -c_member(B,E,c_Set_Oimage(A,B,C,D))|hAPP(C,hAPP(c_Fun_Othe__inv__into(A,B,D,C),E))=E.
% 5.58/5.68 ** KEPT (pick-wt=13): 103 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(A,B))|B!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 5.58/5.68 ** KEPT (pick-wt=10): 104 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(A,B))|c_Finite__Set_Ofinite(A,B).
% 5.58/5.68 ** KEPT (pick-wt=16): 105 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(A,B))|B=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))| -c_Finite__Set_Ofinite(A,B).
% 5.58/5.68 ** KEPT (pick-wt=26): 106 [] -c_Fun_Oinj__on(A,B,C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,tc_HOL_Obool),c_Set_Oimage(A,B,C,D),E)| -c_Finite__Set_Ofinite(B,E)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(A,D),c_Finite__Set_Ocard(B,E)).
% 5.58/5.68 ** KEPT (pick-wt=16): 107 [] -c_Finite__Set_Ofinite(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),D,c_Set_Oimage(A,C,E,B))|c_Finite__Set_Ofinite(C,D).
% 5.58/5.68 Following clause subsumed by 104 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(A,B))|c_Finite__Set_Ofinite(A,B).
% 5.58/5.68 ** KEPT (pick-wt=18): 108 [] -c_Finite__Set_Ofinite(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Set_Oimage(A,A,C,B))|c_Fun_Oinj__on(A,A,C,B).
% 5.58/5.68 ** KEPT (pick-wt=25): 109 [] -c_Finite__Set_Ofinite(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Set_Oimage(A,A,C,B),B)| -c_Fun_Oinj__on(A,A,C,B)|c_Set_Oimage(A,A,C,B)=B.
% 5.58/5.68 Following clause subsumed by 106 during input processing: 0 [] -c_Finite__Set_Ofinite(A,B)| -c_Finite__Set_Ofinite(C,D)| -c_Fun_Oinj__on(A,C,E,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),c_Set_Oimage(A,C,E,B),D)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(A,B),c_Finite__Set_Ocard(C,D)).
% 5.58/5.68 ** KEPT (pick-wt=23): 110 [] -c_Finite__Set_Ofinite(A,B)| -c_Finite__Set_Ofinite(C,D)|c_Fun_Oinj__on(A,C,$f7(D,C,B,A),B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(A,B),c_Finite__Set_Ocard(C,D)).
% 5.58/5.68 ** KEPT (pick-wt=28): 111 [] -c_Finite__Set_Ofinite(A,B)| -c_Finite__Set_Ofinite(C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),c_Set_Oimage(A,C,$f7(D,C,B,A),B),D)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(A,B),c_Finite__Set_Ocard(C,D)).
% 5.58/5.68 ** KEPT (pick-wt=5): 112 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.68 ** KEPT (pick-wt=17): 113 [] A!=hAPP(B,C)| -c_member(D,C,E)|c_member(F,A,c_Set_Oimage(D,F,B,E)).
% 5.58/5.68 ** KEPT (pick-wt=14): 114 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=7): 115 [] -c_member(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 5.58/5.68 ** KEPT (pick-wt=32): 116 [] A=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))| -c_Fun_Oinj__on(B,C,D,A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),c_Set_Oimage(B,C,D,A),E)|c_Set_Oimage(C,B,$f8(E,C,B,A),E)=A.
% 5.58/5.68 ** KEPT (pick-wt=22): 117 [] A=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))|c_Fun_Oinj__on(B,C,$f9(D,C,B,A),A)|c_Set_Oimage(C,B,E,D)!=A.
% 5.58/5.68 ** KEPT (pick-wt=27): 118 [] A=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),c_Set_Oimage(B,C,$f9(D,C,B,A),A),D)|c_Set_Oimage(C,B,E,D)!=A.
% 5.58/5.68 ** KEPT (pick-wt=18): 119 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -hBOOL(hAPP(C,A))|c_member(tc_Nat_Onat,$f10(C,B),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)).
% 5.58/5.68 ** KEPT (pick-wt=14): 120 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -hBOOL(hAPP(C,A))|hBOOL(hAPP(C,$f10(C,B))).
% 5.58/5.68 ** KEPT (pick-wt=18): 121 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f11(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)).
% 5.58/5.68 ** KEPT (pick-wt=18): 122 [] hBOOL(hAPP(A,$f11(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)).
% 5.58/5.68 ** KEPT (pick-wt=11): 123 [] A!=B|c_member(C,D,A)| -c_member(C,D,B).
% 5.58/5.68 ** KEPT (pick-wt=11): 124 [] A!=B|c_member(C,D,B)| -c_member(C,D,A).
% 5.58/5.68 ** KEPT (pick-wt=15): 125 [] -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.
% 5.58/5.68 ** KEPT (pick-wt=14): 126 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)| -c_member(A,D,B)|c_member(A,D,C).
% 5.58/5.68 ** KEPT (pick-wt=9): 127 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 5.58/5.68 ** KEPT (pick-wt=12): 128 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=9): 129 [] -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,C)|B!=C.
% 5.58/5.68 ** KEPT (pick-wt=15): 130 [] 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.
% 5.58/5.68 Following clause subsumed by 130 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.
% 5.58/5.68 Following clause subsumed by 128 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).
% 5.58/5.68 ** KEPT (pick-wt=9): 131 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|B!=C.
% 5.58/5.68 Following clause subsumed by 128 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).
% 5.58/5.68 ** KEPT (pick-wt=18): 132 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=18): 133 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),C,D)|c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),B,D).
% 5.58/5.68 ** KEPT (pick-wt=14): 134 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=14): 135 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=20): 136 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=25): 137 [] -c_Fun_Oinj__on(A,B,C,D)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),E,D)|c_Orderings_Oord__class_Oless(tc_fun(B,tc_HOL_Obool),c_Set_Oimage(A,B,C,E),c_Set_Oimage(A,B,C,D)).
% 5.58/5.68 ** KEPT (pick-wt=17): 138 [] -c_Finite__Set_Ofinite(A,B)| -c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),C,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(A,C),c_Finite__Set_Ocard(A,B)).
% 5.58/5.68 ** KEPT (pick-wt=8): 139 [] -c_member(A,B,C)|hBOOL(hAPP(C,B)).
% 5.58/5.68 ** KEPT (pick-wt=8): 140 [] c_member(A,B,C)| -hBOOL(hAPP(C,B)).
% 5.58/5.68 Following clause subsumed by 124 during input processing: 0 [] A!=B| -c_member(C,D,A)|c_member(C,D,B).
% 5.58/5.68 Following clause subsumed by 123 during input processing: 0 [] A!=B|c_member(C,D,A)| -c_member(C,D,B).
% 5.58/5.68 ** KEPT (pick-wt=11): 141 [] A!=B| -c_member(C,A,D)|c_member(C,B,D).
% 5.58/5.68 ** KEPT (pick-wt=11): 142 [] A!=B|c_member(C,A,D)| -c_member(C,B,D).
% 5.58/5.68 Following clause subsumed by 142 during input processing: 0 [] A!=B| -c_member(C,B,D)|c_member(C,A,D).
% 5.58/5.68 ** KEPT (pick-wt=4): 143 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 5.58/5.68 ** KEPT (pick-wt=7): 144 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 5.58/5.68 ** KEPT (pick-wt=7): 145 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 5.58/5.68 Following clause subsumed by 143 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 5.58/5.68 Following clause subsumed by 145 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=A.
% 5.58/5.68 Following clause subsumed by 144 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 5.58/5.68 ** KEPT (pick-wt=12): 146 [] -c_Finite__Set_Ofinite(tc_Nat_Onat,A)| -c_member(tc_Nat_Onat,B,A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,$f12(A)).
% 5.58/5.68 ** KEPT (pick-wt=9): 147 [] c_Finite__Set_Ofinite(tc_Nat_Onat,A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f13(A,B),B).
% 5.58/5.68 Following clause subsumed by 131 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,B).
% 5.58/5.68 ** KEPT (pick-wt=9): 148 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),B,A).
% 5.58/5.68 Following clause subsumed by 125 during input processing: 0 [] A=B| -c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),B,A).
% 5.58/5.68 Following clause subsumed by 131 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,B).
% 5.58/5.68 Following clause subsumed by 148 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),B,A).
% 5.58/5.68 ** KEPT (pick-wt=18): 149 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,D).
% 5.58/5.68 Following clause subsumed by 131 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),A,B).
% 5.58/5.68 Following clause subsumed by 148 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),B,A).
% 5.58/5.68 ** KEPT (pick-wt=7): 150 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 5.58/5.68 ** KEPT (pick-wt=12): 151 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 5.58/5.68 ** KEPT (pick-wt=11): 152 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,A)|A=B.
% 5.58/5.68 ** KEPT (pick-wt=12): 153 [] -c_Finite__Set_Ofinite(tc_Nat_Onat,A)| -c_member(tc_Nat_Onat,B,A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,$f14(A)).
% 5.58/5.68 ** KEPT (pick-wt=9): 154 [] c_Finite__Set_Ofinite(tc_Nat_Onat,A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f15(A,B),B).
% 5.58/5.68 ** KEPT (pick-wt=23): 155 [] -c_Finite__Set_Ofinite(A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(A,C),c_Finite__Set_Ocard(A,B))|c_Orderings_Oord__class_Oless(tc_fun(A,tc_HOL_Obool),C,B).
% 5.58/5.68 ** KEPT (pick-wt=10): 156 [] -c_member(A,B,C)|C!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 5.58/5.68 Following clause subsumed by 156 during input processing: 0 [] -c_member(A,B,C)|C!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 5.58/5.68 Following clause subsumed by 115 during input processing: 0 [] -c_member(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 5.58/5.68 Following clause subsumed by 156 during input processing: 0 [] A!=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))| -c_member(B,C,A).
% 5.58/5.68 Following clause subsumed by 114 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_member(A,D,B)|c_member(A,D,C).
% 5.58/5.68 Following clause subsumed by 114 during input processing: 0 [] -c_member(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),C,D)|c_member(A,B,D).
% 5.58/5.68 Following clause subsumed by 114 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)| -c_member(A,D,B)|c_member(A,D,C).
% 5.58/5.68 Following clause subsumed by 113 during input processing: 0 [] -c_member(A,B,C)|D!=hAPP(E,B)|c_member(F,D,c_Set_Oimage(A,F,E,C)).
% 5.58/5.68 ** KEPT (pick-wt=14): 157 [] -c_member(A,B,C)|c_member(D,hAPP(E,B),c_Set_Oimage(A,D,E,C)).
% 5.58/5.68 ** KEPT (pick-wt=17): 158 [] -c_member(A,B,c_Set_Oimage(C,A,D,E))|c_member(C,$f18(E,D,C,B,A),E).
% 5.58/5.68 ** KEPT (pick-wt=18): 160 [copy,159,flip.2] -c_member(A,B,c_Set_Oimage(C,A,D,E))|hAPP(D,$f18(E,D,C,B,A))=B.
% 5.58/5.68 Following clause subsumed by 113 during input processing: 0 [] c_member(A,B,c_Set_Oimage(C,A,D,E))| -c_member(C,F,E)|B!=hAPP(D,F).
% 5.58/5.68 ** KEPT (pick-wt=15): 161 [] -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)).
% 5.58/5.68 Following clause subsumed by 131 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)).
% 5.58/5.68 ** KEPT (pick-wt=9): 162 [] c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 5.58/5.68 ** KEPT (pick-wt=16): 163 [] c_Set_Oimage(A,B,C,D)!=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))|D=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 5.58/5.68 ** KEPT (pick-wt=16): 164 [] c_Set_Oimage(A,B,C,D)=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))|D!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 5.58/5.68 ** KEPT (pick-wt=16): 165 [] c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))!=c_Set_Oimage(B,A,C,D)|D=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool)).
% 5.58/5.68 ** KEPT (pick-wt=16): 166 [] c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))=c_Set_Oimage(B,A,C,D)|D!=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool)).
% 5.58/5.68 ** KEPT (pick-wt=8): 167 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.68 Following clause subsumed by 112 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.68 Following clause subsumed by 145 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).
