TSTP Solution File: SCT102+1 by Otter---3.3

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SCT102+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n007.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 13:12:30 EDT 2022

% Result   : Unknown 5.94s 6.03s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SCT102+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.12  % Command  : otter-tptp-script %s
% 0.12/0.34  % Computer : n007.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Jul 27 08:49:31 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 5.94/6.00  ----- Otter 3.3f, August 2004 -----
% 5.94/6.00  The process was started by sandbox2 on n007.cluster.edu,
% 5.94/6.00  Wed Jul 27 08:49:31 2022
% 5.94/6.00  The command was "./otter".  The process ID is 18625.
% 5.94/6.00  
% 5.94/6.00  set(prolog_style_variables).
% 5.94/6.00  set(auto).
% 5.94/6.00     dependent: set(auto1).
% 5.94/6.00     dependent: set(process_input).
% 5.94/6.00     dependent: clear(print_kept).
% 5.94/6.00     dependent: clear(print_new_demod).
% 5.94/6.00     dependent: clear(print_back_demod).
% 5.94/6.00     dependent: clear(print_back_sub).
% 5.94/6.00     dependent: set(control_memory).
% 5.94/6.00     dependent: assign(max_mem, 12000).
% 5.94/6.00     dependent: assign(pick_given_ratio, 4).
% 5.94/6.00     dependent: assign(stats_level, 1).
% 5.94/6.00     dependent: assign(max_seconds, 10800).
% 5.94/6.00  clear(print_given).
% 5.94/6.00  
% 5.94/6.00  formula_list(usable).
% 5.94/6.00  all A (A=A).
% 5.94/6.00  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).
% 5.94/6.00  exists B_a B_b B_c c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),B_a),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),B_b),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),B_c),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))).
% 5.94/6.00  all T_a c_List_Odistinct(T_a,c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_list_H V_a_H T_a (c_List_Olist_ONil(T_a)!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H)).
% 5.94/6.00  all V_list_H V_a_H T_a (hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H)!=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_x T_a V_xs (V_xs!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)).
% 5.94/6.00  all V_xs V_x T_a (hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)!=V_xs).
% 5.94/6.00  all V_list_H_2 V_a_H_2 V_list_2 V_aa_2 T_a (hAPP(hAPP(c_List_Olist_OCons(T_a),V_aa_2),V_list_2)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H_2),V_list_H_2)<->V_aa_2=V_a_H_2&V_list_2=V_list_H_2).
% 5.94/6.00  all V_va V_v T_a (c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va)).
% 5.94/6.00  all V_x T_a (c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))).
% 5.94/6.00  all T_a V_xs (V_xs!=c_List_Olist_ONil(T_a)-> (c_List_Odistinct(T_a,V_xs)->c_List_Odistinct(T_a,c_List_Obutlast(T_a,V_xs)))).
% 5.94/6.00  all V_x T_a (class_Orderings_Olinorder(T_a)->c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))).
% 5.94/6.00  all V_x T_a V_xs ((V_xs=c_List_Olist_ONil(T_a)->c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=V_x)& (V_xs!=c_List_Olist_ONil(T_a)->c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=c_List_Olast(T_a,V_xs))).
% 5.94/6.00  all T_a (class_Orderings_Olinorder(T_a)->c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a))).
% 5.94/6.00  all V_xs T_a (class_Orderings_Olinorder(T_a)-> (V_xs!=c_List_Olist_ONil(T_a)-> (c_List_Olinorder__class_Osorted(T_a,V_xs)->c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs))))).
% 5.94/6.00  all T_a (class_Orderings_Olinorder(T_a)->c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a))).
% 5.94/6.00  all T_a (c_List_Obutlast(T_a,c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_x V_xs T_a (c_List_Odistinct(T_a,V_xs)->c_List_Odistinct(T_a,c_List_Oinsert(T_a,V_x,V_xs))).
% 5.94/6.00  all V_ys V_y V_xs V_x T_a (c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys)))).
% 5.94/6.00  all V_xs T_a (c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a))=V_xs).
% 5.94/6.00  all V_ys T_a (c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys)=V_ys).
% 5.94/6.00  all V_x T_a V_xs ((V_xs=c_List_Olist_ONil(T_a)->c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=c_List_Olist_ONil(T_a))& (V_xs!=c_List_Olist_ONil(T_a)->c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Obutlast(T_a,V_xs)))).
% 5.94/6.00  all V_x T_a V_xs (V_xs=c_List_Olist_ONil(T_a)->c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=V_x).
% 5.94/6.00  all V_x T_a V_xs (V_xs!=c_List_Olist_ONil(T_a)->c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=c_List_Olast(T_a,V_xs)).
% 5.94/6.00  all V_f2_2 V_f1_2 T_b T_a (c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2,c_List_Olist_ONil(T_b))=V_f1_2).
% 5.94/6.00  all V_list_2 V_aa_2 V_f2_2 V_f1_2 T_b T_a (c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_aa_2),V_list_2))=hAPP(hAPP(V_f2_2,V_aa_2),V_list_2)).
% 5.94/6.00  all T_a V_xs (V_xs!=c_List_Olist_ONil(T_a)->hAPP(hAPP(c_List_Oappend(T_a),c_List_Obutlast(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Olast(T_a,V_xs)),c_List_Olist_ONil(T_a)))=V_xs).
% 5.94/6.00  all V_ys_2 V_x_2 V_xs_2 T_a (hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))=V_ys_2<->V_ys_2!=c_List_Olist_ONil(T_a)&c_List_Obutlast(T_a,V_ys_2)=V_xs_2&c_List_Olast(T_a,V_ys_2)=V_x_2).
% 5.94/6.00  all V_f2_2 V_f1_2 T_b T_a (c_List_Olist_Olist__rec(T_a,T_b,V_f1_2,V_f2_2,c_List_Olist_ONil(T_b))=V_f1_2).
% 5.94/6.00  all V_list_2 V_aa_2 V_f2_2 V_f1_2 T_b T_a (c_List_Olist_Olist__rec(T_a,T_b,V_f1_2,V_f2_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_aa_2),V_list_2))=hAPP(hAPP(hAPP(V_f2_2,V_aa_2),V_list_2),c_List_Olist_Olist__rec(T_a,T_b,V_f1_2,V_f2_2,V_list_2))).
% 5.94/6.00  all T_a V_xs_2 (V_xs_2=c_List_Olist_ONil(T_a)<->c_List_Onull(T_a,V_xs_2)).
% 5.94/6.00  all V_xs_2 T_a (c_List_Onull(T_a,V_xs_2)<->V_xs_2=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all T_b c_List_Onull(T_b,c_List_Olist_ONil(T_b)).
% 5.94/6.00  all V_xs V_x T_a (-c_List_Onull(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))).
% 5.94/6.00  all V_x V_xs T_a (c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))))=V_x).
% 5.94/6.00  all V_zs V_ys V_xs T_a (hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs)=hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs))).
% 5.94/6.00  all V_ts_2 V_zs_2 V_ys_2 V_xs_2 T_a (hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)=hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_ts_2)<-> (exists B_us (V_xs_2=hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us)&hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2)=V_ts_2|hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us)=V_zs_2&V_ys_2=hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2)))).
% 5.94/6.00  all V_zs_2 V_ys_2 V_xs_2 T_a (hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)=hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2)<->V_ys_2=V_zs_2).
% 5.94/6.00  all V_zs_2 V_xs_2 V_ys_2 T_a (hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_xs_2)=hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_xs_2)<->V_ys_2=V_zs_2).
% 5.94/6.00  all V_us V_ys V_zs V_xs1 V_xs T_a (hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1)=V_zs-> (V_ys=hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)->hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)=hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us))).
% 5.94/6.00  all V_ys V_xs V_x T_a (hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_ys)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))).
% 5.94/6.00  all V_zs V_xs V_ys V_xs1 V_x T_a (hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1)=V_ys-> (V_xs=hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)->hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)=hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs))).
% 5.94/6.00  all V_ys T_a (hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys)=V_ys).
% 5.94/6.00  all V_ys_2 V_xs_2 T_a (c_List_Olist_ONil(T_a)=hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)<->V_xs_2=c_List_Olist_ONil(T_a)&V_ys_2=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_xs T_a (hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a))=V_xs).
% 5.94/6.00  all V_ys_2 T_a V_xs_2 (V_xs_2=hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)<->V_ys_2=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_xs_2 T_a V_ys_2 (V_ys_2=hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)<->V_xs_2=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_ys_2 V_xs_2 T_a (hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)=c_List_Olist_ONil(T_a)<->V_xs_2=c_List_Olist_ONil(T_a)&V_ys_2=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_ys_2 V_xs_2 T_a (hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)=V_xs_2<->V_ys_2=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_ys_2 V_xs_2 T_a (hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)=V_ys_2<->V_xs_2=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all T_a V_ys V_xs (V_xs=V_ys->V_xs=hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys)).
% 5.94/6.00  all V_xs_2 V_x_2 V_zs_2 V_ys_2 T_a (hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)<->V_ys_2=c_List_Olist_ONil(T_a)&V_zs_2=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)| (exists B_ys_H (V_ys_2=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H)&hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2)=V_xs_2))).
% 5.94/6.00  all V_zs_2 V_ys_2 V_xs_2 V_x_2 T_a (hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)=hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)<->V_ys_2=c_List_Olist_ONil(T_a)&hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)=V_zs_2| (exists B_ys_H (hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H)=V_ys_2&V_xs_2=hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2)))).
% 5.94/6.00  all V_y_2 V_ys_2 V_x_2 V_xs_2 T_a (hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))=hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a)))<->V_xs_2=V_ys_2&V_x_2=V_y_2).
% 5.94/6.00  all V_xs T_a V_ys ((V_ys=c_List_Olist_ONil(T_a)->c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=c_List_Obutlast(T_a,V_xs))& (V_ys!=c_List_Olist_ONil(T_a)->c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Obutlast(T_a,V_ys)))).
% 5.94/6.00  all V_xs T_a V_ys (V_ys=c_List_Olist_ONil(T_a)->c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=c_List_Olast(T_a,V_xs)).
% 5.94/6.00  all V_xs T_a V_ys (V_ys!=c_List_Olist_ONil(T_a)->c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=c_List_Olast(T_a,V_ys)).
% 5.94/6.00  all V_xs T_a V_ys ((V_ys=c_List_Olist_ONil(T_a)->c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=c_List_Olast(T_a,V_xs))& (V_ys!=c_List_Olist_ONil(T_a)->c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=c_List_Olast(T_a,V_ys))).
% 5.94/6.00  all V_x V_xs T_a (c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))))=V_xs).
% 5.94/6.00  all V_xs_2 T_a (hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a)))<->c_List_Onull(T_a,V_xs_2)).
% 5.94/6.00  all V_xs V_x T_b T_a (c_List_Orotate1(T_a,c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a)&c_List_Orotate1(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),V_xs))=hAPP(hAPP(c_List_Oappend(T_b),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),c_List_Olist_ONil(T_b)))).
% 5.94/6.00  all V_xs_2 V_x_2 V_f_2 T_a T_b (c_List_Omaps(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))=hAPP(hAPP(c_List_Oappend(T_a),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_b,T_a,V_f_2,V_xs_2))).
% 5.94/6.00  all V_xs_2 T_a V_P_2 (hBOOL(hAPP(V_P_2,c_List_Olist_ONil(T_a)))-> ((all B_x B_xs (hBOOL(hAPP(V_P_2,B_xs))->hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Oappend(T_a),B_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),c_List_Olist_ONil(T_a)))))))->hBOOL(hAPP(V_P_2,V_xs_2)))).
% 5.94/6.00  all T_a V_xs (V_xs!=c_List_Olist_ONil(T_a)-> -(all B_ys B_y (V_xs!=hAPP(hAPP(c_List_Oappend(T_a),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),c_List_Olist_ONil(T_a)))))).
% 5.94/6.00  all V_x V_i T_a (hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_i,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_i,V_x))).
% 5.94/6.00  all V_xs V_x T_a (c_List_Orev(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=hAPP(hAPP(c_List_Oappend(T_a),c_List_Orev(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))).
% 5.94/6.00  all V_ys_2 V_y_2 V_xs_2 T_a (c_List_Orev(T_a,V_xs_2)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)<->V_xs_2=hAPP(hAPP(c_List_Oappend(T_a),c_List_Orev(T_a,V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a)))).
% 5.94/6.00  all V_ys T_a V_xs (V_xs!=c_List_Olist_ONil(T_a)->c_List_Ohd(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=c_List_Ohd(T_a,V_xs)).
% 5.94/6.00  all V_ys T_a V_xs ((V_xs=c_List_Olist_ONil(T_a)->c_List_Ohd(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=c_List_Ohd(T_a,V_ys))& (V_xs!=c_List_Olist_ONil(T_a)->c_List_Ohd(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=c_List_Ohd(T_a,V_xs))).
% 5.94/6.00  all V_ys_2 V_xs_2 T_a (c_List_Orev(T_a,V_xs_2)=c_List_Orev(T_a,V_ys_2)<->V_xs_2=V_ys_2).
% 5.94/6.00  all V_ys_2 V_xs_2 T_a (c_List_Orev(T_a,V_xs_2)=V_ys_2<->V_xs_2=c_List_Orev(T_a,V_ys_2)).
% 5.94/6.00  all V_x V_n T_a (c_List_Orev(T_a,c_List_Oreplicate(T_a,V_n,V_x))=c_List_Oreplicate(T_a,V_n,V_x)).
% 5.94/6.00  all V_xs T_a (c_List_Orev(T_a,c_List_Orev(T_a,V_xs))=V_xs).
% 5.94/6.00  all V_y_2 V_x_2 T_a (hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(tc_List_Olist(T_a)),V_x_2),V_y_2))<->V_x_2=V_y_2).
% 5.94/6.00  all V_xs_2 T_a (c_List_Orev(T_a,V_xs_2)=c_List_Olist_ONil(T_a)<->V_xs_2=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_xs_2 T_a (c_List_Olist_ONil(T_a)=c_List_Orev(T_a,V_xs_2)<->V_xs_2=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all T_a (c_List_Orev(T_a,c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_ys V_xs T_a (c_List_Orev(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=hAPP(hAPP(c_List_Oappend(T_a),c_List_Orev(T_a,V_ys)),c_List_Orev(T_a,V_xs))).
% 5.94/6.00  all V_xs_2 T_a (c_List_Odistinct(T_a,c_List_Orev(T_a,V_xs_2))<->c_List_Odistinct(T_a,V_xs_2)).
% 5.94/6.00  all T_a V_xs (V_xs!=c_List_Olist_ONil(T_a)->c_List_Ohd(T_a,c_List_Orev(T_a,V_xs))=c_List_Olast(T_a,V_xs)).
% 5.94/6.00  all T_a V_xs (V_xs!=c_List_Olist_ONil(T_a)->c_List_Olast(T_a,c_List_Orev(T_a,V_xs))=c_List_Ohd(T_a,V_xs)).
% 5.94/6.00  all V_k V_x V_n T_a (hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_k,V_x))=hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_k,V_x)),c_List_Oreplicate(T_a,V_n,V_x))).