% 5.58/5.68 Following clause subsumed by 112 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.68 ** KEPT (pick-wt=20): 168 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,C)|c_Orderings_Oord__class_Oless__e_q(tc_fun(D,tc_HOL_Obool),c_Set_Oimage(A,D,E,B),c_Set_Oimage(A,D,E,C)).
% 5.58/5.68 ** KEPT (pick-wt=21): 169 [] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Set_Oimage(C,A,D,E))|c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),$f19(E,D,C,B,A),E).
% 5.58/5.68 ** KEPT (pick-wt=22): 171 [copy,170,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Set_Oimage(C,A,D,E))|c_Set_Oimage(C,A,D,$f19(E,D,C,B,A))=B.
% 5.58/5.68 ** KEPT (pick-wt=23): 172 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Set_Oimage(C,A,D,E))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(C,tc_HOL_Obool),F,E)|B!=c_Set_Oimage(C,A,D,F).
% 5.58/5.68 ** KEPT (pick-wt=9): 173 [] -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).
% 5.58/5.68 Following clause subsumed by 150 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).
% 5.58/5.68 ** KEPT (pick-wt=8): 174 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 5.58/5.68 Following clause subsumed by 144 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 5.58/5.68 ** KEPT (pick-wt=11): 175 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B.
% 5.58/5.68 Following clause subsumed by 175 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.
% 5.58/5.68 Following clause subsumed by 174 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).
% 5.58/5.68 Following clause subsumed by 150 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A!=B.
% 5.58/5.68 Following clause subsumed by 174 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).
% 5.58/5.68 Following clause subsumed by 175 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).
% 5.58/5.68 Following clause subsumed by 174 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).
% 5.58/5.68 Following clause subsumed by 150 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 5.58/5.68 ** KEPT (pick-wt=22): 176 [] -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.
% 5.58/5.68 ** KEPT (pick-wt=22): 177 [] -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.
% 5.58/5.68 Following clause subsumed by 177 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.
% 5.58/5.68 Following clause subsumed by 176 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.
% 5.58/5.68 ** KEPT (pick-wt=25): 178 [] -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.
% 5.58/5.68 ** KEPT (pick-wt=16): 179 [] A!=hAPP(B,C)|c_member(D,A,c_Set_Oimage(E,D,B,c_Orderings_Otop__class_Otop(tc_fun(E,tc_HOL_Obool)))).
% 5.58/5.68 ** KEPT (pick-wt=15): 180 [] -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)).
% 5.58/5.68 ** KEPT (pick-wt=15): 181 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=15): 182 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=15): 183 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=15): 184 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=22): 185 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=22): 186 [] -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).
% 5.58/5.68 ** KEPT (pick-wt=18): 187 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f20(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)).
% 5.58/5.68 ** KEPT (pick-wt=18): 188 [] -hBOOL(hAPP(A,$f20(A,B)))| -c_member(tc_Nat_Onat,C,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B))|hBOOL(hAPP(A,C)).
% 5.58/5.68 ** KEPT (pick-wt=18): 189 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|hBOOL(hAPP(C,A))|c_member(tc_Nat_Onat,$f21(C,B),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)).
% 5.58/5.69 ** KEPT (pick-wt=14): 190 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|hBOOL(hAPP(C,A))| -hBOOL(hAPP(C,$f21(C,B))).
% 5.58/5.69 ** KEPT (pick-wt=13): 191 [] -c_member(A,B,c_SetInterval_Oord_OatMost(A,C,D))|hBOOL(hAPP(hAPP(C,B),D)).
% 5.58/5.69 ** KEPT (pick-wt=13): 192 [] c_member(A,B,c_SetInterval_Oord_OatMost(A,C,D))| -hBOOL(hAPP(hAPP(C,B),D)).
% 5.58/5.69 ** KEPT (pick-wt=13): 193 [] -c_member(A,B,c_SetInterval_Oord_OatLeast(A,C,D))|hBOOL(hAPP(hAPP(C,D),B)).
% 5.58/5.69 ** KEPT (pick-wt=13): 194 [] c_member(A,B,c_SetInterval_Oord_OatLeast(A,C,D))| -hBOOL(hAPP(hAPP(C,D),B)).
% 5.58/5.69 ** KEPT (pick-wt=13): 195 [] -c_member(A,B,c_SetInterval_Oord_OlessThan(A,C,D))|hBOOL(hAPP(hAPP(C,B),D)).
% 5.58/5.69 ** KEPT (pick-wt=13): 196 [] c_member(A,B,c_SetInterval_Oord_OlessThan(A,C,D))| -hBOOL(hAPP(hAPP(C,B),D)).
% 5.58/5.69 ** KEPT (pick-wt=13): 197 [] -c_member(A,B,c_SetInterval_Oord_OgreaterThan(A,C,D))|hBOOL(hAPP(hAPP(C,D),B)).
% 5.58/5.69 ** KEPT (pick-wt=13): 198 [] c_member(A,B,c_SetInterval_Oord_OgreaterThan(A,C,D))| -hBOOL(hAPP(hAPP(C,D),B)).
% 5.58/5.69 ** KEPT (pick-wt=14): 199 [] -c_member(A,B,c_SetInterval_Oord_OatLeastAtMost(A,C,D,E))|hBOOL(hAPP(hAPP(C,D),B)).
% 5.58/5.69 ** KEPT (pick-wt=14): 200 [] -c_member(A,B,c_SetInterval_Oord_OatLeastAtMost(A,C,D,E))|hBOOL(hAPP(hAPP(C,B),E)).
% 5.58/5.69 ** KEPT (pick-wt=20): 201 [] c_member(A,B,c_SetInterval_Oord_OatLeastAtMost(A,C,D,E))| -hBOOL(hAPP(hAPP(C,D),B))| -hBOOL(hAPP(hAPP(C,B),E)).
% 5.58/5.69 ** KEPT (pick-wt=14): 202 [] -c_member(A,B,c_SetInterval_Oord_OgreaterThanLessThan(A,C,D,E))|hBOOL(hAPP(hAPP(C,D),B)).
% 5.58/5.69 ** KEPT (pick-wt=14): 203 [] -c_member(A,B,c_SetInterval_Oord_OgreaterThanLessThan(A,C,D,E))|hBOOL(hAPP(hAPP(C,B),E)).
% 5.58/5.69 ** KEPT (pick-wt=20): 204 [] c_member(A,B,c_SetInterval_Oord_OgreaterThanLessThan(A,C,D,E))| -hBOOL(hAPP(hAPP(C,D),B))| -hBOOL(hAPP(hAPP(C,B),E)).
% 5.58/5.69 ** KEPT (pick-wt=18): 205 [] -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).
% 5.58/5.69 ** KEPT (pick-wt=6): 206 [] -c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))).
% 5.58/5.69 ** KEPT (pick-wt=15): 207 [] -c_member(A,B,c_SetInterval_Oord_OgreaterThanAtMost(A,C,D,E,F))|hBOOL(hAPP(hAPP(D,E),B)).
% 5.58/5.69 ** KEPT (pick-wt=15): 208 [] -c_member(A,B,c_SetInterval_Oord_OgreaterThanAtMost(A,C,D,E,F))|hBOOL(hAPP(hAPP(C,B),F)).
% 5.58/5.69 ** KEPT (pick-wt=21): 209 [] 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)).
% 5.58/5.69 ** KEPT (pick-wt=15): 210 [] -c_member(A,B,c_SetInterval_Oord_OatLeastLessThan(A,C,D,E,F))|hBOOL(hAPP(hAPP(C,E),B)).
% 5.58/5.69 ** KEPT (pick-wt=15): 211 [] -c_member(A,B,c_SetInterval_Oord_OatLeastLessThan(A,C,D,E,F))|hBOOL(hAPP(hAPP(D,B),F)).
% 5.58/5.69 ** KEPT (pick-wt=21): 212 [] 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)).
% 5.58/5.69 Following clause subsumed by 174 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).
% 5.58/5.69 ** KEPT (pick-wt=27): 213 [] -c_Finite__Set_Ofinite(tc_fun(A,B),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(A,B),tc_HOL_Obool)))|c_Finite__Set_Ocard(B,c_Orderings_Otop__class_Otop(tc_fun(B,tc_HOL_Obool)))=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_Finite__Set_Ofinite(A,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))).
% 5.58/5.69 ** KEPT (pick-wt=32): 214 [] -c_Finite__Set_Ofolding__one__idem(A,B,C)| -c_Finite__Set_Ofinite(A,D)|E=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))| -c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),E,D)|hAPP(hAPP(B,hAPP(C,E)),hAPP(C,D))=hAPP(C,D).
% 5.58/5.69 ** KEPT (pick-wt=29): 215 [] -c_Finite__Set_Ofolding__image__simple__idem(A,B,C,D,E,F)| -c_Finite__Set_Ofinite(B,G)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,tc_HOL_Obool),H,G)|hAPP(hAPP(C,hAPP(F,H)),hAPP(F,G))=hAPP(F,G).
% 5.58/5.69 ** KEPT (pick-wt=27): 216 [] -c_Finite__Set_Ofolding__image__simple__idem(A,B,C,D,E,F)| -c_Finite__Set_Ofinite(B,G)| -c_member(B,H,G)|hAPP(hAPP(C,hAPP(E,H)),hAPP(F,G))=hAPP(F,G).
% 5.58/5.69 ** KEPT (pick-wt=12): 217 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),hAPP(c_Nat_OSuc,B)).
% 5.58/5.69 ** KEPT (pick-wt=5): 219 [copy,218,flip.1] hAPP(c_Nat_OSuc,A)!=A.
% 5.58/5.69 Following clause subsumed by 219 during input processing: 0 [] hAPP(c_Nat_OSuc,A)!=A.
% 5.58/5.69 ** KEPT (pick-wt=10): 220 [] hAPP(c_Nat_OSuc,A)!=hAPP(c_Nat_OSuc,B)|A=B.
% 5.58/5.69 ** KEPT (pick-wt=10): 221 [] hAPP(c_Nat_OSuc,A)=hAPP(c_Nat_OSuc,B)|A!=B.
% 5.58/5.69 Following clause subsumed by 220 during input processing: 0 [] hAPP(c_Nat_OSuc,A)!=hAPP(c_Nat_OSuc,B)|A=B.
% 5.58/5.69 ** KEPT (pick-wt=11): 222 [] -c_Finite__Set_Ofolding__one__idem(A,B,C)|hAPP(hAPP(B,D),D)=D.
% 5.58/5.69 ** KEPT (pick-wt=14): 223 [] -c_Finite__Set_Ofolding__image__simple__idem(A,B,C,D,E,F)|hAPP(hAPP(C,G),G)=G.
% 5.58/5.69 ** KEPT (pick-wt=6): 224 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),A).
% 5.58/5.69 ** KEPT (pick-wt=10): 225 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,B),A).
% 5.58/5.69 ** KEPT (pick-wt=15): 226 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=hAPP(c_Nat_OSuc,B).
% 5.58/5.69 ** KEPT (pick-wt=10): 227 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 5.58/5.69 Following clause subsumed by 150 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))|A!=hAPP(c_Nat_OSuc,B).
% 5.58/5.69 ** KEPT (pick-wt=12): 228 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),hAPP(c_Nat_OSuc,B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 5.58/5.69 ** KEPT (pick-wt=12): 229 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),hAPP(c_Nat_OSuc,B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 5.58/5.69 Following clause subsumed by 227 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,hAPP(c_Nat_OSuc,B)).
% 5.58/5.69 Following clause subsumed by 226 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=hAPP(c_Nat_OSuc,B).
% 5.58/5.69 ** KEPT (pick-wt=10): 230 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 5.58/5.69 ** KEPT (pick-wt=10): 231 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,hAPP(c_Nat_OSuc,A)).
% 5.58/5.69 ** KEPT (pick-wt=13): 232 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B.
% 5.58/5.69 ** KEPT (pick-wt=10): 233 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 5.58/5.69 ** KEPT (pick-wt=9): 234 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))|A!=B.
% 5.58/5.69 ** KEPT (pick-wt=12): 235 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),hAPP(c_Nat_OSuc,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 5.58/5.69 Following clause subsumed by 217 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),hAPP(c_Nat_OSuc,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 5.58/5.69 Following clause subsumed by 232 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))|A=B.