% 5.94/6.00  all V_xs V_x T_a (c_List_Ohd(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=V_x).
% 5.94/6.00  all V_xs_2 T_a (c_List_Orotate1(T_a,V_xs_2)=c_List_Olist_ONil(T_a)<->V_xs_2=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_xs_2 T_a (c_List_Odistinct(T_a,c_List_Orotate1(T_a,V_xs_2))<->c_List_Odistinct(T_a,V_xs_2)).
% 5.94/6.00  all V_xs_2 V_x_2 T_a (hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))=c_List_Orev(T_a,V_xs_2)<->V_xs_2=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))).
% 5.94/6.00  all V_x_2 V_xs_2 T_a (c_List_Orev(T_a,V_xs_2)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))<->V_xs_2=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))).
% 5.94/6.00  all V_xs V_x V_n T_a (hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_xs))).
% 5.94/6.00  all V_f_2 T_a T_b (c_List_Omaps(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b))=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all T_a V_xs (V_xs!=c_List_Olist_ONil(T_a)->c_List_Orotate1(T_a,V_xs)=hAPP(hAPP(c_List_Oappend(T_a),c_List_Otl(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Ohd(T_a,V_xs)),c_List_Olist_ONil(T_a)))).
% 5.94/6.00  all T_a (class_HOL_Oe_qual(T_a)->c_HOL_Oe_qual__class_Oe_qual(T_a)=c_fe_qual).
% 5.94/6.00  all V_x T_a (class_HOL_Oe_qual(T_a)->hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(T_a),V_x),V_x))).
% 5.94/6.00  all V_y_2 V_x_2 T_a (class_HOL_Oe_qual(T_a)-> (hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(T_a),V_x_2),V_y_2))<->V_x_2=V_y_2)).
% 5.94/6.00  all T_a (class_HOL_Oe_qual(T_a)->c_fe_qual=c_HOL_Oe_qual__class_Oe_qual(T_a)).
% 5.94/6.00  all V_xs_2 V_P_2 T_a (c_List_OdropWhile(T_a,V_P_2,V_xs_2)!=c_List_Olist_ONil(T_a)-> -hBOOL(hAPP(V_P_2,c_List_Ohd(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2))))).
% 5.94/6.00  all V_ys T_a V_xs (V_xs!=c_List_Olist_ONil(T_a)->c_List_Otl(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=hAPP(hAPP(c_List_Oappend(T_a),c_List_Otl(T_a,V_xs)),V_ys)).
% 5.94/6.00  all V_P_2 T_a (-c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a))).
% 5.94/6.00  all V_y T_a (-c_List_Omember(T_a,c_List_Olist_ONil(T_a),V_y)).
% 5.94/6.00  all V_xs V_x T_a (c_List_Otl(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=V_xs).
% 5.94/6.00  all T_a (c_List_Otl(T_a,c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_xs_2 T_a V_x_2 V_P_2 ((hBOOL(hAPP(V_P_2,V_x_2))->c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=c_List_OdropWhile(T_a,V_P_2,V_xs_2))& (-hBOOL(hAPP(V_P_2,V_x_2))->c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))).
% 5.94/6.00  all V_P_2 T_a (c_List_OdropWhile(T_a,V_P_2,c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_xs T_a (c_List_Odistinct(T_a,V_xs)->c_List_Odistinct(T_a,c_List_Otl(T_a,V_xs))).
% 5.94/6.00  all V_P_2 V_xs_2 T_a (c_List_Odistinct(T_a,V_xs_2)->c_List_Odistinct(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2))).
% 5.94/6.00  all V_xs T_a (class_Orderings_Olinorder(T_a)-> (c_List_Olinorder__class_Osorted(T_a,V_xs)->c_List_Olinorder__class_Osorted(T_a,c_List_Otl(T_a,V_xs)))).
% 5.94/6.00  all V_P_2 V_xs_2 T_a (class_Orderings_Olinorder(T_a)-> (c_List_Olinorder__class_Osorted(T_a,V_xs_2)->c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)))).
% 5.94/6.00  all V_y_2 V_xs_2 V_x_2 T_a (c_List_Omember(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),V_y_2)<->V_x_2=V_y_2|c_List_Omember(T_a,V_xs_2,V_y_2)).
% 5.94/6.00  all V_ys_2 V_y_2 V_xs_2 V_P_2 T_a (c_List_OdropWhile(T_a,V_P_2,V_xs_2)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)<->V_xs_2=hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))& -hBOOL(hAPP(V_P_2,V_y_2))).
% 5.94/6.00  all V_xs_2 V_P_2 T_a (hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),c_List_OdropWhile(T_a,V_P_2,V_xs_2))=V_xs_2).
% 5.94/6.00  all V_x T_a V_n (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_List_Ohd(T_a,c_List_Oreplicate(T_a,V_n,V_x))=V_x).
% 5.94/6.00  all V_x T_a V_n (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x))=V_x).
% 5.94/6.00  all T_a V_xs_2 (V_xs_2!=c_List_Olist_ONil(T_a)<-> (exists B_y B_ys (V_xs_2=hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys)))).
% 5.94/6.00  all T_a V_y (V_y!=c_List_Olist_ONil(T_a)-> -(all B_a B_list (V_y!=hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_list)))).
% 5.94/6.00  all V_f_2 T_a T_b (c_List_Omap__filter(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b))=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_l_2 V_xs_2 T_a V_x_2 V_P_2 (-hBOOL(hAPP(V_P_2,V_x_2))->c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2)))=c_List_OtakeWhile(T_a,V_P_2,V_xs_2)).
% 5.94/6.00  all V_P_2 T_a (c_List_OtakeWhile(T_a,V_P_2,c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_y_2 V_n_2 V_x_2 V_m_2 T_a (c_List_Oreplicate(T_a,V_m_2,V_x_2)=c_List_Oreplicate(T_a,V_n_2,V_y_2)<->V_m_2=V_n_2& (V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->V_x_2=V_y_2)).
% 5.94/6.00  all V_P_2 V_xs_2 T_a (c_List_Odistinct(T_a,V_xs_2)->c_List_Odistinct(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2))).
% 5.94/6.00  all V_P_2 V_xs_2 T_a (class_Orderings_Olinorder(T_a)-> (c_List_Olinorder__class_Osorted(T_a,V_xs_2)->c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))).
% 5.94/6.00  all V_x T_a (c_List_Oreplicate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x)=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_x_2 V_n_2 T_a (c_List_Olist_ONil(T_a)=c_List_Oreplicate(T_a,V_n_2,V_x_2)<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  all V_x_2 V_n_2 T_a (c_List_Oreplicate(T_a,V_n_2,V_x_2)=c_List_Olist_ONil(T_a)<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  all V_xs_2 T_a V_x_2 V_P_2 ((hBOOL(hAPP(V_P_2,V_x_2))->c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))& (-hBOOL(hAPP(V_P_2,V_x_2))->c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=c_List_Olist_ONil(T_a))).
% 5.94/6.00  all V_fa_2 T_a (c_List_Olist_Olist__size(T_a,V_fa_2,c_List_Olist_ONil(T_a))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  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))).
% 5.94/6.00  all T_a V_xs (V_xs!=c_List_Olist_ONil(T_a)->c_List_Ohd(T_a,V_xs)=hAPP(c_List_Onth(T_a,V_xs),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.94/6.00  all V_x_2 V_f_2 T_a T_b (class_Orderings_Olinorder(T_b)->hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olist_ONil(T_a))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))).
% 5.94/6.00  all T_a V_xs_2 (V_xs_2!=c_List_Olist_ONil(T_a)-> (c_List_Odistinct(T_a,V_xs_2)->c_List_OtakeWhile(T_a,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool,c_fe_qual),c_List_Olast(T_a,V_xs_2))),V_xs_2)=c_List_Obutlast(T_a,V_xs_2))).
% 5.94/6.00  all T_a (class_Groups_Omonoid__add(T_a)->hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 5.94/6.00  all V_xs_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2))<->c_List_Olinorder__class_Osorted(T_a,V_xs_2))).
% 5.94/6.00  all V_xs_2 V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)->hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),V_xs_2))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2))).
% 5.94/6.00  all V_xs_2 T_b V_y_2 V_x_2 V_f_2 T_a (class_Orderings_Olinorder(T_a)-> (hAPP(V_f_2,V_x_2)!=hAPP(V_f_2,V_y_2)->hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),V_xs_2)))).
% 5.94/6.00  all V_ys_2 V_xs_2 T_a (c_List_Otl(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))=c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Otl(T_a,V_ys_2),c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a,hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a)),V_ys_2)),V_xs_2)).
% 5.94/6.00  all V_xs_2 V_aa_2 V_f_2 T_a T_b (class_Orderings_Olinorder(T_b)->hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_aa_2),V_xs_2)!=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_xs T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Orev(T_a,V_xs))=hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)).
% 5.94/6.00  all V_xs_2 T_a (c_List_Orotate1(T_a,V_xs_2)=c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a,c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a)),hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))),V_xs_2)).
% 5.94/6.00  all V_xs V_x T_a (hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_x).
% 5.94/6.00  all V_xs_2 V_x_2 V_f_2 T_a T_b (c_List_Omap__filter(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))=c_Option_Ooption_Ooption__case(tc_List_Olist(T_a),T_a,c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2),hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olist_OCons(T_a)),c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2)),hAPP(V_f_2,V_x_2))).
% 5.94/6.00  all V_n_2 V_xs_2 V_x_2 T_a (hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_n_2)=c_Nat_Onat_Onat__case(T_a,V_x_2,c_List_Onth(T_a,V_xs_2),V_n_2)).
% 5.94/6.00  all V_xs_2 V_x_2 V_P_2 T_a (c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))<-> (hBOOL(hAPP(V_P_2,V_x_2))->c_List_Olist__all(T_a,c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool,c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a,c_fdisj,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot,V_P_2)),hAPP(c_fe_qual,V_x_2)),V_xs_2))& (-hBOOL(hAPP(V_P_2,V_x_2))->c_List_Olist__ex1(T_a,V_P_2,V_xs_2))).
% 5.94/6.00  all V_xs_2 T_a (c_List_Orev(T_a,V_xs_2)=hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)),V_xs_2)).
% 5.94/6.00  all V_xs_2 V_x_2 V_f_2 T_a T_b (class_Orderings_Olinorder(T_b)->c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))).
% 5.94/6.00  all V_ys V_x V_xs T_a (hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))=V_x).
% 5.94/6.00  all V_x_2 V_xs_2 T_a (class_Orderings_Olinorder(T_a)-> (c_List_Olinorder__class_Osorted(T_a,V_xs_2)->c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)))).
% 5.94/6.00  all V_ys V_xs T_a (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)->V_xs!=V_ys).
% 5.94/6.00  all V_xs_2 V_f_2 T_a T_b (class_Orderings_Olinorder(T_b)->hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)).
% 5.94/6.00  all V_xs T_a (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Orev(T_a,V_xs))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)).
% 5.94/6.00  all V_xs_2 V_x_2 V_aa_2 V_f_2 T_b T_a (hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_aa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))=hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(hAPP(V_f_2,V_aa_2),V_x_2)),V_xs_2)).
% 5.94/6.00  all V_x V_n T_a (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oreplicate(T_a,V_n,V_x))=V_n).
% 5.94/6.00  all V_aa_2 V_f_2 T_b T_a (hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_aa_2),c_List_Olist_ONil(T_b))=V_aa_2).
% 5.94/6.00  all V_ys_2 V_xs_2 V_aa_2 V_f_2 T_b T_a (hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_aa_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))=hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_aa_2),V_xs_2)),V_ys_2)).
% 5.94/6.00  all V_xs T_a (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Orotate1(T_a,V_xs))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)).
% 5.94/6.00  all V_xs_2 T_a (class_Orderings_Olinorder(T_a)->c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)=hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))),c_List_Olist_ONil(T_a)),V_xs_2)).
% 5.94/6.00  all V_xs_2 V_x_2 V_P_2 T_a (c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))<->hBOOL(hAPP(V_P_2,V_x_2))&c_List_Olist__all(T_a,V_P_2,V_xs_2)).
% 5.94/6.00  all V_P_2 T_a c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_ys_2 V_xs_2 V_P_2 T_a (c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))<->c_List_Olist__all(T_a,V_P_2,V_xs_2)&c_List_Olist__all(T_a,V_P_2,V_ys_2)).
% 5.94/6.00  all V_f_2 T_a T_b (class_Orderings_Olinorder(T_b)->c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_xs_2 V_P_2 T_a (c_List_Olist__all(T_a,V_P_2,c_List_Orev(T_a,V_xs_2))<->c_List_Olist__all(T_a,V_P_2,V_xs_2)).
% 5.94/6.00  all V_xs_2 V_f_2 T_a T_b (class_Orderings_Olinorder(T_b)-> (c_List_Odistinct(T_a,c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))<->c_List_Odistinct(T_a,V_xs_2))).
% 5.94/6.00  all V_xs_2 T_a (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_xs_2=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all T_a (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  all V_x_2 V_f_2 V_xs_2 T_a T_b (class_Orderings_Olinorder(T_b)-> (c_List_Odistinct(T_a,V_xs_2)->c_List_Odistinct(T_a,c_List_Olinorder__class_Oinsort__insert__key(T_a,T_b,V_f_2,V_x_2,V_xs_2)))).
% 5.94/6.00  all V_xs_2 T_a (class_Orderings_Olinorder(T_a)->c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2))).
% 5.94/6.00  all V_f2_2 V_f1_2 T_a (c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_f1_2).
% 5.94/6.00  all V_aa_2 V_xs_2 V_f_2 T_a T_b (c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_aa_2)=hAPP(c_List_Ofoldl(T_a,T_b,c_COMBC(T_b,T_a,T_a,V_f_2),V_aa_2),c_List_Orev(T_b,V_xs_2))).
% 5.94/6.00  all V_xs_2 V_aa_2 V_f_2 T_b T_a (hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_aa_2),V_xs_2)=c_List_Ofoldr(T_b,T_a,c_COMBC(T_a,T_b,T_a,V_f_2),c_List_Orev(T_b,V_xs_2),V_aa_2)).
% 5.94/6.00  all V_P_2 V_ys_2 T_b V_xs_2 T_a (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)-> (hBOOL(hAPP(hAPP(V_P_2,c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_b)))-> ((all B_x B_xs B_y B_ys (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),B_xs)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),B_ys)-> (hBOOL(hAPP(hAPP(V_P_2,B_xs),B_ys))->hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys))))))->hBOOL(hAPP(hAPP(V_P_2,V_xs_2),V_ys_2))))).
% 5.94/6.00  all V_xs_2 V_P_2 T_a (c_List_Olist__all(T_a,V_P_2,V_xs_2)<-> (all B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))->hBOOL(hAPP(V_P_2,hAPP(c_List_Onth(T_a,V_xs_2),B_n)))))).
% 5.94/6.00  all V_xs_2 V_P_2 T_a (c_List_OdropWhile(T_a,V_P_2,V_xs_2)=hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2)).