% 5.58/5.69 Following clause subsumed by 234 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))|A!=B.
% 5.58/5.69 ** KEPT (pick-wt=13): 236 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))|B=A.
% 5.58/5.69 Following clause subsumed by 233 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B)).
% 5.58/5.69 ** KEPT (pick-wt=15): 237 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|hAPP(c_Nat_OSuc,A)=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B).
% 5.58/5.69 ** KEPT (pick-wt=14): 238 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),C).
% 5.58/5.69 Following clause subsumed by 232 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B.
% 5.58/5.69 ** KEPT (pick-wt=10): 239 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 5.58/5.69 Following clause subsumed by 235 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),hAPP(c_Nat_OSuc,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 5.58/5.69 ** KEPT (pick-wt=6): 240 [] hAPP(c_Nat_OSuc,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.69 ** KEPT (pick-wt=6): 241 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,A).
% 5.58/5.69 Following clause subsumed by 240 during input processing: 0 [] hAPP(c_Nat_OSuc,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.69 Following clause subsumed by 240 during input processing: 0 [] hAPP(c_Nat_OSuc,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.69 Following clause subsumed by 241 during input processing: 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,A).
% 5.58/5.69 Following clause subsumed by 241 during input processing: 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,A).
% 5.58/5.69 ** KEPT (pick-wt=11): 243 [copy,242,flip.2] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|hAPP(c_Nat_OSuc,$f22(A))=A.
% 5.58/5.69 ** KEPT (pick-wt=10): 244 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|A!=hAPP(c_Nat_OSuc,B).
% 5.58/5.69 ** KEPT (pick-wt=11): 245 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.69 Following clause subsumed by 234 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.69 ** KEPT (pick-wt=17): 247 [copy,246,flip.3] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_OSuc,$f23(B,A))=A.
% 5.58/5.69 ** KEPT (pick-wt=16): 248 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f23(B,A),B).
% 5.58/5.69 ** KEPT (pick-wt=10): 249 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.69 ** KEPT (pick-wt=15): 250 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))|A!=hAPP(c_Nat_OSuc,C)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,B).
% 5.58/5.69 ** KEPT (pick-wt=10): 251 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 5.58/5.69 ** KEPT (pick-wt=13): 252 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,hAPP(c_Nat_OSuc,A))|B=A.
% 5.58/5.69 Following clause subsumed by 234 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,hAPP(c_Nat_OSuc,A))|B!=A.
% 5.58/5.69 ** KEPT (pick-wt=10): 253 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B).
% 5.58/5.69 ** KEPT (pick-wt=10): 254 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B)).
% 5.58/5.69 Following clause subsumed by 251 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 5.58/5.69 Following clause subsumed by 253 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 5.58/5.69 ** KEPT (pick-wt=10): 255 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 5.58/5.69 Following clause subsumed by 254 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 5.58/5.69 Following clause subsumed by 253 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B).
% 5.58/5.69 Following clause subsumed by 251 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B).
% 5.58/5.69 ** KEPT (pick-wt=22): 256 [] -c_Finite__Set_Ofolding__one__idem(A,B,C)| -c_Finite__Set_Ofinite(A,D)| -c_member(A,E,D)|hAPP(hAPP(B,E),hAPP(C,D))=hAPP(C,D).
% 5.58/5.69 ** KEPT (pick-wt=63): 258 [copy,257,flip.2] -c_Finite__Set_Ofolding__one__idem(A,B,C)|hAPP(hAPP(B,hAPP(D,$f25(E,D,C,B,A))),hAPP(D,$f24(E,D,C,B,A)))!=hAPP(D,hAPP(hAPP(B,$f25(E,D,C,B,A)),$f24(E,D,C,B,A)))| -c_Finite__Set_Ofinite(A,E)|E=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|hAPP(D,hAPP(C,E))=hAPP(C,c_Set_Oimage(A,A,D,E)).
% 5.58/5.69 ** KEPT (pick-wt=12): 259 [] -c_Finite__Set_Ofinite(tc_sum(A,B),c_Sum__Type_OPlus(A,B,C,D))|c_Finite__Set_Ofinite(B,D).
% 5.58/5.69 ** KEPT (pick-wt=12): 260 [] -class_Orderings_Olinorder(A)|c_SetInterval_Oord__class_OgreaterThan(A,B)!=c_SetInterval_Oord__class_OgreaterThan(A,C)|B=C.
% 5.58/5.69 ** KEPT (pick-wt=12): 261 [] -class_Orderings_Olinorder(A)|c_SetInterval_Oord__class_OgreaterThan(A,B)=c_SetInterval_Oord__class_OgreaterThan(A,C)|B!=C.
% 5.58/5.69 ** KEPT (pick-wt=12): 262 [] -class_Orderings_Oord(A)| -c_member(A,B,c_SetInterval_Oord__class_OgreaterThan(A,C))|c_Orderings_Oord__class_Oless(A,C,B).
% 5.58/5.69 ** KEPT (pick-wt=12): 263 [] -class_Orderings_Oord(A)|c_member(A,B,c_SetInterval_Oord__class_OgreaterThan(A,C))| -c_Orderings_Oord__class_Oless(A,C,B).
% 5.58/5.69 ** KEPT (pick-wt=16): 264 [] -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).
% 5.58/5.69 ** KEPT (pick-wt=16): 265 [] -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).
% 5.58/5.69 ** KEPT (pick-wt=12): 266 [] -c_Finite__Set_Ofinite(tc_sum(A,B),c_Sum__Type_OPlus(A,B,C,D))|c_Finite__Set_Ofinite(A,C).
% 5.58/5.69 Following clause subsumed by 259 during input processing: 0 [] -c_Finite__Set_Ofinite(tc_sum(A,B),c_Sum__Type_OPlus(A,B,C,D))|c_Finite__Set_Ofinite(B,D).
% 5.58/5.69 ** KEPT (pick-wt=15): 267 [] c_Finite__Set_Ofinite(tc_sum(A,B),c_Sum__Type_OPlus(A,B,C,D))| -c_Finite__Set_Ofinite(A,C)| -c_Finite__Set_Ofinite(B,D).
% 5.58/5.69 Following clause subsumed by 267 during input processing: 0 [] -c_Finite__Set_Ofinite(A,B)| -c_Finite__Set_Ofinite(C,D)|c_Finite__Set_Ofinite(tc_sum(A,C),c_Sum__Type_OPlus(A,C,B,D)).
% 5.58/5.69 Following clause subsumed by 266 during input processing: 0 [] -c_Finite__Set_Ofinite(tc_sum(A,B),c_Sum__Type_OPlus(A,B,C,D))|c_Finite__Set_Ofinite(A,C).
% 5.58/5.69 ** KEPT (pick-wt=18): 268 [] c_Sum__Type_OPlus(A,B,C,D)!=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(A,B),tc_HOL_Obool))|C=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 5.58/5.69 ** KEPT (pick-wt=18): 269 [] c_Sum__Type_OPlus(A,B,C,D)!=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(A,B),tc_HOL_Obool))|D=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool)).
% 5.58/5.69 ** KEPT (pick-wt=24): 270 [] c_Sum__Type_OPlus(A,B,C,D)=c_Orderings_Obot__class_Obot(tc_fun(tc_sum(A,B),tc_HOL_Obool))|C!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|D!=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool)).
% 5.58/5.69 ** KEPT (pick-wt=24): 271 [] -c_Finite__Set_Ofinite(A,B)| -c_Finite__Set_Ofinite(C,D)|c_Finite__Set_Ocard(tc_sum(A,C),c_Sum__Type_OPlus(A,C,B,D))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Finite__Set_Ocard(A,B),c_Finite__Set_Ocard(C,D)).
% 5.58/5.69 ** KEPT (pick-wt=11): 272 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 5.58/5.69 ** KEPT (pick-wt=11): 273 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 5.58/5.69 ** KEPT (pick-wt=11): 274 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 5.58/5.69 ** KEPT (pick-wt=11): 275 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 5.58/5.69 ** KEPT (pick-wt=12): 276 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)|B=C.
% 5.58/5.69 ** KEPT (pick-wt=12): 277 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)|B!=C.
% 5.58/5.69 ** KEPT (pick-wt=12): 278 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)|A=C.
% 5.58/5.69 ** KEPT (pick-wt=12): 279 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)|A!=C.
% 5.58/5.69 ** KEPT (pick-wt=17): 280 [] -class_Groups_Oab__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 5.58/5.69 ** KEPT (pick-wt=14): 281 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 5.58/5.69 ** KEPT (pick-wt=14): 282 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,B,D)|C!=D.
% 5.58/5.69 ** KEPT (pick-wt=14): 283 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,D,C)|B=D.
% 5.58/5.69 ** KEPT (pick-wt=14): 284 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,D,C)|B!=D.
% 5.58/5.69 Following clause subsumed by 281 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 5.58/5.69 ** KEPT (pick-wt=14): 285 [] -class_Groups_Ocancel__ab__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 5.58/5.69 Following clause subsumed by 283 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,D,C)|B=D.
% 5.58/5.69 ** KEPT (pick-wt=25): 287 [copy,286,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_fun(tc_Nat_Onat,tc_HOL_Obool),A,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,c_Finite__Set_Ocard(tc_Nat_Onat,A))))|c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,c_Finite__Set_Ocard(tc_Nat_Onat,A)))=A.
% 5.58/5.69 ** KEPT (pick-wt=12): 289 [copy,288,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,$f26(B,A))=B.
% 5.58/5.69 ** KEPT (pick-wt=10): 290 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C).
% 5.58/5.69 ** KEPT (pick-wt=14): 291 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 5.58/5.69 ** KEPT (pick-wt=14): 292 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 5.58/5.69 Following clause subsumed by 275 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_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 5.58/5.69 Following clause subsumed by 274 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_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 5.58/5.69 ** KEPT (pick-wt=14): 293 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 5.58/5.69 ** KEPT (pick-wt=18): 294 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)).
% 5.58/5.69 ** KEPT (pick-wt=11): 295 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 5.58/5.69 ** KEPT (pick-wt=11): 296 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 5.58/5.69 Following clause subsumed by 296 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 5.58/5.69 Following clause subsumed by 295 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 5.58/5.69 ** KEPT (pick-wt=7): 297 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),A).
% 5.58/5.69 ** KEPT (pick-wt=7): 298 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),B).
% 5.58/5.69 ** KEPT (pick-wt=14): 299 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 5.58/5.69 ** KEPT (pick-wt=14): 300 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 5.58/5.69 Following clause subsumed by 272 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 5.58/5.69 Following clause subsumed by 273 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 5.58/5.69 ** KEPT (pick-wt=14): 301 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 5.58/5.69 ** KEPT (pick-wt=18): 302 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)).
% 5.58/5.69 ** KEPT (pick-wt=17): 303 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,D)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D).
% 5.58/5.69 ** KEPT (pick-wt=11): 304 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C).
% 5.58/5.69 ** KEPT (pick-wt=10): 305 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=A|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.69 ** KEPT (pick-wt=11): 306 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.69 ** KEPT (pick-wt=11): 307 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.69 ** KEPT (pick-wt=15): 308 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.69 ** KEPT (pick-wt=16): 309 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless(A,C,D).
% 5.58/5.69 ** KEPT (pick-wt=16): 310 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless(A,B,D).
% 5.58/5.69 ** KEPT (pick-wt=20): 311 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 5.58/5.69 ** KEPT (pick-wt=16): 312 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)).
% 5.58/5.69 ** KEPT (pick-wt=16): 313 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)).
% 5.58/5.69 Following clause subsumed by 309 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless(A,C,D).
% 5.58/5.69 ** KEPT (pick-wt=16): 314 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))| -c_Orderings_Oord__class_Oless(A,C,D).
% 5.58/5.69 Following clause subsumed by 310 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless(A,B,D).
% 5.58/5.69 ** KEPT (pick-wt=16): 315 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))| -c_Orderings_Oord__class_Oless(A,B,D).
% 5.58/5.69 ** KEPT (pick-wt=9): 316 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 5.58/5.69 ** KEPT (pick-wt=9): 317 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 5.58/5.69 ** KEPT (pick-wt=13): 318 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oplus__class_Oplus(A,B,B)|B=c_Groups_Ozero__class_Ozero(A).
% 5.58/5.69 ** KEPT (pick-wt=13): 319 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)=c_Groups_Oplus__class_Oplus(A,B,B)|B!=c_Groups_Ozero__class_Ozero(A).
% 5.58/5.69 ** KEPT (pick-wt=9): 320 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 5.58/5.69 ** KEPT (pick-wt=9): 321 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 5.58/5.69 ** KEPT (pick-wt=16): 322 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 5.58/5.69 ** KEPT (pick-wt=16): 323 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 5.58/5.69 ** KEPT (pick-wt=20): 324 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 5.58/5.69 ** KEPT (pick-wt=16): 325 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)).
% 5.58/5.69 ** KEPT (pick-wt=16): 326 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)).
% 5.58/5.69 Following clause subsumed by 322 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 5.58/5.69 ** KEPT (pick-wt=16): 327 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))| -c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 5.58/5.69 Following clause subsumed by 323 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 5.58/5.69 ** KEPT (pick-wt=16): 328 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))| -c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 5.58/5.69 ** KEPT (pick-wt=20): 329 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 5.58/5.69 ** KEPT (pick-wt=18): 330 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Oplus__class_Oplus(A,D,B)).
% 5.58/5.69 ** KEPT (pick-wt=18): 331 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 5.58/5.69 ** KEPT (pick-wt=23): 332 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 5.58/5.69 ** KEPT (pick-wt=23): 333 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 5.58/5.69 ** KEPT (pick-wt=27): 334 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 5.58/5.69 Following clause subsumed by 331 during input processing: 0 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 5.58/5.69 ** KEPT (pick-wt=15): 335 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 5.58/5.69 ** KEPT (pick-wt=15): 336 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 5.58/5.69 ** KEPT (pick-wt=15): 337 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 5.58/5.69 ** KEPT (pick-wt=15): 338 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 5.58/5.69 ** KEPT (pick-wt=20): 339 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 5.58/5.69 ** KEPT (pick-wt=20): 340 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 5.58/5.69 ** KEPT (pick-wt=20): 341 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 5.58/5.69 ** KEPT (pick-wt=20): 342 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 5.58/5.69 ** KEPT (pick-wt=15): 343 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 5.58/5.69 ** KEPT (pick-wt=15): 344 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 5.58/5.69 ** KEPT (pick-wt=15): 345 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 5.58/5.69 ** KEPT (pick-wt=15): 346 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 5.58/5.69 ** KEPT (pick-wt=19): 347 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.69 ** KEPT (pick-wt=21): 348 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.69 ** KEPT (pick-wt=17): 349 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.69 ** KEPT (pick-wt=19): 350 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.69 ** KEPT (pick-wt=19): 351 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.69 ** KEPT (pick-wt=19): 352 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.69 ** KEPT (pick-wt=19): 353 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)|A=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.69 ** KEPT (pick-wt=21): 354 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)|A=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.69 ** KEPT (pick-wt=17): 355 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.69 ** KEPT (pick-wt=19): 356 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.70 ** KEPT (pick-wt=19): 357 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)|A!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.70 ** KEPT (pick-wt=19): 358 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.70 ** KEPT (pick-wt=18): 359 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 5.58/5.70 Following clause subsumed by 272 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 5.58/5.70 Following clause subsumed by 273 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 5.58/5.70 ** KEPT (pick-wt=14): 361 [copy,360,flip.2] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,$f27(B,A)))=B.
% 5.58/5.70 ** KEPT (pick-wt=12): 362 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)).
% 5.58/5.70 ** KEPT (pick-wt=20): 363 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 5.58/5.70 ** KEPT (pick-wt=20): 364 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 5.58/5.70 ** KEPT (pick-wt=18): 365 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 5.58/5.70 ** KEPT (pick-wt=18): 366 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 5.58/5.70 ** KEPT (pick-wt=20): 367 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 5.58/5.70 ** KEPT (pick-wt=20): 368 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 5.58/5.70 Following clause subsumed by 271 during input processing: 0 [] -c_Finite__Set_Ofinite(A,B)| -c_Finite__Set_Ofinite(C,D)|c_Finite__Set_Ocard(tc_sum(A,C),c_Sum__Type_OPlus(A,C,B,D))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Finite__Set_Ocard(A,B),c_Finite__Set_Ocard(C,D)).
% 5.58/5.70 ** KEPT (pick-wt=18): 369 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 5.58/5.70 ** KEPT (pick-wt=15): 370 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 5.58/5.70 ** KEPT (pick-wt=15): 371 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 5.58/5.70 ** KEPT (pick-wt=13): 372 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Oplus__class_Oplus(A,B,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 5.58/5.70 ** KEPT (pick-wt=13): 373 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Oplus__class_Oplus(A,B,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 5.58/5.70 ** KEPT (pick-wt=13): 374 [] -class_Rings_Olinordered__idom(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 5.58/5.70 ** KEPT (pick-wt=9): 375 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 5.58/5.70 ** KEPT (pick-wt=9): 376 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 5.58/5.70 ** KEPT (pick-wt=23): 377 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,E))=c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 5.58/5.70 ** KEPT (pick-wt=17): 378 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,D),C).
% 5.58/5.70 ** KEPT (pick-wt=17): 379 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 5.58/5.70 Following clause subsumed by 379 during input processing: 0 [flip.2] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 5.58/5.70 ** KEPT (pick-wt=17): 380 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 5.58/5.70 ** KEPT (pick-wt=11): 381 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,C,B).
% 5.58/5.70 ** KEPT (pick-wt=12): 383 [copy,382,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=B|C=c_Groups_Ozero__class_Ozero(A).
% 5.58/5.70 ** KEPT (pick-wt=12): 385 [copy,384,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,B,C)=B|C!=c_Groups_Ozero__class_Ozero(A).
% 5.58/5.70 ** KEPT (pick-wt=19): 386 [] -class_Groups_Ocomm__monoid__add(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,D,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C,hAPP(c_Nat_OSuc,B)))=c_Groups_Ozero__class_Ozero(A).
% 5.58/5.70 ** KEPT (pick-wt=30): 387 [] -class_Groups_Ocomm__monoid__add(A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,D,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C,hAPP(c_Nat_OSuc,B)))=c_Groups_Oplus__class_Oplus(A,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,D,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C,B)),hAPP(D,B)).
% 5.58/5.70 ** KEPT (pick-wt=37): 388 [] -class_Groups_Ocomm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Groups_Oplus__class_Oplus(A,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,E,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B,C)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,E,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,C,D)))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,E,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B,D)).
% 5.58/5.70 ** KEPT (pick-wt=30): 389 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(A)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,B,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),C))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,B,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)).
% 5.58/5.70 ** KEPT (pick-wt=30): 391 [copy,390,flip.3] -class_Groups_Ocomm__monoid__add(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|c_Groups_Oplus__class_Oplus(A,hAPP(D,B),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,D,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,B),C)))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,D,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,B,C)).
% 5.58/5.70 ** KEPT (pick-wt=13): 392 [] -class_Groups_Ocomm__monoid__add(A)|c_Finite__Set_Ofinite(B,C)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,D,C)=c_Groups_Ozero__class_Ozero(A).
% 5.58/5.70 Following clause subsumed by 392 during input processing: 0 [] -class_Groups_Ocomm__monoid__add(A)|c_Finite__Set_Ofinite(B,C)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,D,C)=c_Groups_Ozero__class_Ozero(A).
% 5.58/5.70 ** KEPT (pick-wt=21): 393 [] -c_Finite__Set_Ofinite(A,B)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat,C,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_member(A,D,B)|hAPP(C,D)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.70 ** KEPT (pick-wt=18): 394 [] -c_Finite__Set_Ofinite(A,B)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat,C,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_member(A,$f28(C,B,A),B).
% 5.58/5.70 ** KEPT (pick-wt=20): 395 [] -c_Finite__Set_Ofinite(A,B)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat,C,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(C,$f28(C,B,A))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.70 ** KEPT (pick-wt=20): 396 [] -c_Finite__Set_Ofinite(A,B)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat,C,B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_member(A,$f29(C,B,A),B).
% 5.58/5.70 ** KEPT (pick-wt=24): 397 [] -c_Finite__Set_Ofinite(A,B)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat,C,B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(C,$f29(C,B,A))=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.58/5.70 ** KEPT (pick-wt=29): 398 [] -c_Finite__Set_Ofinite(A,B)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat,C,B)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))| -c_member(A,D,B)|$f29(C,B,A)=D|hAPP(C,D)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.70 ** KEPT (pick-wt=33): 399 [] -c_Finite__Set_Ofinite(A,B)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat,C,B)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))| -c_member(A,D,B)|hAPP(C,D)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|c_member(A,$f30(C,B,A,D),B).
% 5.58/5.70 ** KEPT (pick-wt=32): 401 [copy,400,flip.5] -c_Finite__Set_Ofinite(A,B)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat,C,B)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))| -c_member(A,D,B)|hAPP(C,D)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|$f30(C,B,A,D)!=D.
% 5.58/5.70 ** KEPT (pick-wt=35): 402 [] -c_Finite__Set_Ofinite(A,B)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat,C,B)=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))| -c_member(A,D,B)|hAPP(C,D)!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|hAPP(C,$f30(C,B,A,D))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.58/5.70 ** KEPT (pick-wt=13): 403 [] -class_Groups_Ocomm__monoid__add(A)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(A).
% 5.58/5.70 Following clause subsumed by 403 during input processing: 0 [] -class_Groups_Ocomm__monoid__add(A)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(A).
% 5.66/5.70 ** KEPT (pick-wt=34): 404 [] -class_Groups_Ocomm__monoid__add(A)| -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Finite__Set_Ofinite(B,C)|C=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))|c_member(B,$f31(D,E,C,B,A),C)|c_Orderings_Oord__class_Oless(A,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,E,C),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,D,C)).
% 5.66/5.70 ** KEPT (pick-wt=43): 405 [] -class_Groups_Ocomm__monoid__add(A)| -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Finite__Set_Ofinite(B,C)|C=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))| -c_Orderings_Oord__class_Oless(A,hAPP(D,$f31(E,D,C,B,A)),hAPP(E,$f31(E,D,C,B,A)))|c_Orderings_Oord__class_Oless(A,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,D,C),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,E,C)).
% 5.66/5.70 ** KEPT (pick-wt=17): 406 [] c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat,B,C)!=hAPP(c_Nat_OSuc,D)|c_member(A,$f32(D,C,B,A),C).
% 5.66/5.70 ** KEPT (pick-wt=20): 407 [] c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat,B,C)!=hAPP(c_Nat_OSuc,D)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(B,$f32(D,C,B,A))).
% 5.66/5.70 ** KEPT (pick-wt=37): 408 [] -class_Groups_Ocomm__monoid__add(A)| -c_Fun_Oinj__on(B,C,D,E)|F!=c_Set_Oimage(B,C,D,E)|c_member(B,$f33(G,H,F,E,D,C,B,A),E)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,A,G,F)=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,H,E).
% 5.66/5.70 ** KEPT (pick-wt=50): 409 [] -class_Groups_Ocomm__monoid__add(A)| -c_Fun_Oinj__on(B,C,D,E)|F!=c_Set_Oimage(B,C,D,E)|hAPP(G,$f33(H,G,F,E,D,C,B,A))!=hAPP(H,hAPP(D,$f33(H,G,F,E,D,C,B,A)))|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(C,A,H,F)=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,G,E).
% 5.66/5.70 ** KEPT (pick-wt=39): 410 [] -class_Groups_Ocomm__monoid__add(A)| -class_Orderings_Oord(B)|C!=D|E!=F|c_Orderings_Oord__class_Oless__e_q(B,D,$f34(G,H,F,E,D,C,B,A))|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,H,c_SetInterval_Oord__class_OatLeastLessThan(B,C,E))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,G,c_SetInterval_Oord__class_OatLeastLessThan(B,D,F)).
% 5.66/5.70 ** KEPT (pick-wt=39): 411 [] -class_Groups_Ocomm__monoid__add(A)| -class_Orderings_Oord(B)|C!=D|E!=F|c_Orderings_Oord__class_Oless(B,$f34(G,H,F,E,D,C,B,A),F)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,H,c_SetInterval_Oord__class_OatLeastLessThan(B,C,E))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,G,c_SetInterval_Oord__class_OatLeastLessThan(B,D,F)).