% 5.94/6.00  all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 5.94/6.00  all V_P_2 V_n_2 V_m_2 ((hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))-> ((V_m_2=V_n_2->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))-> ((hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))))).
% 5.94/6.00  all V_t V_s (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s),V_t))->V_s!=V_t).
% 5.94/6.00  all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))->V_m!=V_n).
% 5.94/6.00  all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n))).
% 5.94/6.00  all V_y V_x (V_x!=V_y-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y),V_x)))).
% 5.94/6.00  all V_n_2 V_m_2 (V_m_2!=V_n_2<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))).
% 5.94/6.00  all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n))).
% 5.94/6.00  all V_n (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))).
% 5.94/6.00  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 5.94/6.00  all V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))).
% 5.94/6.00  all V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 5.94/6.00  all V_xs T_a V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))->c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))=c_List_Olast(T_a,V_xs)).
% 5.94/6.00  all V_xs T_a (hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs)=V_xs).
% 5.94/6.00  all V_n T_a (hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_i V_xs T_a (c_List_Odistinct(T_a,V_xs)->c_List_Odistinct(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))).
% 5.94/6.00  all V_n V_xs T_a (class_Orderings_Olinorder(T_a)-> (c_List_Olinorder__class_Osorted(T_a,V_xs)->c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)))).
% 5.94/6.00  all V_xs V_n T_a (hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs))=c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))).
% 5.94/6.00  all V_xs V_n T_a (c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))=hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs))).
% 5.94/6.00  all V_xs V_n T_a (c_List_Otl(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))=hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Otl(T_a,V_xs))).
% 5.94/6.00  all V_xs V_n T_a (hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Otl(T_a,V_xs))=c_List_Otl(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))).
% 5.94/6.00  all V_xs_2 V_x_2 V_n_2 T_a (hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Odrop(T_a)),V_xs_2),V_n_2)).
% 5.94/6.00  all V_aa_2 V_xs_2 V_x_2 V_f_2 T_a T_b (c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_aa_2)=hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_aa_2))).
% 5.94/6.00  all V_aa_2 V_f_2 T_a T_b (c_List_Ofoldr(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b),V_aa_2)=V_aa_2).
% 5.94/6.00  all V_aa_2 V_ys_2 V_xs_2 V_f_2 T_a T_b (c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2),V_aa_2)=c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,c_List_Ofoldr(T_b,T_a,V_f_2,V_ys_2,V_aa_2))).
% 5.94/6.00  all V_n T_a V_xs (V_xs!=c_List_Olist_ONil(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))->c_List_Ohd(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))=hAPP(c_List_Onth(T_a,V_xs),V_n))).
% 5.94/6.00  all V_ys V_y V_xs V_n T_a (hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)->hAPP(c_List_Onth(T_a,V_xs),V_n)=V_y).
% 5.94/6.00  all T_a V_ys_2 V_xs_2 (V_xs_2=V_ys_2<->hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2)& (all B_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))->hAPP(c_List_Onth(T_a,V_xs_2),B_i)=hAPP(c_List_Onth(T_a,V_ys_2),B_i)))).
% 5.94/6.00  all V_x T_a V_n V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_n))->hAPP(c_List_Onth(T_a,c_List_Oreplicate(T_a,V_n,V_x)),V_i)=V_x).
% 5.94/6.00  all V_xs_2 T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))<->V_xs_2!=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_xs_2 T_a (c_List_Odistinct(T_a,V_xs_2)<-> (all B_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))-> (all B_j (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))-> (B_i!=B_j->hAPP(c_List_Onth(T_a,V_xs_2),B_i)!=hAPP(c_List_Onth(T_a,V_xs_2),B_j))))))).
% 5.94/6.00  all V_j_2 V_i_2 V_xs_2 T_a (c_List_Odistinct(T_a,V_xs_2)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))-> (hAPP(c_List_Onth(T_a,V_xs_2),V_i_2)=hAPP(c_List_Onth(T_a,V_xs_2),V_j_2)<->V_i_2=V_j_2)))).
% 5.94/6.00  all V_xs_2 V_P_2 T_a (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))-> -hBOOL(hAPP(V_P_2,hAPP(c_List_Onth(T_a,V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))))).
% 5.94/6.00  all V_xs_2 V_P_2 T_a V_j_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))->hAPP(c_List_Onth(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_j_2)=hAPP(c_List_Onth(T_a,V_xs_2),V_j_2)).
% 5.94/6.00  all V_y_2 V_xs_2 T_a (class_Orderings_Olinorder(T_a)-> (c_List_Olinorder__class_Osorted(T_a,c_List_Orev(T_a,V_xs_2))-> (V_xs_2=c_List_Olist_ONil(T_a)->c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2)=V_y_2)& (V_xs_2!=c_List_Olist_ONil(T_a)->c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2)=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_List_Onth(T_a,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2)))).
% 5.94/6.00  all V_xs_2 V_P_2 T_a V_j_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OdropWhile(T_a,V_P_2,V_xs_2))))->hAPP(c_List_Onth(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_j_2)=hAPP(c_List_Onth(T_a,V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))).
% 5.94/6.00  all V_xs T_a V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))->hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Onth(T_a,V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))=hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)).
% 5.94/6.00  all V_xs_2 V_P_2 T_a (c_List_Olist__ex(T_a,V_P_2,V_xs_2)<-> (exists B_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))&hBOOL(hAPP(V_P_2,hAPP(c_List_Onth(T_a,V_xs_2),B_n)))))).
% 5.94/6.00  all V_n_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))).
% 5.94/6.00  all V_ys V_xs T_a V_n ((hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))->hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n)=hAPP(c_List_Onth(T_a,V_xs),V_n))& (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))->hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n)=hAPP(c_List_Onth(T_a,V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))))).
% 5.94/6.00  all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_OSuc,V_n))).
% 5.94/6.00  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))).
% 5.94/6.00  all V_n hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))).
% 5.94/6.00  all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))=c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2))).
% 5.94/6.00  all V_m_2 V_n_2 (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)=c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),V_m_2)).
% 5.94/6.00  all V_n_2 V_m_2 (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))=c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat)),V_n_2)),V_m_2)).
% 5.94/6.00  all V_y V_x (hAPP(c_Nat_OSuc,V_x)=hAPP(c_Nat_OSuc,V_y)->V_x=V_y).
% 5.94/6.00  all V_n V_m (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))=V_m).
% 5.94/6.00  all V_k V_n V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k)).
% 5.94/6.00  all V_n V_k V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)).
% 5.94/6.00  all V_n V_m V_k (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)).
% 5.94/6.00  all V_n_2 V_k_2 V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)<->V_m_2=V_n_2).
% 5.94/6.00  all V_n_2 V_m_2 V_k_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)<->V_m_2=V_n_2).
% 5.94/6.00  all V_k V_j V_i (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j)).
% 5.94/6.00  all V_k V_j V_i (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))).
% 5.94/6.00  all V_k V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))).
% 5.94/6.00  all V_m V_n (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),V_m)=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),V_m)).
% 5.94/6.00  all V_m V_n (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n)=V_m).
% 5.94/6.00  all V_n V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n)=V_m).
% 5.94/6.00  all V_n V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)).
% 5.94/6.00  all V_n_2 V_m_2 T_a (class_Nat_Osemiring__char__0(T_a)-> (c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m_2)=c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n_2)<->V_m_2=V_n_2)).
% 5.94/6.00  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).
% 5.94/6.00  all V_n V_m (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m),V_n))).
% 5.94/6.00  all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))).
% 5.94/6.00  all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))).
% 5.94/6.00  all V_k_2 V_j_2 V_i_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2))).
% 5.94/6.00  all V_z V_y V_x (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z))).
% 5.94/6.00  all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))).
% 5.94/6.00  all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)).
% 5.94/6.00  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))<-> (exists B_k (V_n_2=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k))))).
% 5.94/6.00  all V_n V_m hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m))).
% 5.94/6.00  all V_n V_m T_a (class_Rings_Osemiring__1(T_a)->c_Nat_Osemiring__1__class_Oof__nat(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n))).
% 5.94/6.00  all V_m V_i hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))).
% 5.94/6.00  all V_m V_i hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))).
% 5.94/6.00  all V_n (hAPP(c_Nat_OSuc,V_n)!=V_n).
% 5.94/6.00  all V_n (V_n!=hAPP(c_Nat_OSuc,V_n)).
% 5.94/6.00  all V_d_2 V_c_2 V_ba_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_aa_2),V_ba_2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),V_ba_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),V_d_2))))).
% 5.94/6.00  all V_i V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i))),V_n))).
% 5.94/6.00  all V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))->hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n).
% 5.94/6.00  all V_n_2 V_m_2 (hAPP(hAPP(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))).
% 5.94/6.00  all V_n_2 V_m_2 (hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)<->V_m_2=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))).
% 5.94/6.00  all V_m V_n (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  all V_ba_2 V_aa_2 V_P_2 (hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_aa_2),V_ba_2)))<-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2),V_ba_2))->hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))& (all B_d (V_aa_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),B_d)->hBOOL(hAPP(V_P_2,B_d))))).
% 5.94/6.00  all V_ba_2 V_aa_2 V_P_2 (hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_aa_2),V_ba_2)))<-> -(hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2),V_ba_2))& -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| (exists B_d (V_aa_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),B_d)& -hBOOL(hAPP(V_P_2,B_d)))))).
% 5.94/6.00  all V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 5.94/6.00  all V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 5.94/6.00  all V_ba_2 V_aa_2 T_a (class_Groups_Oab__group__add(T_a)-> (V_aa_2=V_ba_2<->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_aa_2),V_ba_2)=c_Groups_Ozero__class_Ozero(T_a))).
% 5.94/6.00  all V_ba_2 V_aa_2 T_a (class_Groups_Ogroup__add(T_a)-> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_aa_2),V_ba_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_aa_2=V_ba_2)).
% 5.94/6.00  all V_d_2 V_c_2 V_ba_2 V_aa_2 T_a (class_Groups_Oab__group__add(T_a)-> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_aa_2),V_ba_2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2)-> (V_aa_2=V_ba_2<->V_c_2=V_d_2))).
% 5.94/6.00  all V_c V_a V_b T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)->V_b=V_c)).
% 5.94/6.00  all V_c V_b V_a T_a (class_Groups_Ocancel__ab__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)->V_b=V_c)).
% 5.94/6.00  all V_c V_b V_a T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)->V_b=V_c)).
% 5.94/6.00  all V_c_2 V_aa_2 V_ba_2 T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_aa_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_aa_2)<->V_ba_2=V_c_2)).
% 5.94/6.00  all V_c_2 V_ba_2 V_aa_2 T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ba_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_c_2)<->V_ba_2=V_c_2)).
% 5.94/6.00  all V_z V_y V_x T_a (class_Groups_Oordered__ab__group__add(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z)=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))).
% 5.94/6.00  all V_z V_y V_x T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z)=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z))).
% 5.94/6.00  all V_c V_b V_a T_a (class_Groups_Oab__semigroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))).
% 5.94/6.00  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b)=V_a).
% 5.94/6.00  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b)=V_a).
% 5.94/6.00  all V_n (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=V_n).
% 5.94/6.00  all V_n (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_n).
% 5.94/6.00  all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 5.94/6.00  all V_a T_a (class_Groups_Omonoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 5.94/6.00  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 5.94/6.00  all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a).
% 5.94/6.00  all V_a T_a (class_Groups_Omonoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a).
% 5.94/6.00  all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))).
% 5.94/6.00  all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))).
% 5.94/6.00  all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))))).
% 5.94/6.00  all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))))).
% 5.94/6.00  all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))))).
% 5.94/6.00  all V_ba_2 V_aa_2 V_c_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_aa_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_ba_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),V_ba_2)))).
% 5.94/6.00  all V_ba_2 V_c_2 V_aa_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_c_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),V_ba_2)))).
% 5.94/6.00  all V_n (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  all V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 5.94/6.00  all V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  all V_n V_m (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->V_m=V_n)).
% 5.94/6.00  all V_n V_k V_j (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k))).
% 5.94/6.00  all V_l V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_l))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))))).
% 5.94/6.00  all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_m)).
% 5.94/6.00  all V_nat_H (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_nat_H)).
% 5.94/6.00  all V_m (hAPP(c_Nat_OSuc,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  all V_nat_H_1 (hAPP(c_Nat_OSuc,V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_m)).
% 5.94/6.00  all V_m (hAPP(c_Nat_OSuc,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  all V_n_2 V_m_2 (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,V_m_2)))).
% 5.94/6.00  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=V_n_2).
% 5.94/6.00  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 5.94/6.00  all V_m_2 V_n_2 (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,V_m_2)))<->V_n_2=V_m_2)).
% 5.94/6.00  all V_m V_n (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_OSuc,V_m)))->V_m=V_n)).
% 5.94/6.00  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n)))).
% 5.94/6.00  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))-> (hAPP(c_Nat_OSuc,V_m)!=V_n->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)))).
% 5.94/6.00  all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i)),V_k)))).
% 5.94/6.00  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n)))-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->V_m=V_n)).
% 5.94/6.00  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))).
% 5.94/6.00  all V_n V_m (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))).
% 5.94/6.00  all V_n (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=V_n).
% 5.94/6.00  all V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 5.94/6.00  all V_n_2 V_m_2 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=V_m->V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  all V_j V_i (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i))).
% 5.94/6.00  all V_i V_j (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i))).
% 5.94/6.00  all V_n_2 V_m_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 5.94/6.00  all V_m V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)))).
% 5.94/6.00  all V_m V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)))).
% 5.94/6.00  all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)))).
% 5.94/6.00  all V_l V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))))).
% 5.94/6.00  all V_n V_m V_l V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)))).
% 5.94/6.00  all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_k))).
% 5.94/6.00  all V_zs_2 V_y_2 V_x_2 T_a (class_Groups_Osemigroup__add(T_a)->hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)),V_zs_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_y_2),V_zs_2))).
% 5.94/6.00  all V_xs V_m V_n T_a (hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs))=hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs)).
% 5.94/6.00  all V_nat_2 V_f2_2 V_f1_2 T_a (c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2))=hAPP(V_f2_2,V_nat_2)).
% 5.94/6.00  all V_list V_a T_a (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 5.94/6.00  all V_list_2 V_aa_2 V_fa_2 T_a (c_List_Olist_Olist__size(T_a,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_aa_2),V_list_2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_aa_2)),c_List_Olist_Olist__size(T_a,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 5.94/6.00  all V_ba_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),V_ba_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_aa_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_a))))).
% 5.94/6.00  all V_xs_2 V_x_2 V_P_2 T_a (c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))<->hBOOL(hAPP(V_P_2,V_x_2))|c_List_Olist__ex(T_a,V_P_2,V_xs_2)).
% 5.94/6.00  all V_P_2 T_a (-c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a))).
% 5.94/6.00  all V_ys_2 V_xs_2 V_P_2 T_a (c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))<->c_List_Olist__ex(T_a,V_P_2,V_xs_2)|c_List_Olist__ex(T_a,V_P_2,V_ys_2)).
% 5.94/6.00  all V_xs T_a V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))->hAPP(c_List_Onth(T_a,c_List_Orev(T_a,V_xs)),V_n)=hAPP(c_List_Onth(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_OSuc,V_n)))).
% 5.94/6.00  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_aa_2)))).
% 5.94/6.00  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))))).
% 5.94/6.00  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))))).
% 5.94/6.00  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))))).
% 5.94/6.00  all V_m_2 V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 5.94/6.00  all V_m V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)))).
% 5.94/6.00  all V_xs_2 V_P_2 T_a (c_List_Olist__ex(T_a,V_P_2,c_List_Orev(T_a,V_xs_2))<->c_List_Olist__ex(T_a,V_P_2,V_xs_2)).
% 5.94/6.00  all V_m T_a (class_Rings_Olinordered__semidom(T_a)-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m)),c_Groups_Ozero__class_Ozero(T_a)))).
% 5.94/6.00  all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))<-> (exists B_m (V_n_2=hAPP(c_Nat_OSuc,B_m)))).
% 5.94/6.00  all V_n_2 (hBOOL(hAPP(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)).
% 5.94/6.00  all V_n_2 V_m_2 (hBOOL(hAPP(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)&hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_n_2))))).
% 5.94/6.00  all T_a (class_Rings_Osemiring__1(T_a)->c_Nat_Osemiring__1__class_Oof__nat(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(T_a)).
% 5.94/6.00  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))).
% 5.94/6.00  all V_n_2 V_m_2 T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m_2)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)))).
% 5.94/6.00  all V_n V_m T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n))))).
% 5.94/6.00  all V_n V_m T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n)))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)))).
% 5.94/6.00  all V_zs_2 V_x_2 T_a (class_Groups_Omonoid__add(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_zs_2))=hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_zs_2)).
% 5.94/6.00  all V_n V_xs V_x T_a (hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n))=hAPP(c_List_Onth(T_a,V_xs),V_n)).
% 5.94/6.00  all V_xs V_n T_a (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)).
% 5.94/6.00  all V_ys V_xs T_a (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys))).
% 5.94/6.00  all V_xs V_x V_n T_a (hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)).
% 5.94/6.00  all V_xs V_x T_a (class_Groups_Omonoid__add(T_a)->hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs))).
% 5.94/6.00  all V_x V_n T_a (c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n),V_x)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_n,V_x))).
% 5.94/6.00  all V_ys V_xs T_a (class_Groups_Omonoid__add(T_a)->hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_ys))).
% 5.94/6.00  all V_xs_2 V_x_2 V_f_2 T_a T_b (class_Orderings_Olinorder(T_b)->hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))).
% 5.94/6.00  all V_x V_k V_i T_a (hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x))=c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x)).
% 5.94/6.00  all V_x V_m V_n T_a (c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_x)=hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_m,V_x))).
% 5.94/6.00  all V_xs V_n T_a (hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)=hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Otl(T_a,V_xs))).
% 5.94/6.00  all V_aa_2 V_xs_2 T_a (class_Groups_Oab__semigroup__add(T_a)->c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,V_aa_2)=hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_xs_2)).
% 5.94/6.00  all V_ys V_xs T_a (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(T_a,V_xs,V_ys))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys))).
% 5.94/6.00  all V_ys V_xs V_n T_a (hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys))).
% 5.94/6.00  all V_n V_ys V_xs T_a (hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))=hAPP(c_List_Onth(T_a,V_ys),V_n)).
% 5.94/6.00  all T_a (class_Groups_Omonoid__add(T_a)->c_List_Omonoid__add__class_Olistsum(T_a)=c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a))).
% 5.94/6.00  all V_xs_2 V_aa_2 T_a (class_Groups_Omonoid__add(T_a)->hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_xs_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 5.94/6.00  all V_xs_2 T_a (class_Groups_Omonoid__add(T_a)->hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_xs_2)=c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a))).
% 5.94/6.00  all V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))))).
% 5.94/6.00  all V_c V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))))).
% 5.94/6.00  all V_xs T_a V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))->hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Ohd(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))),c_List_Olist_ONil(T_a)))=hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)).
% 5.94/6.00  all V_y V_z V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))).
% 5.94/6.00  all V_z_2 V_w_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))<-> (exists B_n (V_z_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,B_n)))))).
% 5.94/6.00  all V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n))=c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))).
% 5.94/6.00  all V_z V_n V_m (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n)),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z)).
% 5.94/6.00  all V_n T_a (hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_i V_xs T_a (c_List_Odistinct(T_a,V_xs)->c_List_Odistinct(T_a,hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))).
% 5.94/6.00  all V_n V_xs T_a (class_Orderings_Olinorder(T_a)-> (c_List_Olinorder__class_Osorted(T_a,V_xs)->c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)))).
% 5.94/6.00  all V_xs T_a (hAPP(hAPP(c_List_Otake(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs)=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_xs_2 V_n_2 T_a (hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2)=c_List_Olist_ONil(T_a)<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_xs_2=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_xs V_x V_n T_a (hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs))).
% 5.94/6.00  all V_xs T_a V_n V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_n))->hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),V_i)=hAPP(c_List_Onth(T_a,V_xs),V_i)).
% 5.94/6.00  all V_xs V_m V_n T_a (hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs))=hAPP(hAPP(c_List_Odrop(T_a),V_m),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs))).
% 5.94/6.00  all V_xs V_m V_n T_a (hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs))=hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))).
% 5.94/6.00  all V_xs V_n T_a (hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))=V_xs).
% 5.94/6.00  all V_xs_2 V_P_2 T_a (c_List_OtakeWhile(T_a,V_P_2,V_xs_2)=hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2)).
% 5.94/6.00  all V_xs V_n T_a (hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Otl(T_a,V_xs))=c_List_Otl(T_a,hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs))).
% 5.94/6.00  all V_ys V_xs V_n T_a (hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys))).
% 5.94/6.00  all V_zs_2 V_ys_2 V_xs_2 T_a (hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)=V_zs_2<->V_xs_2=hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2)&V_ys_2=hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2)).
% 5.94/6.00  all V_xs T_a V_n (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))->hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Obutlast(T_a,V_xs))=hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)).
% 5.94/6.00  all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (V_x!=V_y-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))))).
% 5.94/6.00  all V_n_2 (c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 5.94/6.00  all V_n_2 V_m_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m_2)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))).
% 5.94/6.00  all V_xs_2 V_x_2 V_n_2 T_a (hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=c_Nat_Onat_Onat__case(tc_List_Olist(T_a),c_List_Olist_ONil(T_a),c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat,hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Otake(T_a)),V_xs_2)),V_n_2)).
% 5.94/6.00  all V_xs V_i T_a (c_List_Orev(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))=hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),c_List_Orev(T_a,V_xs))).
% 5.94/6.00  all V_xs V_i T_a (c_List_Orev(T_a,hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))=hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),c_List_Orev(T_a,V_xs))).
% 5.94/6.00  all V_n T_a V_xs (V_xs!=c_List_Olist_ONil(T_a)->hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)=hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Ohd(T_a,V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Otl(T_a,V_xs)))).
% 5.94/6.00  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 5.94/6.00  all V_xs T_a V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))->hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)=hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Onth(T_a,V_xs),V_i)),c_List_Olist_ONil(T_a)))).
% 5.94/6.00  all V_xs T_a V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))->V_xs=hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Onth(T_a,V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)))).
% 5.94/6.00  all V_n_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))).
% 5.94/6.00  all V_z V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))).
% 5.94/6.00  all V_a V_xs T_a V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))->hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_a)=hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)))).
% 5.94/6.00  all V_y_2 V_x_2 V_z_2 T_a (class_Orderings_Olinorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z_2),V_x_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z_2),V_y_2)))).
% 5.94/6.00  all V_k V_j V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k)))).
% 5.94/6.00  all V_y V_x (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x),V_y))|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y),V_x))).
% 5.94/6.00  all V_l_2 V_k_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_l_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))).
% 5.94/6.00  all V_k (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))).
% 5.94/6.00  all V_l_2 V_k_2 (hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(tc_Int_Oint),V_k_2),V_l_2))<->hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 5.94/6.00  all V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)=V_z).
% 5.94/6.00  all V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z).
% 5.94/6.00  all V_w V_z (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)).
% 5.94/6.00  all V_z V_y V_x (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z))).
% 5.94/6.00  all V_n_2 V_m_2 (c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m_2)=c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2)<->V_m_2=V_n_2).
% 5.94/6.00  all V_z3 V_z2 V_z1 (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3))).
% 5.94/6.00  all V_x V_i V_xs T_a (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)).
% 5.94/6.00  all V_x_2 V_k_2 V_xs_2 T_a (hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2)=c_List_Olist_ONil(T_a)<->V_xs_2=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_v V_i T_a (hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_v)=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_y V_i T_a (hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_y)=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_i V_xs T_a (hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_List_Onth(T_a,V_xs),V_i))=V_xs).
% 5.94/6.00  all V_x V_xs T_a V_j V_i (V_i!=V_j->hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j)=hAPP(c_List_Onth(T_a,V_xs),V_j)).
% 5.94/6.00  all V_y V_xs V_x T_a (hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)).
% 5.94/6.00  all V_y V_i V_xs V_x T_a (hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_i)),V_y)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y))).
% 5.94/6.00  all V_x_H V_x V_xs T_a V_i_H V_i (V_i!=V_i_H->hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H)=hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x)).
% 5.94/6.00  all V_y V_x V_i V_xs T_a (hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y)=hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y)).
% 5.94/6.00  all V_x T_a (class_Orderings_Opreorder(T_a)-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_x))).
% 5.94/6.00  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (V_x_2!=V_y_2<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)))).
% 5.94/6.00  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))|V_x_2=V_y_2)).
% 5.94/6.00  all V_y V_x T_a (class_Orderings_Olinorder(T_a)->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))).
% 5.94/6.00  all V_x_2 V_y_2 T_a (class_Orderings_Olinorder(T_a)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))<->V_x_2=V_y_2))).
% 5.94/6.00  all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (V_x!=V_y-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))))).
% 5.94/6.00  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->V_x!=V_y)).
% 5.94/6.00  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))).
% 5.94/6.00  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))).
% 5.94/6.00  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->V_x!=V_y)).
% 5.94/6.00  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))->V_y!=V_x)).
% 5.94/6.00  all V_b V_a T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)))).
% 5.94/6.00  all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)))).
% 5.94/6.00  all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c))))).
% 5.94/6.00  all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a))))).
% 5.94/6.00  all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))-> (V_b=V_c->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c))))).
% 5.94/6.00  all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))-> (V_b=V_c->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a))))).
% 5.94/6.00  all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z))))).
% 5.94/6.00  all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x))))).
% 5.94/6.00  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))-> -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)))).
% 5.94/6.00  all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))-> (V_x!=V_y->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))))).
% 5.94/6.00  all V_n V_ns V_k (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))->hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(c_List_Onth(tc_Nat_Onat,V_ns),V_k))).
% 5.94/6.00  all V_x V_ys V_xs T_a V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))->hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_i),V_x)=hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_ys)).
% 5.94/6.00  all V_y V_ys V_x V_xs T_a (hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_y)=hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys))).
% 5.94/6.00  all V_x V_xs T_a V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))->hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i)=V_x).
% 5.94/6.00  all V_x_2 V_xs_2 T_a V_i_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))-> (hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2)=V_xs_2<->hAPP(c_List_Onth(T_a,V_xs_2),V_i_2)=V_x_2)).
% 5.94/6.00  all V_x V_j V_xs T_a V_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))-> (V_i=V_j->hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j)=V_x)& (V_i!=V_j->hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j)=hAPP(c_List_Onth(T_a,V_xs),V_j))).
% 5.94/6.00  all V_v_2 V_i_2 V_xs_2 V_x_2 T_a (hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_i_2),V_v_2)=c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_v_2),V_xs_2),c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat,hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_COMBC(tc_Nat_Onat,T_a,tc_List_Olist(T_a),c_List_Olist__update(T_a,V_xs_2)),V_v_2)),V_i_2)).
% 5.94/6.00  all V_x V_ys V_xs T_a V_n ((hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))->hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x)=hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_n),V_x)),V_ys))& (-hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))->hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x)=hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist__update(T_a,V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_x)))).
% 5.94/6.00  all V_z_2 V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_z_2))&hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_z_2)))).
% 5.94/6.00  all V_y V_x (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_x)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_y))=c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y))).
% 5.94/6.00  all V_y_2 V_x_2 (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_x_2)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_y_2)))<->hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2),V_y_2))).
% 5.94/6.00  all V_k hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(tc_Int_Oint),V_k),V_k)).
% 5.94/6.00  all V_y_2 V_x_2 (c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_x_2)=c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_y_2)<->V_x_2=V_y_2).
% 5.94/6.00  c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  all V_b V_a V_x T_a (class_Orderings_Olinorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_a))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))))).
% 5.94/6.00  all V_a V_b V_x T_a (class_Orderings_Olinorder(T_a)-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_b))->hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))))).
% 5.94/6.00  all V_x_2 V_B_2 V_A_2 T_b T_a (class_Groups_Ominus(T_a)->hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2))).
% 5.94/6.00  all V_a T_a (class_Orderings_Olinorder(T_a)->hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a)=V_a).
% 5.94/6.00  all V_b V_a T_a (class_Orderings_Olinorder(T_a)->hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_a)).
% 5.94/6.00  all V_y V_x T_a (class_Orderings_Olinorder(T_a)->hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)).
% 5.94/6.00  all V_b V_a T_a (class_Orderings_Olinorder(T_a)->hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)).
% 5.94/6.00  all V_y V_x T_a (class_Orderings_Olinorder(T_a)->hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)).
% 5.94/6.00  all V_c V_a V_b T_a (class_Orderings_Olinorder(T_a)->hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c))=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c))).
% 5.94/6.00  all V_z V_y V_x T_a (class_Orderings_Olinorder(T_a)->hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z))=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z))).
% 5.94/6.00  all V_c V_b V_a T_a (class_Orderings_Olinorder(T_a)->hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c))).
% 5.94/6.00  all V_z V_y V_x T_a (class_Orderings_Olinorder(T_a)->hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z)=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z))).
% 5.94/6.00  all V_x_2 V_B_2 V_A_2 T_b T_a (class_Groups_Ominus(T_a)->hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2))).
% 5.94/6.00  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a).
% 5.94/6.00  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 5.94/6.00  all V_d V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))).
% 5.94/6.00  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b)).
% 5.94/6.00  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))).
% 5.94/6.00  all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d)).
% 5.94/6.00  all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d))).
% 5.94/6.00  all V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)).
% 5.94/6.00  all V_aa_2 V_ba_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_ba_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_aa_2)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 5.94/6.00  all V_P_2 V_xs_2 T_a V_n_2 ((all B_i (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i),V_n_2))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))->hBOOL(hAPP(V_P_2,hAPP(c_List_Onth(T_a,V_xs_2),B_i))))))-> ((hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))-> -hBOOL(hAPP(V_P_2,hAPP(c_List_Onth(T_a,V_xs_2),V_n_2))))->c_List_OtakeWhile(T_a,V_P_2,V_xs_2)=hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2))).