% 5.66/5.70 ** KEPT (pick-wt=50): 412 [] -class_Groups_Ocomm__monoid__add(A)| -class_Orderings_Oord(B)|C!=D|E!=F|hAPP(G,$f34(H,G,F,E,D,C,B,A))!=hAPP(H,$f34(H,G,F,E,D,C,B,A))|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,G,c_SetInterval_Oord__class_OatLeastLessThan(B,C,E))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,H,c_SetInterval_Oord__class_OatLeastLessThan(B,D,F)).
% 5.66/5.70 ** KEPT (pick-wt=21): 413 [] -class_Groups_Ocomm__monoid__add(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,B),C)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,D,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,C,hAPP(c_Nat_OSuc,B)))=c_Groups_Ozero__class_Ozero(A).
% 5.66/5.70 ** KEPT (pick-wt=34): 414 [] -class_Groups_Ocomm__monoid__add(A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,B),C)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,D,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,C,hAPP(c_Nat_OSuc,B)))=c_Groups_Oplus__class_Oplus(A,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,D,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,C,B)),hAPP(D,hAPP(c_Nat_OSuc,B))).
% 5.66/5.70 ** KEPT (pick-wt=22): 415 [] -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).
% 5.66/5.70 ** KEPT (pick-wt=22): 416 [] -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).
% 5.66/5.70 ** KEPT (pick-wt=18): 417 [] -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).
% 5.66/5.70 ** KEPT (pick-wt=22): 418 [] -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).
% 5.66/5.70 ** KEPT (pick-wt=15): 419 [] -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)).
% 5.66/5.70 ** KEPT (pick-wt=15): 420 [] -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).
% 5.66/5.70 ** KEPT (pick-wt=15): 421 [] -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).
% 5.66/5.70 ** KEPT (pick-wt=15): 422 [] -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).
% 5.66/5.70 ** KEPT (pick-wt=15): 423 [] -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).
% 5.66/5.70 ** KEPT (pick-wt=18): 424 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -hBOOL(hAPP(C,A))|c_member(tc_Nat_Onat,$f35(C,B),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)).
% 5.66/5.70 ** KEPT (pick-wt=14): 425 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -hBOOL(hAPP(C,A))|hBOOL(hAPP(C,$f35(C,B))).
% 5.66/5.70 ** KEPT (pick-wt=18): 426 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f36(A,B),B)| -c_member(tc_Nat_Onat,C,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B))| -hBOOL(hAPP(A,C)).
% 5.66/5.70 ** KEPT (pick-wt=18): 427 [] hBOOL(hAPP(A,$f36(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)).
% 5.66/5.70 ** KEPT (pick-wt=18): 428 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,$f37(A,B),B)| -c_member(tc_Nat_Onat,C,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B))|hBOOL(hAPP(A,C)).
% 5.66/5.70 ** KEPT (pick-wt=18): 429 [] -hBOOL(hAPP(A,$f37(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)).
% 5.66/5.70 ** KEPT (pick-wt=18): 430 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|hBOOL(hAPP(C,A))|c_member(tc_Nat_Onat,$f38(C,B),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)).
% 5.66/5.70 ** KEPT (pick-wt=14): 431 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|hBOOL(hAPP(C,A))| -hBOOL(hAPP(C,$f38(C,B))).
% 5.66/5.70 ** KEPT (pick-wt=28): 432 [] hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat,A,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat,A,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)).
% 5.66/5.70 ** KEPT (pick-wt=22): 433 [] -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).
% 5.66/5.70 ** KEPT (pick-wt=22): 434 [] -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).
% 5.66/5.70 ** KEPT (pick-wt=26): 435 [] -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).
% 5.66/5.70 ** KEPT (pick-wt=18): 436 [] -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).
% 5.66/5.70 ** KEPT (pick-wt=22): 437 [] -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).
% 5.66/5.70 ** KEPT (pick-wt=30): 438 [] -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).
% 5.66/5.70 ** KEPT (pick-wt=30): 439 [] -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).
% 5.66/5.70 ** KEPT (pick-wt=30): 441 [copy,440,flip.3] -class_Groups_Ocomm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C)|c_Groups_Oplus__class_Oplus(A,hAPP(D,B),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,D,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,B),C)))=c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,D,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,C)).
% 5.66/5.70 ** KEPT (pick-wt=47): 442 [] -class_Groups_Ocomm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,c_Groups_Oone__class_Oone(tc_Nat_Onat)))|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,D,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,E)))=c_Groups_Oplus__class_Oplus(A,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,D,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,B,C)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,A,D,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,E)))).
% 5.66/5.70 ** KEPT (pick-wt=10): 443 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))).
% 5.66/5.70 ** KEPT (pick-wt=8): 444 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)).
% 5.66/5.70 ** KEPT (pick-wt=8): 445 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)).
% 5.66/5.70 ** KEPT (pick-wt=8): 446 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)).
% 5.66/5.70 ** KEPT (pick-wt=8): 447 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)).
% 5.66/5.70 ** KEPT (pick-wt=7): 449 [copy,448,flip.2] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 5.66/5.70 Following clause subsumed by 449 during input processing: 0 [] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 5.66/5.70 ** KEPT (pick-wt=10): 450 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)!=B|B=c_Groups_Oone__class_Oone(A).
% 5.66/5.70 ** KEPT (pick-wt=10): 451 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)=B|B!=c_Groups_Oone__class_Oone(A).
% 5.66/5.70 ** KEPT (pick-wt=12): 452 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A))).
% 5.66/5.70 ** KEPT (pick-wt=18): 453 [] -c_Finite__Set_Ofinite(A,B)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat,C,B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_member(A,$f39(C,B,A),B).
% 5.66/5.70 ** KEPT (pick-wt=20): 454 [] -c_Finite__Set_Ofinite(A,B)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat,C,B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(C,$f39(C,B,A))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 5.66/5.70 ** KEPT (pick-wt=27): 455 [] -c_Finite__Set_Ofinite(A,B)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat,C,B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)| -c_member(A,D,B)|$f39(C,B,A)=D|hAPP(C,D)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.70 ** KEPT (pick-wt=29): 456 [] -c_Finite__Set_Ofinite(A,B)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat,C,B)=c_Groups_Oone__class_Oone(tc_Nat_Onat)| -c_member(A,D,B)|hAPP(C,D)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_member(A,$f40(C,B,A,D),B).
% 5.66/5.70 ** KEPT (pick-wt=28): 458 [copy,457,flip.5] -c_Finite__Set_Ofinite(A,B)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat,C,B)=c_Groups_Oone__class_Oone(tc_Nat_Onat)| -c_member(A,D,B)|hAPP(C,D)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|$f40(C,B,A,D)!=D.
% 5.66/5.70 ** KEPT (pick-wt=31): 459 [] -c_Finite__Set_Ofinite(A,B)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(A,tc_Nat_Onat,C,B)=c_Groups_Oone__class_Oone(tc_Nat_Onat)| -c_member(A,D,B)|hAPP(C,D)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|hAPP(C,$f40(C,B,A,D))!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.70 ** KEPT (pick-wt=24): 460 [] -class_Rings_Olinordered__idom(A)| -c_member(A,B,c_Int_Oring__1__class_OInts(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),B),B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 5.66/5.70 ** KEPT (pick-wt=24): 461 [] -class_Rings_Olinordered__idom(A)| -c_member(A,B,c_Int_Oring__1__class_OInts(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),B),B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 5.66/5.70 ** KEPT (pick-wt=15): 462 [] hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f41(B,A),B).
% 5.66/5.70 ** KEPT (pick-wt=19): 463 [] hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,$f41(B,A))| -hBOOL(hAPP(A,C)).
% 5.66/5.70 ** KEPT (pick-wt=19): 464 [] hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,$f41(B,A),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 5.66/5.70 ** KEPT (pick-wt=8): 465 [] -class_Rings_Oring__1(A)|c_member(A,c_Groups_Ozero__class_Ozero(A),c_Int_Oring__1__class_OInts(A)).
% 5.66/5.70 ** KEPT (pick-wt=20): 466 [] -class_Rings_Oring__1(A)| -c_member(A,B,c_Int_Oring__1__class_OInts(A))| -c_member(A,C,c_Int_Oring__1__class_OInts(A))|c_member(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Int_Oring__1__class_OInts(A)).
% 5.66/5.70 ** KEPT (pick-wt=8): 467 [] -class_Rings_Oring__1(A)|c_member(A,c_Groups_Oone__class_Oone(A),c_Int_Oring__1__class_OInts(A)).
% 5.66/5.70 ** KEPT (pick-wt=18): 468 [] -class_Int_Oring__char__0(A)| -c_member(A,B,c_Int_Oring__1__class_OInts(A))|c_Groups_Oplus__class_Oplus(A,B,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 5.66/5.71 ** KEPT (pick-wt=18): 469 [] -class_Int_Oring__char__0(A)| -c_member(A,B,c_Int_Oring__1__class_OInts(A))|c_Groups_Oplus__class_Oplus(A,B,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 5.66/5.71 ** KEPT (pick-wt=18): 470 [] -class_Int_Oring__char__0(A)| -c_member(A,B,c_Int_Oring__1__class_OInts(A))|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),B),B)!=c_Groups_Ozero__class_Ozero(A).
% 5.66/5.71 ** KEPT (pick-wt=15): 471 [] -c_Finite__Set_Ofinite(A,B)|c_member(A,$f42(B,A),B)|c_Finite__Set_Ocard(A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.71 ** KEPT (pick-wt=14): 473 [copy,472,flip.2] -c_Finite__Set_Ofinite(A,B)|c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|c_Finite__Set_Ocard(A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.71 ** KEPT (pick-wt=21): 474 [] -c_Finite__Set_Ofinite(A,B)|c_member(A,C,B)|c_Finite__Set_Ocard(A,c_Set_Oinsert(A,C,B))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Finite__Set_Ocard(A,B)).
% 5.66/5.71 ** KEPT (pick-wt=14): 475 [] -c_member(A,B,c_Set_Oinsert(A,C,D))|B=C|c_member(A,B,D).
% 5.66/5.71 ** KEPT (pick-wt=11): 476 [] -c_member(A,B,C)|c_member(A,B,c_Set_Oinsert(A,D,C)).
% 5.66/5.71 ** KEPT (pick-wt=10): 477 [] A!=B|c_member(C,A,c_Set_Oinsert(C,B,D)).
% 5.66/5.71 ** KEPT (pick-wt=9): 478 [] -c_Finite__Set_Ofinite(A,B)|c_Finite__Set_Ofinite(A,c_Set_Oinsert(A,C,B)).
% 5.66/5.71 ** KEPT (pick-wt=26): 479 [] -c_Finite__Set_Ofolding__image__simple__idem(A,B,C,D,E,F)| -c_Finite__Set_Ofinite(B,G)|hAPP(F,c_Set_Oinsert(B,H,G))=hAPP(hAPP(C,hAPP(E,H)),hAPP(F,G)).
% 5.66/5.71 ** KEPT (pick-wt=18): 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),c_Set_Oinsert(A,D,B),c_Set_Oinsert(A,D,C)).
% 5.66/5.71 ** KEPT (pick-wt=15): 481 [] -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)).
% 5.66/5.71 ** KEPT (pick-wt=13): 482 [] -c_member(A,B,c_Set_Oinsert(A,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))|B=C.
% 5.66/5.71 Following clause subsumed by 477 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.
% 5.66/5.71 Following clause subsumed by 482 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.
% 5.66/5.71 ** KEPT (pick-wt=13): 483 [] -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).
% 5.66/5.71 ** KEPT (pick-wt=15): 484 [] -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).
% 5.66/5.71 ** KEPT (pick-wt=19): 485 [] 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).
% 5.66/5.71 ** KEPT (pick-wt=19): 486 [] 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).
% 5.66/5.71 Following clause subsumed by 481 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).
% 5.66/5.71 ** KEPT (pick-wt=20): 487 [] -c_member(A,B,C)|c_Set_Oinsert(D,hAPP(E,B),c_Set_Oimage(A,D,E,C))=c_Set_Oimage(A,D,E,C).
% 5.66/5.71 ** KEPT (pick-wt=27): 488 [] -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))).
% 5.66/5.71 ** KEPT (pick-wt=14): 489 [] -hBOOL(hAPP(c_Set_Oinsert(A,B,C),D))|B=D|hBOOL(hAPP(C,D)).
% 5.66/5.71 ** KEPT (pick-wt=10): 490 [] hBOOL(hAPP(c_Set_Oinsert(A,B,C),D))|B!=D.
% 5.66/5.71 ** KEPT (pick-wt=11): 491 [] hBOOL(hAPP(c_Set_Oinsert(A,B,C),D))| -hBOOL(hAPP(C,D)).
% 5.66/5.71 ** KEPT (pick-wt=9): 492 [] -c_Finite__Set_Ofinite(A,c_Set_Oinsert(A,B,C))|c_Finite__Set_Ofinite(A,C).
% 5.66/5.71 Following clause subsumed by 478 during input processing: 0 [] c_Finite__Set_Ofinite(A,c_Set_Oinsert(A,B,C))| -c_Finite__Set_Ofinite(A,C).
% 5.66/5.71 Following clause subsumed by 475 during input processing: 0 [] -c_member(A,B,c_Set_Oinsert(A,C,D))|B=C|c_member(A,B,D).
% 5.66/5.71 Following clause subsumed by 477 during input processing: 0 [] c_member(A,B,c_Set_Oinsert(A,C,D))|B!=C.
% 5.66/5.71 Following clause subsumed by 476 during input processing: 0 [] c_member(A,B,c_Set_Oinsert(A,C,D))| -c_member(A,B,D).
% 5.66/5.71 ** KEPT (pick-wt=20): 493 [] c_member(A,B,C)|c_member(A,B,D)|c_Set_Oinsert(A,B,C)!=c_Set_Oinsert(A,B,D)|C=D.
% 5.66/5.71 ** KEPT (pick-wt=20): 494 [] c_member(A,B,C)|c_member(A,B,D)|c_Set_Oinsert(A,B,C)=c_Set_Oinsert(A,B,D)|C!=D.
% 5.66/5.71 Following clause subsumed by 476 during input processing: 0 [] -c_member(A,B,C)|c_member(A,B,c_Set_Oinsert(A,D,C)).
% 5.66/5.71 ** KEPT (pick-wt=10): 495 [] -c_member(A,B,C)|c_Set_Oinsert(A,B,C)=C.
% 5.66/5.71 ** KEPT (pick-wt=18): 496 [] 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.
% 5.66/5.71 ** KEPT (pick-wt=27): 497 [] 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.
% 5.66/5.71 ** KEPT (pick-wt=27): 498 [] 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.
% 5.66/5.71 ** KEPT (pick-wt=27): 499 [] 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.
% 5.66/5.71 ** KEPT (pick-wt=27): 500 [] 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.
% 5.66/5.71 ** KEPT (pick-wt=27): 501 [] 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.
% 5.66/5.71 ** KEPT (pick-wt=27): 502 [] 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.
% 5.66/5.71 ** KEPT (pick-wt=9): 503 [] c_Set_Oinsert(A,B,C)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 5.66/5.71 ** KEPT (pick-wt=9): 504 [] c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))!=c_Set_Oinsert(A,B,C).
% 5.66/5.71 ** KEPT (pick-wt=17): 505 [] -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))).
% 5.66/5.71 ** KEPT (pick-wt=17): 506 [] -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.
% 5.66/5.71 ** KEPT (pick-wt=17): 507 [] -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.
% 5.66/5.71 ** KEPT (pick-wt=20): 508 [] -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.
% 5.66/5.71 ** KEPT (pick-wt=14): 510 [copy,509,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).
% 5.66/5.71 ** KEPT (pick-wt=14): 511 [] -c_Finite__Set_Ofinite(A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Finite__Set_Ocard(A,B),c_Finite__Set_Ocard(A,c_Set_Oinsert(A,C,B))).
% 5.66/5.71 ** KEPT (pick-wt=22): 513 [copy,512,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))|c_Set_Oinsert(tc_Nat_Onat,hAPP(c_Nat_OSuc,B),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B)).
% 5.66/5.71 ** KEPT (pick-wt=27): 514 [] -c_Finite__Set_Ofolding__one__idem(A,B,C)| -c_Finite__Set_Ofinite(A,D)|D=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|hAPP(C,c_Set_Oinsert(A,E,D))=hAPP(hAPP(B,E),hAPP(C,D)).
% 5.66/5.72 ** KEPT (pick-wt=28): 515 [] -class_Groups_Ocomm__monoid__add(A)| -c_Finite__Set_Ofinite(B,C)|c_member(B,D,C)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,E,c_Set_Oinsert(B,D,C))=c_Groups_Oplus__class_Oplus(A,hAPP(E,D),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,E,C)).
% 5.66/5.72 Following clause subsumed by 515 during input processing: 0 [] -class_Groups_Ocomm__monoid__add(A)| -c_Finite__Set_Ofinite(B,C)|c_member(B,D,C)|c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,E,c_Set_Oinsert(B,D,C))=c_Groups_Oplus__class_Oplus(A,hAPP(E,D),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(B,A,E,C)).
% 5.66/5.72 ** KEPT (pick-wt=19): 516 [] -c_Finite__Set_Ofinite(A,B)|c_member(A,C,B)|c_Finite__Set_Ocard(A,c_Set_Oinsert(A,C,B))=hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(A,B)).
% 5.66/5.72 ** KEPT (pick-wt=17): 517 [] -c_Finite__Set_Ofinite(A,B)| -c_member(A,C,B)|c_Finite__Set_Ocard(A,c_Set_Oinsert(A,C,B))=c_Finite__Set_Ocard(A,B).
% 5.66/5.72 Following clause subsumed by 516 during input processing: 0 [] -c_Finite__Set_Ofinite(A,B)|c_member(A,C,B)|c_Finite__Set_Ocard(A,c_Set_Oinsert(A,C,B))=hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(A,B)).
% 5.66/5.72 ** KEPT (pick-wt=18): 518 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))=c_Set_Oinsert(tc_Nat_Onat,B,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B)).
% 5.66/5.72 ** KEPT (pick-wt=19): 520 [copy,519,flip.2] c_Finite__Set_Ocard(A,B)!=hAPP(c_Nat_OSuc,C)|c_Set_Oinsert(A,$f44(C,B,A),$f43(C,B,A))=B.
% 5.66/5.72 ** KEPT (pick-wt=17): 521 [] c_Finite__Set_Ocard(A,B)!=hAPP(c_Nat_OSuc,C)| -c_member(A,$f44(C,B,A),$f43(C,B,A)).
% 5.66/5.72 ** KEPT (pick-wt=15): 522 [] c_Finite__Set_Ocard(A,B)!=hAPP(c_Nat_OSuc,C)|c_Finite__Set_Ocard(A,$f43(C,B,A))=C.
% 5.66/5.72 ** KEPT (pick-wt=20): 523 [] c_Finite__Set_Ocard(A,B)!=hAPP(c_Nat_OSuc,C)|C!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|$f43(C,B,A)=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 5.66/5.72 ** KEPT (pick-wt=26): 524 [] c_Finite__Set_Ocard(A,B)=hAPP(c_Nat_OSuc,C)|B!=c_Set_Oinsert(A,D,E)|c_member(A,D,E)|c_Finite__Set_Ocard(A,E)!=C|C=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.72 ** KEPT (pick-wt=28): 525 [] c_Finite__Set_Ocard(A,B)=hAPP(c_Nat_OSuc,C)|B!=c_Set_Oinsert(A,D,E)|c_member(A,D,E)|c_Finite__Set_Ocard(A,E)!=C|E!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 5.66/5.72 ** KEPT (pick-wt=31): 526 [] -c_Finite__Set_Ofolding__one(A,B,C)| -c_Finite__Set_Ofinite(A,D)|c_member(A,E,D)|D=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))|hAPP(C,c_Set_Oinsert(A,E,D))=hAPP(hAPP(B,E),hAPP(C,D)).
% 5.66/5.72 ** KEPT (pick-wt=29): 528 [copy,527,flip.3] -c_Finite__Set_Ofinite(A,B)| -c_member(A,C,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Finite__Set_Ocard(A,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))))))=c_Finite__Set_Ocard(A,B).
% 5.66/5.72 ** KEPT (pick-wt=6): 529 [] -class_Orderings_Opreorder(A)|class_Orderings_Opreorder(tc_fun(B,A)).
% 5.66/5.72 ** KEPT (pick-wt=8): 530 [] -class_Finite__Set_Ofinite(A)| -class_Finite__Set_Ofinite(B)|class_Finite__Set_Ofinite(tc_fun(A,B)).
% 5.66/5.72 ** KEPT (pick-wt=6): 531 [] -class_Orderings_Oorder(A)|class_Orderings_Oorder(tc_fun(B,A)).
% 5.66/5.72 ** KEPT (pick-wt=6): 532 [] -class_Orderings_Otop(A)|class_Orderings_Otop(tc_fun(B,A)).
% 5.66/5.72 ** KEPT (pick-wt=6): 533 [] -class_Orderings_Oord(A)|class_Orderings_Oord(tc_fun(B,A)).
% 5.66/5.72 ** KEPT (pick-wt=6): 534 [] -class_Orderings_Obot(A)|class_Orderings_Obot(tc_fun(B,A)).
% 5.66/5.72 ** KEPT (pick-wt=8): 535 [] -class_Finite__Set_Ofinite(A)| -class_Finite__Set_Ofinite(B)|class_Finite__Set_Ofinite(tc_sum(A,B)).
% 5.66/5.72 ** KEPT (pick-wt=5): 536 [] -class_Finite__Set_Ofinite(A)|class_Finite__Set_Ofinite(tc_Option_Ooption(A)).
% 5.66/5.72 ** KEPT (pick-wt=8): 537 [] -class_Finite__Set_Ofinite(A)| -class_Finite__Set_Ofinite(B)|class_Finite__Set_Ofinite(tc_prod(A,B)).
% 5.66/5.72 ** KEPT (pick-wt=8): 538 [] -hBOOL(hAPP(c_fe_qual(A),B))|A=B.
% 5.66/5.72 ** KEPT (pick-wt=8): 539 [] A!=B|hBOOL(hAPP(c_fe_qual(A),B)).
% 5.66/5.72 ** KEPT (pick-wt=2): 540 [] -hBOOL(c_fFalse).
% 5.66/5.72 ** KEPT (pick-wt=28): 541 [] -c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,A,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))|c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,A,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))!=c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))|v_thesis____.
% 5.66/5.72 ** KEPT (pick-wt=1): 542 [] -v_thesis____.
% 5.66/5.72 157 back subsumes 37.
% 5.66/5.72 168 back subsumes 35.
% 5.66/5.72 179 back subsumes 43.
% 5.66/5.72 179 back subsumes 42.
% 5.66/5.72 Following clause subsumed by 241 during input processing: 0 [copy,240,flip.1] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,A).
% 5.66/5.72 Following clause subsumed by 240 during input processing: 0 [copy,241,flip.1] hAPP(c_Nat_OSuc,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.72 365 back subsumes 363.
% 5.66/5.72 366 back subsumes 364.
% 5.66/5.72 Following clause subsumed by 504 during input processing: 0 [copy,503,flip.1] c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))!=c_Set_Oinsert(A,B,C).
% 5.66/5.72 Following clause subsumed by 503 during input processing: 0 [copy,504,flip.1] c_Set_Oinsert(A,B,C)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 5.66/5.72
% 5.66/5.72 ------------> process sos:
% 5.66/5.72 ** KEPT (pick-wt=3): 612 [] A=A.
% 5.66/5.72 ** KEPT (pick-wt=7): 613 [] hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),B)).
% 5.66/5.72 ** KEPT (pick-wt=13): 614 [] c_Fun_Oinj__on(A,B,C,D)|c_member(A,$f3(D,C,B,A),D).
% 5.66/5.72 ** KEPT (pick-wt=13): 615 [] c_Fun_Oinj__on(A,B,C,D)|c_member(A,$f2(D,C,B,A),D).