% 5.94/6.00  all V_xss_2 T_b V_xs_2 T_a (hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b),c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b),c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_Nat_Onat,c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b),c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_List_Ofilter(tc_List_Olist(T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b),c_fNot,hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool,c_fe_qual),c_List_Olist_ONil(T_b))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))).
% 5.94/6.00  all V_xs_2 V_P_2 T_a (hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Ofilter(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Ofilter(T_a,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot,V_P_2),V_xs_2)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)).
% 5.94/6.00  all V_xs_2 V_x_2 T_a (c_List_Oreplicate(T_a,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Ofilter(T_a,hAPP(c_fe_qual,V_x_2),V_xs_2)),V_x_2)=c_List_Ofilter(T_a,hAPP(c_fe_qual,V_x_2),V_xs_2)).
% 5.94/6.00  all V_xs_2 V_f_2 T_a V_x_2 V_P_2 T_b (class_Orderings_Olinorder(T_b)-> (-hBOOL(hAPP(V_P_2,V_x_2))->c_List_Ofilter(T_a,V_P_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2))=c_List_Ofilter(T_a,V_P_2,V_xs_2))).
% 5.94/6.00  all V_xs_2 V_f_2 V_P_2 T_a T_b (class_Orderings_Olinorder(T_b)->c_List_Ofilter(T_a,V_P_2,c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))=c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,c_List_Ofilter(T_a,V_P_2,V_xs_2))).
% 5.94/6.00  all V_xs_2 V_g_2 T_a (class_Orderings_Olinorder(T_a)->c_List_Olinorder__class_Osorted(T_a,c_List_Ofilter(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool,c_fe_qual),hAPP(V_g_2,V_xs_2)),V_xs_2))).
% 5.94/6.00  all V_n_2 T_a V_x_2 V_P_2 ((hBOOL(hAPP(V_P_2,V_x_2))->c_List_Ofilter(T_a,V_P_2,c_List_Oreplicate(T_a,V_n_2,V_x_2))=c_List_Oreplicate(T_a,V_n_2,V_x_2))& (-hBOOL(hAPP(V_P_2,V_x_2))->c_List_Ofilter(T_a,V_P_2,c_List_Oreplicate(T_a,V_n_2,V_x_2))=c_List_Olist_ONil(T_a))).
% 5.94/6.00  all V_xs_2 V_Q_2 V_P_2 T_a (c_List_Ofilter(T_a,V_P_2,c_List_Ofilter(T_a,V_Q_2,V_xs_2))=c_List_Ofilter(T_a,c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool,c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a,c_fconj,V_Q_2),V_P_2),V_xs_2)).
% 5.94/6.00  all V_xs_2 V_P_2 T_a (c_List_Orev(T_a,c_List_Ofilter(T_a,V_P_2,V_xs_2))=c_List_Ofilter(T_a,V_P_2,c_List_Orev(T_a,V_xs_2))).
% 5.94/6.00  all V_P_2 V_xs_2 T_a (c_List_Odistinct(T_a,V_xs_2)->c_List_Odistinct(T_a,c_List_Ofilter(T_a,V_P_2,V_xs_2))).
% 5.94/6.00  all V_ys_2 V_xs_2 V_P_2 T_a (c_List_Ofilter(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))=hAPP(hAPP(c_List_Oappend(T_a),c_List_Ofilter(T_a,V_P_2,V_xs_2)),c_List_Ofilter(T_a,V_P_2,V_ys_2))).
% 5.94/6.00  all V_P_2 T_a (c_List_Ofilter(T_a,V_P_2,c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a)).
% 5.94/6.00  all V_xs_2 T_a V_x_2 V_P_2 ((hBOOL(hAPP(V_P_2,V_x_2))->c_List_Ofilter(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Ofilter(T_a,V_P_2,V_xs_2)))& (-hBOOL(hAPP(V_P_2,V_x_2))->c_List_Ofilter(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=c_List_Ofilter(T_a,V_P_2,V_xs_2))).
% 5.94/6.00  all V_xs_2 T_a (c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a),c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Ofilter(tc_List_Olist(T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a),c_fNot,hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool,c_fe_qual),c_List_Olist_ONil(T_a))),V_xs_2))).
% 5.94/6.00  all V_xs_2 T_a (hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2))=c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a),c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.94/6.00  all T_a (c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a)))=c_List_Olist_ONil(tc_List_Olist(T_a))).
% 5.94/6.00  all V_xss T_a (c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss))=c_List_Otranspose(T_a,V_xss)).
% 5.94/6.00  all V_j_2 V_i_2 V_xs_2 T_a (c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Orev(tc_Nat_Onat,c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2))))-> (hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Ofilter(tc_List_Olist(T_a),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a),c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))))->hAPP(c_List_Onth(T_a,hAPP(c_List_Onth(tc_List_Olist(T_a),c_List_Otranspose(T_a,V_xs_2)),V_i_2)),V_j_2)=hAPP(c_List_Onth(T_a,hAPP(c_List_Onth(tc_List_Olist(T_a),V_xs_2),V_j_2)),V_i_2)))).
% 5.94/6.00  class_Enum_Oenum(tc_HOL_Obool).
% 5.94/6.00  all T_1 T_2 (class_Enum_Oenum(T_2)&class_Enum_Oenum(T_1)->class_Enum_Oenum(tc_fun(T_2,T_1))).
% 5.94/6.00  all T_2 T_1 (class_Orderings_Opreorder(T_1)->class_Orderings_Opreorder(tc_fun(T_2,T_1))).
% 5.94/6.00  all T_2 T_1 (class_Orderings_Oorder(T_1)->class_Orderings_Oorder(tc_fun(T_2,T_1))).
% 5.94/6.00  all T_2 T_1 (class_Orderings_Oord(T_1)->class_Orderings_Oord(tc_fun(T_2,T_1))).
% 5.94/6.00  all T_2 T_1 (class_Groups_Ominus(T_1)->class_Groups_Ominus(tc_fun(T_2,T_1))).
% 5.94/6.00  all T_1 T_2 (class_Enum_Oenum(T_2)&class_HOL_Oe_qual(T_1)->class_HOL_Oe_qual(tc_fun(T_2,T_1))).
% 5.94/6.00  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 5.94/6.00  class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 5.94/6.00  class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 5.94/6.00  class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 5.94/6.00  class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 5.94/6.00  class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 5.94/6.00  class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 5.94/6.00  class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 5.94/6.00  class_Rings_Olinordered__semidom(tc_Int_Oint).
% 5.94/6.00  class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 5.94/6.00  class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 5.94/6.00  class_Rings_Olinordered__idom(tc_Int_Oint).
% 5.94/6.00  class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 5.94/6.00  class_Groups_Osemigroup__add(tc_Int_Oint).
% 5.94/6.00  class_Nat_Osemiring__char__0(tc_Int_Oint).
% 5.94/6.00  class_Groups_Oab__group__add(tc_Int_Oint).
% 5.94/6.00  class_Orderings_Opreorder(tc_Int_Oint).
% 5.94/6.00  class_Orderings_Olinorder(tc_Int_Oint).
% 5.94/6.00  class_Groups_Omonoid__add(tc_Int_Oint).
% 5.94/6.00  class_Rings_Osemiring__1(tc_Int_Oint).
% 5.94/6.00  class_Groups_Ogroup__add(tc_Int_Oint).
% 5.94/6.00  class_Orderings_Oorder(tc_Int_Oint).
% 5.94/6.00  class_Orderings_Oord(tc_Int_Oint).
% 5.94/6.00  class_Groups_Ominus(tc_Int_Oint).
% 5.94/6.00  class_Groups_Ozero(tc_Int_Oint).
% 5.94/6.00  class_HOL_Oe_qual(tc_Int_Oint).
% 5.94/6.00  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 5.94/6.00  class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 5.94/6.00  class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 5.94/6.00  class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 5.94/6.00  class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 5.94/6.00  class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 5.94/6.00  class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 5.94/6.00  class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 5.94/6.00  class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 5.94/6.00  class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 5.94/6.00  class_Groups_Osemigroup__add(tc_Nat_Onat).
% 5.94/6.00  class_Nat_Osemiring__char__0(tc_Nat_Onat).
% 5.94/6.00  class_Orderings_Opreorder(tc_Nat_Onat).
% 5.94/6.00  class_Orderings_Olinorder(tc_Nat_Onat).
% 5.94/6.00  class_Groups_Omonoid__add(tc_Nat_Onat).
% 5.94/6.00  class_Rings_Osemiring__1(tc_Nat_Onat).
% 5.94/6.00  class_Orderings_Oorder(tc_Nat_Onat).
% 5.94/6.00  class_Orderings_Oord(tc_Nat_Onat).
% 5.94/6.00  class_Groups_Ominus(tc_Nat_Onat).
% 5.94/6.00  class_Groups_Ozero(tc_Nat_Onat).
% 5.94/6.00  class_HOL_Oe_qual(tc_Nat_Onat).
% 5.94/6.00  class_Orderings_Opreorder(tc_HOL_Obool).
% 5.94/6.00  class_Orderings_Oorder(tc_HOL_Obool).
% 5.94/6.00  class_Orderings_Oord(tc_HOL_Obool).
% 5.94/6.00  class_Groups_Ominus(tc_HOL_Obool).
% 5.94/6.00  class_HOL_Oe_qual(tc_HOL_Obool).
% 5.94/6.00  all T_1 class_HOL_Oe_qual(tc_List_Olist(T_1)).
% 5.94/6.00  all V_P T_a (hAPP(c_COMBI(T_a),V_P)=V_P).
% 5.94/6.00  all V_Q V_P T_b T_a (hAPP(c_COMBK(T_a,T_b,V_P),V_Q)=V_P).
% 5.94/6.00  all V_R_2 V_Q_2 V_P_2 T_c T_a T_b (hAPP(c_COMBB(T_b,T_a,T_c,V_P_2,V_Q_2),V_R_2)=hAPP(V_P_2,hAPP(V_Q_2,V_R_2))).
% 5.94/6.00  all V_R_2 V_Q_2 V_P_2 T_a T_c T_b (hAPP(hAPP(c_COMBC(T_b,T_c,T_a,V_P_2),V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),V_Q_2)).
% 5.94/6.00  all V_R_2 V_Q_2 V_P_2 T_a T_c T_b (hAPP(c_COMBS(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2))).
% 5.94/6.00  all V_y_2 V_x_2 (-hBOOL(hAPP(hAPP(c_fe_qual,V_x_2),V_y_2))|V_x_2=V_y_2).
% 5.94/6.00  all V_y_2 V_x_2 (V_x_2!=V_y_2|hBOOL(hAPP(hAPP(c_fe_qual,V_x_2),V_y_2))).
% 5.94/6.00  all V_P_2 (-hBOOL(hAPP(c_fNot,V_P_2))| -hBOOL(V_P_2)).
% 5.94/6.00  all V_P_2 (-(-hBOOL(V_P_2))|hBOOL(hAPP(c_fNot,V_P_2))).
% 5.94/6.00  all V_Q_2 V_P_2 (-hBOOL(V_P_2)| -hBOOL(V_Q_2)|hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))).
% 5.94/6.00  all V_Q_2 V_P_2 (-hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))|hBOOL(V_P_2)).
% 5.94/6.00  all V_Q_2 V_P_2 (-hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))|hBOOL(V_Q_2)).
% 5.94/6.00  all V_Q_2 V_P_2 (-hBOOL(V_P_2)|hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))).
% 5.94/6.00  all V_P_2 V_Q_2 (-hBOOL(V_Q_2)|hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))).
% 5.94/6.00  all V_Q_2 V_P_2 (-hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))|hBOOL(V_P_2)|hBOOL(V_Q_2)).
% 5.94/6.00  v_a!=v_b.
% 5.94/6.00  -(exists B_c c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_a),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_b),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),B_c),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt)))))).
% 5.94/6.00  end_of_list.
% 5.94/6.00  
% 5.94/6.00  -------> usable clausifies to:
% 5.94/6.00  
% 5.94/6.00  list(usable).
% 5.94/6.00  0 [] A=A.
% 5.94/6.00  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.
% 5.94/6.00  0 [] c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),$c3),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),$c2),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),$c1),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))).
% 5.94/6.00  0 [] c_List_Odistinct(T_a,c_List_Olist_ONil(T_a)).
% 5.94/6.00  0 [] c_List_Olist_ONil(T_a)!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H)!=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] V_xs!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)!=V_xs.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Olist_OCons(T_a),V_aa_2),V_list_2)!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H_2),V_list_H_2)|V_aa_2=V_a_H_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Olist_OCons(T_a),V_aa_2),V_list_2)!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H_2),V_list_H_2)|V_list_2=V_list_H_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Olist_OCons(T_a),V_aa_2),V_list_2)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H_2),V_list_H_2)|V_aa_2!=V_a_H_2|V_list_2!=V_list_H_2.
% 5.94/6.00  0 [] c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va).
% 5.94/6.00  0 [] c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)).
% 5.94/6.00  0 [] V_xs=c_List_Olist_ONil(T_a)| -c_List_Odistinct(T_a,V_xs)|c_List_Odistinct(T_a,c_List_Obutlast(T_a,V_xs)).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_a)|c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))).
% 5.94/6.00  0 [] V_xs!=c_List_Olist_ONil(T_a)|c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=V_x.
% 5.94/6.00  0 [] V_xs=c_List_Olist_ONil(T_a)|c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=c_List_Olast(T_a,V_xs).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_a)|c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_a)|V_xs=c_List_Olist_ONil(T_a)| -c_List_Olinorder__class_Osorted(T_a,V_xs)|c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_a)|c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)).
% 5.94/6.00  0 [] c_List_Obutlast(T_a,c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] -c_List_Odistinct(T_a,V_xs)|c_List_Odistinct(T_a,c_List_Oinsert(T_a,V_x,V_xs)).
% 5.94/6.00  0 [] c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys))).
% 5.94/6.00  0 [] c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a))=V_xs.
% 5.94/6.00  0 [] c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys)=V_ys.
% 5.94/6.00  0 [] V_xs!=c_List_Olist_ONil(T_a)|c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] V_xs=c_List_Olist_ONil(T_a)|c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Obutlast(T_a,V_xs)).
% 5.94/6.00  0 [] V_xs!=c_List_Olist_ONil(T_a)|c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=V_x.
% 5.94/6.00  0 [] V_xs=c_List_Olist_ONil(T_a)|c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=c_List_Olast(T_a,V_xs).
% 5.94/6.00  0 [] c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2,c_List_Olist_ONil(T_b))=V_f1_2.
% 5.94/6.00  0 [] c_List_Olist_Olist__case(T_a,T_b,V_f1_2,V_f2_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_aa_2),V_list_2))=hAPP(hAPP(V_f2_2,V_aa_2),V_list_2).
% 5.94/6.00  0 [] V_xs=c_List_Olist_ONil(T_a)|hAPP(hAPP(c_List_Oappend(T_a),c_List_Obutlast(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Olast(T_a,V_xs)),c_List_Olist_ONil(T_a)))=V_xs.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))!=V_ys_2|V_ys_2!=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))!=V_ys_2|c_List_Obutlast(T_a,V_ys_2)=V_xs_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))!=V_ys_2|c_List_Olast(T_a,V_ys_2)=V_x_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))=V_ys_2|V_ys_2=c_List_Olist_ONil(T_a)|c_List_Obutlast(T_a,V_ys_2)!=V_xs_2|c_List_Olast(T_a,V_ys_2)!=V_x_2.
% 5.94/6.00  0 [] c_List_Olist_Olist__rec(T_a,T_b,V_f1_2,V_f2_2,c_List_Olist_ONil(T_b))=V_f1_2.
% 5.94/6.00  0 [] c_List_Olist_Olist__rec(T_a,T_b,V_f1_2,V_f2_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_aa_2),V_list_2))=hAPP(hAPP(hAPP(V_f2_2,V_aa_2),V_list_2),c_List_Olist_Olist__rec(T_a,T_b,V_f1_2,V_f2_2,V_list_2)).
% 5.94/6.00  0 [] V_xs_2!=c_List_Olist_ONil(T_a)|c_List_Onull(T_a,V_xs_2).
% 5.94/6.00  0 [] V_xs_2=c_List_Olist_ONil(T_a)| -c_List_Onull(T_a,V_xs_2).
% 5.94/6.00  0 [] -c_List_Onull(T_a,V_xs_2)|V_xs_2=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] c_List_Onull(T_a,V_xs_2)|V_xs_2!=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] c_List_Onull(T_b,c_List_Olist_ONil(T_b)).
% 5.94/6.00  0 [] -c_List_Onull(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)).
% 5.94/6.00  0 [] c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))))=V_x.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs)=hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)!=hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_ts_2)|V_xs_2=hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),$f2(V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a))|hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),$f2(V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a))=V_zs_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)!=hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_ts_2)|V_xs_2=hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),$f2(V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a))|V_ys_2=hAPP(hAPP(c_List_Oappend(T_a),$f2(V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a)),V_ts_2).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)!=hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_ts_2)|hAPP(hAPP(c_List_Oappend(T_a),$f2(V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a)),V_ys_2)=V_ts_2|hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),$f2(V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a))=V_zs_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)!=hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_ts_2)|hAPP(hAPP(c_List_Oappend(T_a),$f2(V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a)),V_ys_2)=V_ts_2|V_ys_2=hAPP(hAPP(c_List_Oappend(T_a),$f2(V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a)),V_ts_2).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)=hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_ts_2)|V_xs_2!=hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us)|hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2)!=V_ts_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)=hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_ts_2)|hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us)!=V_zs_2|V_ys_2!=hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)!=hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2)|V_ys_2=V_zs_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)=hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_zs_2)|V_ys_2!=V_zs_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_xs_2)!=hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_xs_2)|V_ys_2=V_zs_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_xs_2)=hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),V_xs_2)|V_ys_2!=V_zs_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1)!=V_zs|V_ys!=hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)|hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)=hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_ys)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1)!=V_ys|V_xs!=hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)|hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)=hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys)=V_ys.
% 5.94/6.00  0 [] c_List_Olist_ONil(T_a)!=hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)|V_xs_2=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] c_List_Olist_ONil(T_a)!=hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)|V_ys_2=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] c_List_Olist_ONil(T_a)=hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)|V_xs_2!=c_List_Olist_ONil(T_a)|V_ys_2!=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a))=V_xs.
% 5.94/6.00  0 [] V_xs_2!=hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)|V_ys_2=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] V_xs_2=hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)|V_ys_2!=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] V_ys_2!=hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)|V_xs_2=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] V_ys_2=hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)|V_xs_2!=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)!=c_List_Olist_ONil(T_a)|V_xs_2=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)!=c_List_Olist_ONil(T_a)|V_ys_2=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)=c_List_Olist_ONil(T_a)|V_xs_2!=c_List_Olist_ONil(T_a)|V_ys_2!=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)!=V_xs_2|V_ys_2=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)=V_xs_2|V_ys_2!=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)!=V_ys_2|V_xs_2=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)=V_ys_2|V_xs_2!=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] V_xs!=V_ys|V_xs=hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)|V_ys_2=c_List_Olist_ONil(T_a)|V_ys_2=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),$f3(V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a)).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)|V_ys_2=c_List_Olist_ONil(T_a)|hAPP(hAPP(c_List_Oappend(T_a),$f3(V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a)),V_zs_2)=V_xs_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)|V_zs_2=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)|V_ys_2=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),$f3(V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a)).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)|V_zs_2=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)|hAPP(hAPP(c_List_Oappend(T_a),$f3(V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a)),V_zs_2)=V_xs_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)|V_ys_2!=c_List_Olist_ONil(T_a)|V_zs_2!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)|V_ys_2!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H)|hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2)!=V_xs_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)!=hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)|V_ys_2=c_List_Olist_ONil(T_a)|hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),$f4(V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a))=V_ys_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)!=hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)|V_ys_2=c_List_Olist_ONil(T_a)|V_xs_2=hAPP(hAPP(c_List_Oappend(T_a),$f4(V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a)),V_zs_2).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)!=hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)|hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)=V_zs_2|hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),$f4(V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a))=V_ys_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)!=hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)|hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)=V_zs_2|V_xs_2=hAPP(hAPP(c_List_Oappend(T_a),$f4(V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a)),V_zs_2).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)=hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)|V_ys_2!=c_List_Olist_ONil(T_a)|hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)!=V_zs_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)=hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),V_zs_2)|hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H)!=V_ys_2|V_xs_2!=hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))!=hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a)))|V_xs_2=V_ys_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))!=hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a)))|V_x_2=V_y_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)))=hAPP(hAPP(c_List_Oappend(T_a),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a)))|V_xs_2!=V_ys_2|V_x_2!=V_y_2.
% 5.94/6.00  0 [] V_ys!=c_List_Olist_ONil(T_a)|c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=c_List_Obutlast(T_a,V_xs).
% 5.94/6.00  0 [] V_ys=c_List_Olist_ONil(T_a)|c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Obutlast(T_a,V_ys)).
% 5.94/6.00  0 [] V_ys!=c_List_Olist_ONil(T_a)|c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=c_List_Olast(T_a,V_xs).
% 5.94/6.00  0 [] V_ys=c_List_Olist_ONil(T_a)|c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=c_List_Olast(T_a,V_ys).
% 5.94/6.00  0 [] V_ys!=c_List_Olist_ONil(T_a)|c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=c_List_Olast(T_a,V_xs).
% 5.94/6.00  0 [] V_ys=c_List_Olist_ONil(T_a)|c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=c_List_Olast(T_a,V_ys).
% 5.94/6.00  0 [] c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))))=V_xs.
% 5.94/6.00  0 [] -hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a)))|c_List_Onull(T_a,V_xs_2).
% 5.94/6.00  0 [] hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(tc_List_Olist(T_a)),V_xs_2),c_List_Olist_ONil(T_a)))| -c_List_Onull(T_a,V_xs_2).
% 5.94/6.00  0 [] c_List_Orotate1(T_a,c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] c_List_Orotate1(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),V_xs))=hAPP(hAPP(c_List_Oappend(T_b),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),c_List_Olist_ONil(T_b))).
% 5.94/6.00  0 [] c_List_Omaps(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))=hAPP(hAPP(c_List_Oappend(T_a),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_b,T_a,V_f_2,V_xs_2)).
% 5.94/6.00  0 [] -hBOOL(hAPP(V_P_2,c_List_Olist_ONil(T_a)))|hBOOL(hAPP(V_P_2,$f5(V_xs_2,T_a,V_P_2)))|hBOOL(hAPP(V_P_2,V_xs_2)).
% 5.94/6.00  0 [] -hBOOL(hAPP(V_P_2,c_List_Olist_ONil(T_a)))| -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Oappend(T_a),$f5(V_xs_2,T_a,V_P_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),$f6(V_xs_2,T_a,V_P_2)),c_List_Olist_ONil(T_a)))))|hBOOL(hAPP(V_P_2,V_xs_2)).
% 5.94/6.00  0 [] V_xs=c_List_Olist_ONil(T_a)|V_xs=hAPP(hAPP(c_List_Oappend(T_a),$f8(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),$f7(T_a,V_xs)),c_List_Olist_ONil(T_a))).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_i,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_i,V_x)).
% 5.94/6.00  0 [] c_List_Orev(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=hAPP(hAPP(c_List_Oappend(T_a),c_List_Orev(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))).
% 5.94/6.00  0 [] c_List_Orev(T_a,V_xs_2)!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)|V_xs_2=hAPP(hAPP(c_List_Oappend(T_a),c_List_Orev(T_a,V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))).
% 5.94/6.00  0 [] c_List_Orev(T_a,V_xs_2)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)|V_xs_2!=hAPP(hAPP(c_List_Oappend(T_a),c_List_Orev(T_a,V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),c_List_Olist_ONil(T_a))).
% 5.94/6.00  0 [] V_xs=c_List_Olist_ONil(T_a)|c_List_Ohd(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=c_List_Ohd(T_a,V_xs).
% 5.94/6.00  0 [] V_xs!=c_List_Olist_ONil(T_a)|c_List_Ohd(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=c_List_Ohd(T_a,V_ys).
% 5.94/6.00  0 [] V_xs=c_List_Olist_ONil(T_a)|c_List_Ohd(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=c_List_Ohd(T_a,V_xs).
% 5.94/6.00  0 [] c_List_Orev(T_a,V_xs_2)!=c_List_Orev(T_a,V_ys_2)|V_xs_2=V_ys_2.
% 5.94/6.00  0 [] c_List_Orev(T_a,V_xs_2)=c_List_Orev(T_a,V_ys_2)|V_xs_2!=V_ys_2.
% 5.94/6.00  0 [] c_List_Orev(T_a,V_xs_2)!=V_ys_2|V_xs_2=c_List_Orev(T_a,V_ys_2).
% 5.94/6.00  0 [] c_List_Orev(T_a,V_xs_2)=V_ys_2|V_xs_2!=c_List_Orev(T_a,V_ys_2).
% 5.94/6.00  0 [] c_List_Orev(T_a,c_List_Oreplicate(T_a,V_n,V_x))=c_List_Oreplicate(T_a,V_n,V_x).
% 5.94/6.00  0 [] c_List_Orev(T_a,c_List_Orev(T_a,V_xs))=V_xs.
% 5.94/6.00  0 [] -hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(tc_List_Olist(T_a)),V_x_2),V_y_2))|V_x_2=V_y_2.
% 5.94/6.00  0 [] hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(tc_List_Olist(T_a)),V_x_2),V_y_2))|V_x_2!=V_y_2.
% 5.94/6.00  0 [] c_List_Orev(T_a,V_xs_2)!=c_List_Olist_ONil(T_a)|V_xs_2=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] c_List_Orev(T_a,V_xs_2)=c_List_Olist_ONil(T_a)|V_xs_2!=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] c_List_Olist_ONil(T_a)!=c_List_Orev(T_a,V_xs_2)|V_xs_2=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] c_List_Olist_ONil(T_a)=c_List_Orev(T_a,V_xs_2)|V_xs_2!=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] c_List_Orev(T_a,c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] c_List_Orev(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=hAPP(hAPP(c_List_Oappend(T_a),c_List_Orev(T_a,V_ys)),c_List_Orev(T_a,V_xs)).
% 5.94/6.00  0 [] -c_List_Odistinct(T_a,c_List_Orev(T_a,V_xs_2))|c_List_Odistinct(T_a,V_xs_2).
% 5.94/6.00  0 [] c_List_Odistinct(T_a,c_List_Orev(T_a,V_xs_2))| -c_List_Odistinct(T_a,V_xs_2).
% 5.94/6.00  0 [] V_xs=c_List_Olist_ONil(T_a)|c_List_Ohd(T_a,c_List_Orev(T_a,V_xs))=c_List_Olast(T_a,V_xs).
% 5.94/6.00  0 [] V_xs=c_List_Olist_ONil(T_a)|c_List_Olast(T_a,c_List_Orev(T_a,V_xs))=c_List_Ohd(T_a,V_xs).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_k,V_x))=hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_k,V_x)),c_List_Oreplicate(T_a,V_n,V_x)).
% 5.94/6.00  0 [] c_List_Ohd(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=V_x.
% 5.94/6.00  0 [] c_List_Orotate1(T_a,V_xs_2)!=c_List_Olist_ONil(T_a)|V_xs_2=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] c_List_Orotate1(T_a,V_xs_2)=c_List_Olist_ONil(T_a)|V_xs_2!=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] -c_List_Odistinct(T_a,c_List_Orotate1(T_a,V_xs_2))|c_List_Odistinct(T_a,V_xs_2).
% 5.94/6.00  0 [] c_List_Odistinct(T_a,c_List_Orotate1(T_a,V_xs_2))| -c_List_Odistinct(T_a,V_xs_2).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))!=c_List_Orev(T_a,V_xs_2)|V_xs_2=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))=c_List_Orev(T_a,V_xs_2)|V_xs_2!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)).
% 5.94/6.00  0 [] c_List_Orev(T_a,V_xs_2)!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))|V_xs_2=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)).
% 5.94/6.00  0 [] c_List_Orev(T_a,V_xs_2)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a))|V_xs_2!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_xs)).
% 5.94/6.00  0 [] c_List_Omaps(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b))=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] V_xs=c_List_Olist_ONil(T_a)|c_List_Orotate1(T_a,V_xs)=hAPP(hAPP(c_List_Oappend(T_a),c_List_Otl(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Ohd(T_a,V_xs)),c_List_Olist_ONil(T_a))).
% 5.94/6.00  0 [] -class_HOL_Oe_qual(T_a)|c_HOL_Oe_qual__class_Oe_qual(T_a)=c_fe_qual.
% 5.94/6.00  0 [] -class_HOL_Oe_qual(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(T_a),V_x),V_x)).
% 5.94/6.00  0 [] -class_HOL_Oe_qual(T_a)| -hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(T_a),V_x_2),V_y_2))|V_x_2=V_y_2.
% 5.94/6.00  0 [] -class_HOL_Oe_qual(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(T_a),V_x_2),V_y_2))|V_x_2!=V_y_2.
% 5.94/6.00  0 [] -class_HOL_Oe_qual(T_a)|c_fe_qual=c_HOL_Oe_qual__class_Oe_qual(T_a).
% 5.94/6.00  0 [] c_List_OdropWhile(T_a,V_P_2,V_xs_2)=c_List_Olist_ONil(T_a)| -hBOOL(hAPP(V_P_2,c_List_Ohd(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)))).
% 5.94/6.00  0 [] V_xs=c_List_Olist_ONil(T_a)|c_List_Otl(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=hAPP(hAPP(c_List_Oappend(T_a),c_List_Otl(T_a,V_xs)),V_ys).
% 5.94/6.00  0 [] -c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a)).
% 5.94/6.00  0 [] -c_List_Omember(T_a,c_List_Olist_ONil(T_a),V_y).
% 5.94/6.00  0 [] c_List_Otl(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=V_xs.
% 5.94/6.00  0 [] c_List_Otl(T_a,c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] -hBOOL(hAPP(V_P_2,V_x_2))|c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=c_List_OdropWhile(T_a,V_P_2,V_xs_2).