% 5.66/5.72 ** KEPT (pick-wt=20): 616 [] c_Fun_Oinj__on(A,B,C,D)|hAPP(C,$f3(D,C,B,A))=hAPP(C,$f2(D,C,B,A)).
% 5.66/5.72 ** KEPT (pick-wt=2): 617 [] c_Arrow__Order__Mirabelle_OIIA(v_F).
% 5.66/5.72 ** KEPT (pick-wt=2): 618 [] c_Arrow__Order__Mirabelle_Ounanimity(v_F).
% 5.66/5.72 ** KEPT (pick-wt=6): 619 [] c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))).
% 5.66/5.72 ** KEPT (pick-wt=9): 620 [] c_Finite__Set_Ofinite(A,B)|c_Finite__Set_Ocard(A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.72 Following clause subsumed by 620 during input processing: 0 [] c_Finite__Set_Ocard(A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Finite__Set_Ofinite(A,B).
% 5.66/5.72 ** KEPT (pick-wt=6): 621 [] c_Finite__Set_Ofinite(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 5.66/5.72 ** KEPT (pick-wt=8): 622 [] c_Fun_Oinj__on(A,B,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 5.66/5.72 Following clause subsumed by 621 during input processing: 0 [] c_Finite__Set_Ofinite(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))).
% 5.66/5.72 ** KEPT (pick-wt=9): 623 [] c_Finite__Set_Ocard(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.72 ---> New Demodulator: 624 [new_demod,623] c_Finite__Set_Ocard(A,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.72 ** KEPT (pick-wt=5): 625 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 5.66/5.72 ** KEPT (pick-wt=9): 626 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)),B).
% 5.66/5.72 ** KEPT (pick-wt=7): 627 [] c_member(A,B,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))).
% 5.66/5.72 ** KEPT (pick-wt=6): 628 [] c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B)).
% 5.66/5.72 ** KEPT (pick-wt=5): 629 [] c_Orderings_Obot__class_Obot(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.72 ---> New Demodulator: 630 [new_demod,629] c_Orderings_Obot__class_Obot(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.72 ** KEPT (pick-wt=11): 631 [] A=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 5.66/5.72 Following clause subsumed by 631 during input processing: 0 [] A=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 5.66/5.72 Following clause subsumed by 631 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A)|hBOOL(hAPP(hAPP(C,B),A)).
% 5.66/5.72 ** KEPT (pick-wt=9): 632 [] c_Finite__Set_Ofinite(tc_Nat_Onat,A)|c_member(tc_Nat_Onat,$f13(A,B),A).
% 5.66/5.72 ** KEPT (pick-wt=6): 633 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,B).
% 5.66/5.72 ** KEPT (pick-wt=4): 634 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,A).
% 5.66/5.72 ** KEPT (pick-wt=8): 635 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,A).
% 5.66/5.72 ** KEPT (pick-wt=9): 636 [] c_Finite__Set_Ofinite(tc_Nat_Onat,A)|c_member(tc_Nat_Onat,$f15(A,B),A).
% 5.66/5.72 ** KEPT (pick-wt=12): 637 [] c_member(A,$f16(B,A),B)|B=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 5.66/5.72 ** KEPT (pick-wt=12): 638 [] c_member(A,$f17(B,A),B)|B=c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)).
% 5.66/5.72 ** KEPT (pick-wt=13): 639 [] c_Set_Oimage(A,B,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool)).
% 5.66/5.72 ** KEPT (pick-wt=9): 640 [] 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).
% 5.66/5.72 Following clause subsumed by 640 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).
% 5.66/5.72 ** KEPT (pick-wt=9): 641 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))).
% 5.66/5.72 Following clause subsumed by 625 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 5.66/5.72 ** KEPT (pick-wt=10): 642 [] c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)).
% 5.66/5.72 ** KEPT (pick-wt=13): 643 [] c_member(A,hAPP(B,C),c_Set_Oimage(D,A,B,c_Orderings_Otop__class_Otop(tc_fun(D,tc_HOL_Obool)))).
% 5.66/5.72 Following clause subsumed by 627 during input processing: 0 [] c_member(A,B,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool))).
% 5.66/5.72 ** KEPT (pick-wt=6): 644 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,A)).
% 5.66/5.72 ** KEPT (pick-wt=7): 645 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,A)).
% 5.66/5.72 ** KEPT (pick-wt=5): 646 [] c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,A).
% 5.66/5.72 ** KEPT (pick-wt=17): 648 [copy,647,flip.1] c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),hAPP(c_Nat_OSuc,B))=c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B)).
% 5.66/5.72 ---> New Demodulator: 649 [new_demod,648] c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),hAPP(c_Nat_OSuc,B))=c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B)).
% 5.66/5.72 ** KEPT (pick-wt=10): 650 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,hAPP(c_Nat_OSuc,B),A).
% 5.66/5.72 ** KEPT (pick-wt=10): 651 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,hAPP(c_Nat_OSuc,A)).
% 5.66/5.72 ** KEPT (pick-wt=13): 653 [copy,652,flip.1] c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.66/5.72 ---> New Demodulator: 654 [new_demod,653] c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.66/5.72 ** KEPT (pick-wt=18): 656 [copy,655,flip.1] c_Orderings_Otop__class_Otop(tc_fun(tc_sum(A,B),tc_HOL_Obool))=c_Sum__Type_OPlus(A,B,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(B,tc_HOL_Obool))).
% 5.66/5.72 ---> New Demodulator: 657 [new_demod,656] c_Orderings_Otop__class_Otop(tc_fun(tc_sum(A,B),tc_HOL_Obool))=c_Sum__Type_OPlus(A,B,c_Orderings_Otop__class_Otop(tc_fun(A,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(B,tc_HOL_Obool))).
% 5.66/5.72 ** KEPT (pick-wt=15): 658 [] c_Finite__Set_Ofinite(A,B)|c_Finite__Set_Ocard(tc_sum(A,C),c_Sum__Type_OPlus(A,C,B,D))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.72 ** KEPT (pick-wt=15): 659 [] c_Finite__Set_Ofinite(A,B)|c_Finite__Set_Ocard(tc_sum(C,A),c_Sum__Type_OPlus(C,A,D,B))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.72 ** KEPT (pick-wt=9): 660 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,A).
% 5.66/5.72 ** KEPT (pick-wt=15): 661 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)).
% 5.66/5.72 ** KEPT (pick-wt=15): 662 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 5.66/5.72 ---> New Demodulator: 663 [new_demod,662] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 5.66/5.72 ** KEPT (pick-wt=7): 664 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,A)).
% 5.66/5.72 ** KEPT (pick-wt=7): 665 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)).
% 5.66/5.72 ** KEPT (pick-wt=7): 666 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=A.
% 5.66/5.72 ---> New Demodulator: 667 [new_demod,666] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=A.
% 5.66/5.72 ** KEPT (pick-wt=7): 668 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)=A.
% 5.66/5.72 ---> New Demodulator: 669 [new_demod,668] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)=A.
% 5.66/5.72 ** KEPT (pick-wt=13): 670 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B)).
% 5.66/5.72 ** KEPT (pick-wt=13): 672 [copy,671,flip.1] hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B).
% 5.66/5.72 ---> New Demodulator: 673 [new_demod,672] hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B).
% 5.66/5.72 ** KEPT (pick-wt=13): 675 [copy,674,demod,673] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B).
% 5.66/5.72 ** KEPT (pick-wt=9): 677 [copy,676,demod,673] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B)).
% 5.66/5.72 ** KEPT (pick-wt=9): 679 [copy,678,demod,673] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,B),A)).
% 5.66/5.72 ** KEPT (pick-wt=13): 680 [] c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,A))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(A),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.66/5.72 ---> New Demodulator: 681 [new_demod,680] c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,A))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(A),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.66/5.72 ** KEPT (pick-wt=6): 682 [] c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.72 ---> New Demodulator: 683 [new_demod,682] c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.72 ** KEPT (pick-wt=15): 684 [] c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,A))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.66/5.72 ** KEPT (pick-wt=5): 685 [] c_Nat_Osize__class_Osize(tc_Nat_Onat,A)=A.
% 5.66/5.72 ---> New Demodulator: 686 [new_demod,685] c_Nat_Osize__class_Osize(tc_Nat_Onat,A)=A.
% 5.66/5.72 Following clause subsumed by 612 during input processing: 0 [demod,686] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.72 ** KEPT (pick-wt=6): 687 [] c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)).
% 5.66/5.72 ** KEPT (pick-wt=11): 688 [] c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B).
% 5.66/5.72 ---> New Demodulator: 689 [new_demod,688] c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B).
% 5.66/5.72 ** KEPT (pick-wt=17): 691 [copy,690,flip.1] c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),hAPP(c_Nat_OSuc,B))=c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)).
% 5.66/5.72 ---> New Demodulator: 692 [new_demod,691] c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),hAPP(c_Nat_OSuc,B))=c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)).
% 5.66/5.72 ** KEPT (pick-wt=5): 693 [] c_HOL_Obool_Obool__size(c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.72 ---> New Demodulator: 694 [new_demod,693] c_HOL_Obool_Obool__size(c_fTrue)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.72 ** KEPT (pick-wt=9): 695 [] c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 5.66/5.72 ---> New Demodulator: 696 [new_demod,695] c_Finite__Set_Ocard(tc_Product__Type_Ounit,c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool)))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 5.66/5.72 ** KEPT (pick-wt=7): 698 [copy,697,flip.1] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 5.66/5.72 ---> New Demodulator: 699 [new_demod,698] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 5.66/5.72 ** KEPT (pick-wt=9): 700 [] hAPP(c_Nat_OSuc,A)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A).
% 5.66/5.72 ** KEPT (pick-wt=9): 701 [] hAPP(c_Nat_OSuc,A)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 5.66/5.72 ** KEPT (pick-wt=5): 702 [] c_HOL_Obool_Obool__size(c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.72 ---> New Demodulator: 703 [new_demod,702] c_HOL_Obool_Obool__size(c_fFalse)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.66/5.72 ** KEPT (pick-wt=9): 704 [] c_Orderings_Oord__class_Oless__e_q(tc_fun(A,tc_HOL_Obool),B,c_Set_Oinsert(A,C,B)).
% 5.66/5.72 ** KEPT (pick-wt=19): 705 [] c_Set_Oimage(A,B,C,c_Set_Oinsert(A,D,E))=c_Set_Oinsert(B,hAPP(C,D),c_Set_Oimage(A,B,C,E)).
% 5.66/5.72 ** KEPT (pick-wt=12): 706 [] c_Set_Oinsert(A,B,c_Set_Oinsert(A,B,C))=c_Set_Oinsert(A,B,C).
% 5.66/5.72 ---> New Demodulator: 707 [new_demod,706] c_Set_Oinsert(A,B,c_Set_Oinsert(A,B,C))=c_Set_Oinsert(A,B,C).
% 5.66/5.72 ** KEPT (pick-wt=15): 708 [] c_Set_Oinsert(A,B,c_Set_Oinsert(A,C,D))=c_Set_Oinsert(A,C,c_Set_Oinsert(A,B,D)).
% 5.66/5.72 ** KEPT (pick-wt=7): 709 [] c_member(A,B,c_Set_Oinsert(A,B,C)).
% 5.66/5.72 ** KEPT (pick-wt=12): 711 [copy,710,demod,689,flip.1] c_Set_Oinsert(tc_Nat_Onat,A,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,A).
% 5.66/5.72 ---> New Demodulator: 712 [new_demod,711] c_Set_Oinsert(tc_Nat_Onat,A,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,A).
% 5.66/5.72 ** KEPT (pick-wt=13): 714 [copy,713,demod,689] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,A,B)=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)).
% 5.66/5.72 ** KEPT (pick-wt=11): 715 [] c_Set_Othe__elem(A,c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))=B.
% 5.66/5.72 ---> New Demodulator: 716 [new_demod,715] c_Set_Othe__elem(A,c_Set_Oinsert(A,B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))))=B.