% 5.94/6.00  0 [] hBOOL(hAPP(V_P_2,V_x_2))|c_List_OdropWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2).
% 5.94/6.00  0 [] c_List_OdropWhile(T_a,V_P_2,c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] -c_List_Odistinct(T_a,V_xs)|c_List_Odistinct(T_a,c_List_Otl(T_a,V_xs)).
% 5.94/6.00  0 [] -c_List_Odistinct(T_a,V_xs_2)|c_List_Odistinct(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_a)| -c_List_Olinorder__class_Osorted(T_a,V_xs)|c_List_Olinorder__class_Osorted(T_a,c_List_Otl(T_a,V_xs)).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_a)| -c_List_Olinorder__class_Osorted(T_a,V_xs_2)|c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)).
% 5.94/6.00  0 [] -c_List_Omember(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),V_y_2)|V_x_2=V_y_2|c_List_Omember(T_a,V_xs_2,V_y_2).
% 5.94/6.00  0 [] c_List_Omember(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),V_y_2)|V_x_2!=V_y_2.
% 5.94/6.00  0 [] c_List_Omember(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),V_y_2)| -c_List_Omember(T_a,V_xs_2,V_y_2).
% 5.94/6.00  0 [] c_List_OdropWhile(T_a,V_P_2,V_xs_2)!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)|V_xs_2=hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)).
% 5.94/6.00  0 [] c_List_OdropWhile(T_a,V_P_2,V_xs_2)!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)| -hBOOL(hAPP(V_P_2,V_y_2)).
% 5.94/6.00  0 [] c_List_OdropWhile(T_a,V_P_2,V_xs_2)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2)|V_xs_2!=hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2))|hBOOL(hAPP(V_P_2,V_y_2)).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Oappend(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),c_List_OdropWhile(T_a,V_P_2,V_xs_2))=V_xs_2.
% 5.94/6.00  0 [] V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Ohd(T_a,c_List_Oreplicate(T_a,V_n,V_x))=V_x.
% 5.94/6.00  0 [] V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x))=V_x.
% 5.94/6.00  0 [] V_xs_2=c_List_Olist_ONil(T_a)|V_xs_2=hAPP(hAPP(c_List_Olist_OCons(T_a),$f10(T_a,V_xs_2)),$f9(T_a,V_xs_2)).
% 5.94/6.00  0 [] V_xs_2!=c_List_Olist_ONil(T_a)|V_xs_2!=hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys).
% 5.94/6.00  0 [] V_y=c_List_Olist_ONil(T_a)|V_y=hAPP(hAPP(c_List_Olist_OCons(T_a),$f12(T_a,V_y)),$f11(T_a,V_y)).
% 5.94/6.00  0 [] c_List_Omap__filter(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b))=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] hBOOL(hAPP(V_P_2,V_x_2))|c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_l_2)))=c_List_OtakeWhile(T_a,V_P_2,V_xs_2).
% 5.94/6.00  0 [] c_List_OtakeWhile(T_a,V_P_2,c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] c_List_Oreplicate(T_a,V_m_2,V_x_2)!=c_List_Oreplicate(T_a,V_n_2,V_y_2)|V_m_2=V_n_2.
% 5.94/6.00  0 [] c_List_Oreplicate(T_a,V_m_2,V_x_2)!=c_List_Oreplicate(T_a,V_n_2,V_y_2)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x_2=V_y_2.
% 5.94/6.00  0 [] c_List_Oreplicate(T_a,V_m_2,V_x_2)=c_List_Oreplicate(T_a,V_n_2,V_y_2)|V_m_2!=V_n_2|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] c_List_Oreplicate(T_a,V_m_2,V_x_2)=c_List_Oreplicate(T_a,V_n_2,V_y_2)|V_m_2!=V_n_2|V_x_2!=V_y_2.
% 5.94/6.00  0 [] -c_List_Odistinct(T_a,V_xs_2)|c_List_Odistinct(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_a)| -c_List_Olinorder__class_Osorted(T_a,V_xs_2)|c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)).
% 5.94/6.00  0 [] c_List_Oreplicate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x)=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] c_List_Olist_ONil(T_a)!=c_List_Oreplicate(T_a,V_n_2,V_x_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] c_List_Olist_ONil(T_a)=c_List_Oreplicate(T_a,V_n_2,V_x_2)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] c_List_Oreplicate(T_a,V_n_2,V_x_2)!=c_List_Olist_ONil(T_a)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] c_List_Oreplicate(T_a,V_n_2,V_x_2)=c_List_Olist_ONil(T_a)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] -hBOOL(hAPP(V_P_2,V_x_2))|c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)).
% 5.94/6.00  0 [] hBOOL(hAPP(V_P_2,V_x_2))|c_List_OtakeWhile(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] c_List_Olist_Olist__size(T_a,V_fa_2,c_List_Olist_ONil(T_a))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  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).
% 5.94/6.00  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).
% 5.94/6.00  0 [] V_xs=c_List_Olist_ONil(T_a)|c_List_Ohd(T_a,V_xs)=hAPP(c_List_Onth(T_a,V_xs),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_b)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olist_ONil(T_a))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)).
% 5.94/6.00  0 [] V_xs_2=c_List_Olist_ONil(T_a)| -c_List_Odistinct(T_a,V_xs_2)|c_List_OtakeWhile(T_a,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool,c_fe_qual),c_List_Olast(T_a,V_xs_2))),V_xs_2)=c_List_Obutlast(T_a,V_xs_2).
% 5.94/6.00  0 [] -class_Groups_Omonoid__add(T_a)|hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_a)| -c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2))|c_List_Olinorder__class_Osorted(T_a,V_xs_2).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_a)|c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2))| -c_List_Olinorder__class_Osorted(T_a,V_xs_2).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_a)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),V_xs_2))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a)),V_x_2),V_xs_2)).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_a)|hAPP(V_f_2,V_x_2)=hAPP(V_f_2,V_y_2)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),V_xs_2))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_a,V_f_2),V_y_2),V_xs_2)).
% 5.94/6.00  0 [] c_List_Otl(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))=c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Otl(T_a,V_ys_2),c_COMBK(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a,hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a)),V_ys_2)),V_xs_2).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_b)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_aa_2),V_xs_2)!=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Orev(T_a,V_xs))=hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs).
% 5.94/6.00  0 [] c_List_Orotate1(T_a,V_xs_2)=c_List_Olist_Olist__case(tc_List_Olist(T_a),T_a,c_List_Olist_ONil(T_a),c_COMBB(tc_List_Olist(T_a),tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),T_a,c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Oappend(T_a)),hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a))),V_xs_2).
% 5.94/6.00  0 [] hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_x.
% 5.94/6.00  0 [] c_List_Omap__filter(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))=c_Option_Ooption_Ooption__case(tc_List_Olist(T_a),T_a,c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2),hAPP(c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olist_OCons(T_a)),c_List_Omap__filter(T_b,T_a,V_f_2,V_xs_2)),hAPP(V_f_2,V_x_2)).
% 5.94/6.00  0 [] hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_n_2)=c_Nat_Onat_Onat__case(T_a,V_x_2,c_List_Onth(T_a,V_xs_2),V_n_2).
% 5.94/6.00  0 [] -c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))| -hBOOL(hAPP(V_P_2,V_x_2))|c_List_Olist__all(T_a,c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool,c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a,c_fdisj,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot,V_P_2)),hAPP(c_fe_qual,V_x_2)),V_xs_2).
% 5.94/6.00  0 [] -c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))|hBOOL(hAPP(V_P_2,V_x_2))|c_List_Olist__ex1(T_a,V_P_2,V_xs_2).
% 5.94/6.00  0 [] c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))|hBOOL(hAPP(V_P_2,V_x_2))| -c_List_Olist__ex1(T_a,V_P_2,V_xs_2).
% 5.94/6.00  0 [] c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))| -c_List_Olist__all(T_a,c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool,c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a,c_fdisj,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot,V_P_2)),hAPP(c_fe_qual,V_x_2)),V_xs_2)| -hBOOL(hAPP(V_P_2,V_x_2)).
% 5.94/6.00  0 [] c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))| -c_List_Olist__all(T_a,c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool,c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a,c_fdisj,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot,V_P_2)),hAPP(c_fe_qual,V_x_2)),V_xs_2)| -c_List_Olist__ex1(T_a,V_P_2,V_xs_2).
% 5.94/6.00  0 [] c_List_Orev(T_a,V_xs_2)=hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olist_OCons(T_a)),c_List_Olist_ONil(T_a)),V_xs_2).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_b)|c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2)).
% 5.94/6.00  0 [] hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))=V_x.
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_a)| -c_List_Olinorder__class_Osorted(T_a,V_xs_2)|c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2)).
% 5.94/6.00  0 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)|V_xs!=V_ys.
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_b)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2).
% 5.94/6.00  0 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Orev(T_a,V_xs))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs).
% 5.94/6.00  0 [] hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_aa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))=hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(hAPP(V_f_2,V_aa_2),V_x_2)),V_xs_2).
% 5.94/6.00  0 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oreplicate(T_a,V_n,V_x))=V_n.
% 5.94/6.00  0 [] hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_aa_2),c_List_Olist_ONil(T_b))=V_aa_2.
% 5.94/6.00  0 [] hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_aa_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))=hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_aa_2),V_xs_2)),V_ys_2).
% 5.94/6.00  0 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Orotate1(T_a,V_xs))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_a)|c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)=hAPP(c_List_Ofoldl(tc_List_Olist(T_a),T_a,c_COMBC(T_a,tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Olinorder__class_Oinsort__key(T_a,T_a,c_COMBI(T_a))),c_List_Olist_ONil(T_a)),V_xs_2).
% 5.94/6.00  0 [] -c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))|hBOOL(hAPP(V_P_2,V_x_2)).
% 5.94/6.00  0 [] -c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))|c_List_Olist__all(T_a,V_P_2,V_xs_2).
% 5.94/6.00  0 [] c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))| -hBOOL(hAPP(V_P_2,V_x_2))| -c_List_Olist__all(T_a,V_P_2,V_xs_2).
% 5.94/6.00  0 [] c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)).
% 5.94/6.00  0 [] -c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))|c_List_Olist__all(T_a,V_P_2,V_xs_2).
% 5.94/6.00  0 [] -c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))|c_List_Olist__all(T_a,V_P_2,V_ys_2).
% 5.94/6.00  0 [] c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))| -c_List_Olist__all(T_a,V_P_2,V_xs_2)| -c_List_Olist__all(T_a,V_P_2,V_ys_2).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_b)|c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] -c_List_Olist__all(T_a,V_P_2,c_List_Orev(T_a,V_xs_2))|c_List_Olist__all(T_a,V_P_2,V_xs_2).
% 5.94/6.00  0 [] c_List_Olist__all(T_a,V_P_2,c_List_Orev(T_a,V_xs_2))| -c_List_Olist__all(T_a,V_P_2,V_xs_2).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_b)| -c_List_Odistinct(T_a,c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))|c_List_Odistinct(T_a,V_xs_2).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_b)|c_List_Odistinct(T_a,c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))| -c_List_Odistinct(T_a,V_xs_2).
% 5.94/6.00  0 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_xs_2=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_xs_2!=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_b)| -c_List_Odistinct(T_a,V_xs_2)|c_List_Odistinct(T_a,c_List_Olinorder__class_Oinsort__insert__key(T_a,T_b,V_f_2,V_x_2,V_xs_2)).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_a)|c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)).
% 5.94/6.00  0 [] c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_f1_2.
% 5.94/6.00  0 [] c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_aa_2)=hAPP(c_List_Ofoldl(T_a,T_b,c_COMBC(T_b,T_a,T_a,V_f_2),V_aa_2),c_List_Orev(T_b,V_xs_2)).
% 5.94/6.00  0 [] hAPP(c_List_Ofoldl(T_a,T_b,V_f_2,V_aa_2),V_xs_2)=c_List_Ofoldr(T_b,T_a,c_COMBC(T_a,T_b,T_a,V_f_2),c_List_Orev(T_b,V_xs_2),V_aa_2).
% 5.94/6.00  0 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)| -hBOOL(hAPP(hAPP(V_P_2,c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_b)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),$f15(V_P_2,V_ys_2,T_b,V_xs_2,T_a))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),$f13(V_P_2,V_ys_2,T_b,V_xs_2,T_a))|hBOOL(hAPP(hAPP(V_P_2,V_xs_2),V_ys_2)).
% 5.94/6.00  0 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)| -hBOOL(hAPP(hAPP(V_P_2,c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_b)))|hBOOL(hAPP(hAPP(V_P_2,$f15(V_P_2,V_ys_2,T_b,V_xs_2,T_a)),$f13(V_P_2,V_ys_2,T_b,V_xs_2,T_a)))|hBOOL(hAPP(hAPP(V_P_2,V_xs_2),V_ys_2)).
% 5.94/6.00  0 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)| -hBOOL(hAPP(hAPP(V_P_2,c_List_Olist_ONil(T_a)),c_List_Olist_ONil(T_b)))| -hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),$f16(V_P_2,V_ys_2,T_b,V_xs_2,T_a)),$f15(V_P_2,V_ys_2,T_b,V_xs_2,T_a))),hAPP(hAPP(c_List_Olist_OCons(T_b),$f14(V_P_2,V_ys_2,T_b,V_xs_2,T_a)),$f13(V_P_2,V_ys_2,T_b,V_xs_2,T_a))))|hBOOL(hAPP(hAPP(V_P_2,V_xs_2),V_ys_2)).
% 5.94/6.00  0 [] -c_List_Olist__all(T_a,V_P_2,V_xs_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))|hBOOL(hAPP(V_P_2,hAPP(c_List_Onth(T_a,V_xs_2),B_n))).
% 5.94/6.00  0 [] c_List_Olist__all(T_a,V_P_2,V_xs_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f17(V_xs_2,V_P_2,T_a)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))).
% 5.94/6.00  0 [] c_List_Olist__all(T_a,V_P_2,V_xs_2)| -hBOOL(hAPP(V_P_2,hAPP(c_List_Onth(T_a,V_xs_2),$f17(V_xs_2,V_P_2,T_a)))).
% 5.94/6.00  0 [] c_List_OdropWhile(T_a,V_P_2,V_xs_2)=hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=V_n_2|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))|hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s),V_t))|V_s!=V_t.
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))|V_m!=V_n.
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n)).
% 5.94/6.00  0 [] V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y),V_x)).
% 5.94/6.00  0 [] V_m_2=V_n_2|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)).
% 5.94/6.00  0 [] V_m_2!=V_n_2| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 5.94/6.00  0 [] V_m_2!=V_n_2| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n)).
% 5.94/6.00  0 [] V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.94/6.00  0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 5.94/6.00  0 [] V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))|c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))=c_List_Olast(T_a,V_xs).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs)=V_xs.
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] -c_List_Odistinct(T_a,V_xs)|c_List_Odistinct(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_a)| -c_List_Olinorder__class_Osorted(T_a,V_xs)|c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs))=c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)).