% 5.66/5.72 ** KEPT (pick-wt=2): 717 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 5.66/5.72 ** KEPT (pick-wt=2): 718 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 5.66/5.72 ** KEPT (pick-wt=2): 719 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 5.66/5.72 ** KEPT (pick-wt=2): 720 [] class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 5.66/5.73 ** KEPT (pick-wt=2): 721 [] class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 5.66/5.73 ** KEPT (pick-wt=2): 722 [] class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 5.66/5.73 ** KEPT (pick-wt=2): 723 [] class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 5.66/5.73 ** KEPT (pick-wt=2): 724 [] class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 5.66/5.73 ** KEPT (pick-wt=2): 725 [] class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 5.66/5.73 ** KEPT (pick-wt=2): 726 [] class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 5.66/5.73 ** KEPT (pick-wt=2): 727 [] class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 5.66/5.73 ** KEPT (pick-wt=2): 728 [] class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 5.66/5.73 ** KEPT (pick-wt=2): 729 [] class_Orderings_Opreorder(tc_Nat_Onat).
% 5.66/5.73 ** KEPT (pick-wt=2): 730 [] class_Orderings_Olinorder(tc_Nat_Onat).
% 5.66/5.73 ** KEPT (pick-wt=2): 731 [] class_Groups_Omonoid__add(tc_Nat_Onat).
% 5.66/5.73 ** KEPT (pick-wt=2): 732 [] class_Orderings_Oorder(tc_Nat_Onat).
% 5.66/5.73 ** KEPT (pick-wt=2): 733 [] class_Orderings_Oord(tc_Nat_Onat).
% 5.66/5.73 ** KEPT (pick-wt=2): 734 [] class_Orderings_Obot(tc_Nat_Onat).
% 5.66/5.73 ** KEPT (pick-wt=2): 735 [] class_Groups_Ozero(tc_Nat_Onat).
% 5.66/5.73 ** KEPT (pick-wt=2): 736 [] class_Groups_Oone(tc_Nat_Onat).
% 5.66/5.73 ** KEPT (pick-wt=2): 737 [] class_Orderings_Opreorder(tc_HOL_Obool).
% 5.66/5.73 ** KEPT (pick-wt=2): 738 [] class_Finite__Set_Ofinite(tc_HOL_Obool).
% 5.66/5.73 ** KEPT (pick-wt=2): 739 [] class_Orderings_Oorder(tc_HOL_Obool).
% 5.66/5.73 ** KEPT (pick-wt=2): 740 [] class_Orderings_Otop(tc_HOL_Obool).
% 5.66/5.73 ** KEPT (pick-wt=2): 741 [] class_Orderings_Oord(tc_HOL_Obool).
% 5.66/5.73 ** KEPT (pick-wt=2): 742 [] class_Orderings_Obot(tc_HOL_Obool).
% 5.66/5.73 ** KEPT (pick-wt=2): 743 [] class_Finite__Set_Ofinite(tc_Product__Type_Ounit).
% 5.66/5.73 ** KEPT (pick-wt=2): 744 [] hBOOL(c_fTrue).
% 5.66/5.73 Following clause subsumed by 612 during input processing: 0 [copy,612,flip.1] A=A.
% 5.66/5.73 612 back subsumes 601.
% 5.66/5.73 612 back subsumes 600.
% 5.66/5.73 612 back subsumes 586.
% 5.66/5.73 612 back subsumes 559.
% 5.66/5.73 612 back subsumes 558.
% 5.66/5.73 612 back subsumes 557.
% 5.66/5.73 612 back subsumes 556.
% 5.66/5.73 612 back subsumes 555.
% 5.66/5.73 612 back subsumes 552.
% 5.66/5.73 612 back subsumes 550.
% 5.66/5.73 612 back subsumes 547.
% 5.66/5.73 612 back subsumes 546.
% 5.66/5.73 612 back subsumes 543.
% 5.66/5.73 >>>> Starting back demodulation with 624.
% 5.66/5.73 >>>> Starting back demodulation with 630.
% 5.66/5.73 ** KEPT (pick-wt=13): 745 [copy,639,flip.1] c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool))=c_Set_Oimage(B,A,C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool))).
% 5.66/5.73 ** KEPT (pick-wt=10): 746 [copy,642,flip.1] c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))=c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.66/5.73 >>>> Starting back demodulation with 649.
% 5.66/5.73 >>>> Starting back demodulation with 654.
% 5.66/5.73 >>>> Starting back demodulation with 657.
% 5.66/5.73 >> back demodulating 544 with 657.
% 5.66/5.73 >> back demodulating 18 with 657.
% 5.66/5.73 >> back demodulating 17 with 657.
% 5.66/5.73 >> back demodulating 16 with 657.
% 5.66/5.73 Following clause subsumed by 660 during input processing: 0 [copy,660,flip.1] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,A).
% 5.66/5.73 Following clause subsumed by 661 during input processing: 0 [copy,661,flip.1] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)).
% 5.66/5.73 >>>> Starting back demodulation with 663.
% 5.66/5.73 >>>> Starting back demodulation with 667.
% 5.66/5.73 >>>> Starting back demodulation with 669.
% 5.66/5.73 Following clause subsumed by 675 during input processing: 0 [copy,670,flip.1] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B).
% 5.66/5.73 >>>> Starting back demodulation with 673.
% 5.66/5.73 >> back demodulating 362 with 673.
% 5.66/5.73 >> back demodulating 361 with 673.
% 5.66/5.73 Following clause subsumed by 670 during input processing: 0 [copy,675,flip.1] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,hAPP(c_Nat_OSuc,B)).
% 5.66/5.73 >>>> Starting back demodulation with 681.
% 5.66/5.73 >>>> Starting back demodulation with 683.
% 5.66/5.73 ** KEPT (pick-wt=9): 749 [copy,684,flip.1,demod,686,699,686] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_OSuc,A).
% 5.66/5.73 >>>> Starting back demodulation with 686.
% 5.66/5.73 >> back demodulating 684 with 686.
% 5.66/5.73 >>>> Starting back demodulation with 689.
% 5.66/5.73 >> back demodulating 648 with 689.
% 5.66/5.73 >> back demodulating 518 with 689.
% 5.66/5.73 >> back demodulating 387 with 689.
% 5.66/5.73 >> back demodulating 386 with 689.
% 5.66/5.73 >>>> Starting back demodulation with 692.
% 5.66/5.73 >>>> Starting back demodulation with 694.
% 5.66/5.73 >>>> Starting back demodulation with 696.
% 5.66/5.73 >>>> Starting back demodulation with 699.
% 5.66/5.73 >> back demodulating 680 with 699.
% 5.66/5.73 >> back demodulating 583 with 699.
% 5.66/5.73 >> back demodulating 582 with 699.
% 5.66/5.73 >> back demodulating 581 with 699.
% 5.66/5.73 >> back demodulating 580 with 699.
% 5.66/5.73 >> back demodulating 432 with 699.
% 5.66/5.73 >> back demodulating 402 with 699.
% 5.66/5.73 >> back demodulating 401 with 699.
% 5.66/5.73 >> back demodulating 399 with 699.
% 5.66/5.73 >> back demodulating 398 with 699.
% 5.66/5.73 >> back demodulating 397 with 699.
% 5.66/5.73 >> back demodulating 396 with 699.
% 5.66/5.73 >> back demodulating 389 with 699.
% 5.66/5.73 >> back demodulating 358 with 699.
% 5.66/5.73 >> back demodulating 357 with 699.
% 5.66/5.73 >> back demodulating 356 with 699.
% 5.66/5.73 >> back demodulating 355 with 699.
% 5.66/5.73 >> back demodulating 354 with 699.
% 5.66/5.73 >> back demodulating 353 with 699.
% 5.66/5.73 >> back demodulating 352 with 699.
% 5.66/5.73 >> back demodulating 351 with 699.
% 5.66/5.73 >> back demodulating 350 with 699.
% 5.66/5.73 >> back demodulating 349 with 699.
% 5.66/5.73 >> back demodulating 348 with 699.
% 5.66/5.73 >> back demodulating 347 with 699.
% 5.66/5.73 >> back demodulating 245 with 699.
% 5.66/5.73 >> back demodulating 213 with 699.
% 5.66/5.73 ** KEPT (pick-wt=9): 782 [copy,700,flip.1] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A)=hAPP(c_Nat_OSuc,A).
% 5.66/5.73 Following clause subsumed by 749 during input processing: 0 [copy,701,flip.1] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat))=hAPP(c_Nat_OSuc,A).
% 5.66/5.73 >>>> Starting back demodulation with 703.
% 5.66/5.73 ** KEPT (pick-wt=19): 783 [copy,705,flip.1] c_Set_Oinsert(A,hAPP(B,C),c_Set_Oimage(D,A,B,E))=c_Set_Oimage(D,A,B,c_Set_Oinsert(D,C,E)).
% 5.66/5.73 >>>> Starting back demodulation with 707.
% 5.66/5.73 >> back demodulating 606 with 707.
% 5.66/5.73 >> back demodulating 605 with 707.
% 5.66/5.73 >> back demodulating 604 with 707.
% 5.66/5.73 >> back demodulating 603 with 707.
% 5.66/5.73 >> back demodulating 602 with 707.
% 5.66/5.73 Following clause subsumed by 708 during input processing: 0 [copy,708,flip.1] c_Set_Oinsert(A,B,c_Set_Oinsert(A,C,D))=c_Set_Oinsert(A,C,c_Set_Oinsert(A,B,D)).
% 5.66/5.73 >>>> Starting back demodulation with 712.
% 5.66/5.73 >>>> Starting back demodulation with 716.
% 5.66/5.73 Following clause subsumed by 639 during input processing: 0 [copy,745,flip.1] c_Set_Oimage(A,B,C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_HOL_Obool)))=c_Orderings_Obot__class_Obot(tc_fun(B,tc_HOL_Obool)).
% 5.66/5.73 Following clause subsumed by 642 during input processing: 0 [copy,746,flip.1] c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)).
% 5.66/5.73 Following clause subsumed by 701 during input processing: 0 [copy,749,flip.1] hAPP(c_Nat_OSuc,A)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 5.66/5.73 ** KEPT (pick-wt=15): 789 [copy,750,flip.1] c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B))=c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B).
% 5.66/5.73 753 back subsumes 413.
% 5.66/5.73 >>>> Starting back demodulation with 755.
% 5.66/5.73 Following clause subsumed by 700 during input processing: 0 [copy,782,flip.1] hAPP(c_Nat_OSuc,A)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),A).
% 5.66/5.73 Following clause subsumed by 705 during input processing: 0 [copy,783,flip.1] c_Set_Oimage(A,B,C,c_Set_Oinsert(A,D,E))=c_Set_Oinsert(B,hAPP(C,D),c_Set_Oimage(A,B,C,E)).
% 5.66/5.73 Following clause subsumed by 750 during input processing: 0 [copy,789,flip.1] c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,A),B)=c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,A,B)).
% 7.99/8.10
% 7.99/8.10 ======= end of input processing =======
% 7.99/8.10
% 7.99/8.10 =========== start of search ===========
% 7.99/8.10
% 7.99/8.10
% 7.99/8.10 Resetting weight limit to 2.
% 7.99/8.10
% 7.99/8.10
% 7.99/8.10 Resetting weight limit to 2.
% 7.99/8.10
% 7.99/8.10 sos_size=141
% 7.99/8.10
% 7.99/8.10 Search stopped because sos empty.
% 7.99/8.10
% 7.99/8.10
% 7.99/8.10 Search stopped because sos empty.
% 7.99/8.10
% 7.99/8.10 ============ end of search ============
% 7.99/8.10
% 7.99/8.10 -------------- statistics -------------
% 7.99/8.10 clauses given 142
% 7.99/8.10 clauses generated 152290
% 7.99/8.10 clauses kept 733
% 7.99/8.10 clauses forward subsumed 193
% 7.99/8.10 clauses back subsumed 20
% 7.99/8.10 Kbytes malloced 11718
% 7.99/8.10
% 7.99/8.10 ----------- times (seconds) -----------
% 7.99/8.10 user CPU time 2.49 (0 hr, 0 min, 2 sec)
% 7.99/8.10 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 7.99/8.10 wall-clock time 8 (0 hr, 0 min, 8 sec)
% 7.99/8.10
% 7.99/8.10 Process 26408 finished Wed Jul 27 09:16:59 2022
% 7.99/8.10 Otter interrupted
% 7.99/8.10 PROOF NOT FOUND
%------------------------------------------------------------------------------