% 5.94/6.00  0 [] c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))=hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)).
% 5.94/6.00  0 [] c_List_Otl(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))=hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Otl(T_a,V_xs)).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Otl(T_a,V_xs))=c_List_Otl(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Odrop(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2),hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Odrop(T_a)),V_xs_2),V_n_2).
% 5.94/6.00  0 [] c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_aa_2)=hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,V_aa_2)).
% 5.94/6.00  0 [] c_List_Ofoldr(T_b,T_a,V_f_2,c_List_Olist_ONil(T_b),V_aa_2)=V_aa_2.
% 5.94/6.00  0 [] c_List_Ofoldr(T_b,T_a,V_f_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2),V_aa_2)=c_List_Ofoldr(T_b,T_a,V_f_2,V_xs_2,c_List_Ofoldr(T_b,T_a,V_f_2,V_ys_2,V_aa_2)).
% 5.94/6.00  0 [] V_xs=c_List_Olist_ONil(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))|c_List_Ohd(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))=hAPP(c_List_Onth(T_a,V_xs),V_n).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)!=hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)|hAPP(c_List_Onth(T_a,V_xs),V_n)=V_y.
% 5.94/6.00  0 [] V_xs_2!=V_ys_2|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2).
% 5.94/6.00  0 [] V_xs_2!=V_ys_2| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))|hAPP(c_List_Onth(T_a,V_xs_2),B_i)=hAPP(c_List_Onth(T_a,V_ys_2),B_i).
% 5.94/6.00  0 [] V_xs_2=V_ys_2|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f18(T_a,V_ys_2,V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))).
% 5.94/6.00  0 [] V_xs_2=V_ys_2|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2)|hAPP(c_List_Onth(T_a,V_xs_2),$f18(T_a,V_ys_2,V_xs_2))!=hAPP(c_List_Onth(T_a,V_ys_2),$f18(T_a,V_ys_2,V_xs_2)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_n))|hAPP(c_List_Onth(T_a,c_List_Oreplicate(T_a,V_n,V_x)),V_i)=V_x.
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))|V_xs_2!=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))|V_xs_2=c_List_Olist_ONil(T_a).
% 5.94/6.00  0 [] -c_List_Odistinct(T_a,V_xs_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))|B_i=B_j|hAPP(c_List_Onth(T_a,V_xs_2),B_i)!=hAPP(c_List_Onth(T_a,V_xs_2),B_j).
% 5.94/6.00  0 [] c_List_Odistinct(T_a,V_xs_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f20(V_xs_2,T_a)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))).
% 5.94/6.00  0 [] c_List_Odistinct(T_a,V_xs_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f19(V_xs_2,T_a)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))).
% 5.94/6.00  0 [] c_List_Odistinct(T_a,V_xs_2)|$f20(V_xs_2,T_a)!=$f19(V_xs_2,T_a).
% 5.94/6.00  0 [] c_List_Odistinct(T_a,V_xs_2)|hAPP(c_List_Onth(T_a,V_xs_2),$f20(V_xs_2,T_a))=hAPP(c_List_Onth(T_a,V_xs_2),$f19(V_xs_2,T_a)).
% 5.94/6.00  0 [] -c_List_Odistinct(T_a,V_xs_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))|hAPP(c_List_Onth(T_a,V_xs_2),V_i_2)!=hAPP(c_List_Onth(T_a,V_xs_2),V_j_2)|V_i_2=V_j_2.
% 5.94/6.00  0 [] -c_List_Odistinct(T_a,V_xs_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))|hAPP(c_List_Onth(T_a,V_xs_2),V_i_2)=hAPP(c_List_Onth(T_a,V_xs_2),V_j_2)|V_i_2!=V_j_2.
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))| -hBOOL(hAPP(V_P_2,hAPP(c_List_Onth(T_a,V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))))|hAPP(c_List_Onth(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)),V_j_2)=hAPP(c_List_Onth(T_a,V_xs_2),V_j_2).
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_a)| -c_List_Olinorder__class_Osorted(T_a,c_List_Orev(T_a,V_xs_2))|V_xs_2!=c_List_Olist_ONil(T_a)|c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2)=V_y_2.
% 5.94/6.00  0 [] -class_Orderings_Olinorder(T_a)| -c_List_Olinorder__class_Osorted(T_a,c_List_Orev(T_a,V_xs_2))|V_xs_2=c_List_Olist_ONil(T_a)|c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2)=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_List_Onth(T_a,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OdropWhile(T_a,V_P_2,V_xs_2))))|hAPP(c_List_Onth(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)),V_j_2)=hAPP(c_List_Onth(T_a,V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2)))).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))|hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Onth(T_a,V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))=hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs).
% 5.94/6.00  0 [] -c_List_Olist__ex(T_a,V_P_2,V_xs_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f21(V_xs_2,V_P_2,T_a)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))).
% 5.94/6.00  0 [] -c_List_Olist__ex(T_a,V_P_2,V_xs_2)|hBOOL(hAPP(V_P_2,hAPP(c_List_Onth(T_a,V_xs_2),$f21(V_xs_2,V_P_2,T_a)))).
% 5.94/6.00  0 [] c_List_Olist__ex(T_a,V_P_2,V_xs_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))| -hBOOL(hAPP(V_P_2,hAPP(c_List_Onth(T_a,V_xs_2),B_n))).
% 5.94/6.00  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 5.94/6.00  0 [] -class_Rings_Olinordered__semidom(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))|hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n)=hAPP(c_List_Onth(T_a,V_xs),V_n).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))|hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n)=hAPP(c_List_Onth(T_a,V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_OSuc,V_n))).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))=c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2)).
% 5.94/6.00  0 [] hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)=c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),V_m_2).
% 5.94/6.00  0 [] hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))=c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat)),V_n_2)),V_m_2).
% 5.94/6.00  0 [] hAPP(c_Nat_OSuc,V_x)!=hAPP(c_Nat_OSuc,V_y)|V_x=V_y.
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))=V_m.
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)|V_m_2=V_n_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)|V_m_2!=V_n_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2=V_n_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)|V_m_2!=V_n_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),V_m)=hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),V_m).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n)=V_m.
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n)=V_m.
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n).
% 5.94/6.00  0 [] -class_Nat_Osemiring__char__0(T_a)|c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m_2)!=c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n_2)|V_m_2=V_n_2.
% 5.94/6.00  0 [] -class_Nat_Osemiring__char__0(T_a)|c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m_2)=c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n_2)|V_m_2!=V_n_2.
% 5.94/6.00  0 [] hAPP(c_Nat_OSuc,V_nat_2)!=hAPP(c_Nat_OSuc,V_nat_H_2)|V_nat_2=V_nat_H_2.
% 5.94/6.00  0 [] hAPP(c_Nat_OSuc,V_nat_2)=hAPP(c_Nat_OSuc,V_nat_H_2)|V_nat_2!=V_nat_H_2.
% 5.94/6.00  0 [] hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m),V_n)).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_n_2=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),$f22(V_n_2,V_m_2))).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_n_2!=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m))).
% 5.94/6.00  0 [] -class_Rings_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n)).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))).
% 5.94/6.00  0 [] hAPP(c_Nat_OSuc,V_n)!=V_n.
% 5.94/6.00  0 [] V_n!=hAPP(c_Nat_OSuc,V_n).
% 5.94/6.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_aa_2),V_ba_2)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),V_ba_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),V_d_2)).
% 5.94/6.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_aa_2),V_ba_2)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),V_ba_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),V_d_2)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i))),V_n)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n.
% 5.94/6.00  0 [] hAPP(hAPP(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).
% 5.94/6.00  0 [] hAPP(hAPP(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)).
% 5.94/6.00  0 [] hAPP(hAPP(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).
% 5.94/6.00  0 [] hAPP(hAPP(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)).
% 5.94/6.00  0 [] hAPP(hAPP(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).
% 5.94/6.00  0 [] hAPP(hAPP(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)).
% 5.94/6.00  0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2=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)).
% 5.94/6.00  0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_aa_2),V_ba_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2),V_ba_2))|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.94/6.00  0 [] -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_aa_2),V_ba_2)))|V_aa_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 5.94/6.00  0 [] hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_aa_2),V_ba_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2),V_ba_2))|V_aa_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),$f23(V_ba_2,V_aa_2,V_P_2)).
% 5.94/6.00  0 [] hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_aa_2),V_ba_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2),V_ba_2))| -hBOOL(hAPP(V_P_2,$f23(V_ba_2,V_aa_2,V_P_2))).
% 5.94/6.00  0 [] hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_aa_2),V_ba_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_aa_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),$f23(V_ba_2,V_aa_2,V_P_2)).
% 5.94/6.00  0 [] hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_aa_2),V_ba_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f23(V_ba_2,V_aa_2,V_P_2))).
% 5.94/6.00  0 [] -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_aa_2),V_ba_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2),V_ba_2))|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.94/6.00  0 [] -hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_aa_2),V_ba_2)))|V_aa_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 5.94/6.00  0 [] hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_aa_2),V_ba_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2),V_ba_2))|V_aa_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),$f24(V_ba_2,V_aa_2,V_P_2)).
% 5.94/6.00  0 [] hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_aa_2),V_ba_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2),V_ba_2))| -hBOOL(hAPP(V_P_2,$f24(V_ba_2,V_aa_2,V_P_2))).
% 5.94/6.00  0 [] hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_aa_2),V_ba_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_aa_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),$f24(V_ba_2,V_aa_2,V_P_2)).
% 5.94/6.00  0 [] hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_aa_2),V_ba_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f24(V_ba_2,V_aa_2,V_P_2))).
% 5.94/6.00  0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 5.94/6.00  0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 5.94/6.00  0 [] -class_Groups_Oab__group__add(T_a)|V_aa_2!=V_ba_2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_aa_2),V_ba_2)=c_Groups_Ozero__class_Ozero(T_a).
% 5.94/6.00  0 [] -class_Groups_Oab__group__add(T_a)|V_aa_2=V_ba_2|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_aa_2),V_ba_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 5.94/6.00  0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_aa_2),V_ba_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=V_ba_2.
% 5.94/6.00  0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_aa_2),V_ba_2)=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=V_ba_2.
% 5.94/6.00  0 [] -class_Groups_Oab__group__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_aa_2),V_ba_2)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2)|V_aa_2!=V_ba_2|V_c_2=V_d_2.
% 5.94/6.00  0 [] -class_Groups_Oab__group__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_aa_2),V_ba_2)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2)|V_aa_2=V_ba_2|V_c_2!=V_d_2.
% 5.94/6.00  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)|V_b=V_c.
% 5.94/6.00  0 [] -class_Groups_Ocancel__ab__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)|V_b=V_c.
% 5.94/6.00  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)|V_b=V_c.
% 5.94/6.00  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_aa_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_aa_2)|V_ba_2=V_c_2.
% 5.94/6.00  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_aa_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_aa_2)|V_ba_2!=V_c_2.
% 5.94/6.00  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ba_2)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_c_2)|V_ba_2=V_c_2.
% 5.94/6.00  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_ba_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_c_2)|V_ba_2!=V_c_2.
% 5.94/6.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z)=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)).
% 5.94/6.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z)=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)).
% 5.94/6.00  0 [] -class_Groups_Oab__semigroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)).
% 5.94/6.00  0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b)=V_a.
% 5.94/6.00  0 [] -class_Groups_Ogroup__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b)=V_a.
% 5.94/6.00  0 [] hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=V_n.
% 5.94/6.00  0 [] hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_n.
% 5.94/6.00  0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 5.94/6.00  0 [] -class_Groups_Omonoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 5.94/6.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 5.94/6.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 5.94/6.00  0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 5.94/6.00  0 [] -class_Groups_Omonoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 5.94/6.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 5.94/6.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 5.94/6.00  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))).
% 5.94/6.00  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))).
% 5.94/6.00  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))).
% 5.94/6.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_aa_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_ba_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),V_ba_2)).
% 5.94/6.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_aa_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_ba_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),V_ba_2)).
% 5.94/6.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_c_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),V_ba_2)).
% 5.94/6.00  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_c_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),V_ba_2)).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m=V_n.
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_l))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))).
% 5.94/6.00  0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_m).
% 5.94/6.00  0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_nat_H).
% 5.94/6.00  0 [] hAPP(c_Nat_OSuc,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] hAPP(c_Nat_OSuc,V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,V_m).
% 5.94/6.00  0 [] hAPP(c_Nat_OSuc,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,V_m_2))).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,V_m_2))).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))|V_m_2=V_n_2.
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))|V_m_2!=V_n_2.
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,V_m_2)))|V_n_2=V_m_2.
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,V_m_2)))|V_n_2!=V_m_2.
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_OSuc,V_m)))|V_m=V_n.
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n))).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hAPP(c_Nat_OSuc,V_m)=V_n|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i)),V_k)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),hAPP(c_Nat_OSuc,V_n)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|V_m=V_n.
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)=V_n.
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)!=V_m|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_k)).
% 5.94/6.00  0 [] -class_Groups_Osemigroup__add(T_a)|hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2)),V_zs_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_y_2),V_zs_2)).
% 5.94/6.00  0 [] hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs))=hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs).
% 5.94/6.00  0 [] c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2))=hAPP(V_f2_2,V_nat_2).
% 5.94/6.00  0 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.94/6.00  0 [] c_List_Olist_Olist__size(T_a,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_aa_2),V_list_2))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_aa_2)),c_List_Olist_Olist__size(T_a,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.94/6.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),V_ba_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_aa_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_a))).
% 5.94/6.00  0 [] -class_Groups_Oordered__ab__group__add(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),V_ba_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_aa_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_a))).
% 5.94/6.00  0 [] -c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))|hBOOL(hAPP(V_P_2,V_x_2))|c_List_Olist__ex(T_a,V_P_2,V_xs_2).
% 5.94/6.00  0 [] c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))| -hBOOL(hAPP(V_P_2,V_x_2)).
% 5.94/6.00  0 [] c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))| -c_List_Olist__ex(T_a,V_P_2,V_xs_2).
% 5.94/6.00  0 [] -c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)).
% 5.94/6.00  0 [] -c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))|c_List_Olist__ex(T_a,V_P_2,V_xs_2)|c_List_Olist__ex(T_a,V_P_2,V_ys_2).
% 5.94/6.00  0 [] c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))| -c_List_Olist__ex(T_a,V_P_2,V_xs_2).
% 5.94/6.00  0 [] c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))| -c_List_Olist__ex(T_a,V_P_2,V_ys_2).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))|hAPP(c_List_Onth(T_a,c_List_Orev(T_a,V_xs)),V_n)=hAPP(c_List_Onth(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_OSuc,V_n))).
% 5.94/6.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_aa_2)).
% 5.94/6.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_aa_2)).
% 5.94/6.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))).
% 5.94/6.00  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))).
% 5.94/6.00  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))).
% 5.94/6.00  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)).
% 5.94/6.00  0 [] -c_List_Olist__ex(T_a,V_P_2,c_List_Orev(T_a,V_xs_2))|c_List_Olist__ex(T_a,V_P_2,V_xs_2).
% 5.94/6.00  0 [] c_List_Olist__ex(T_a,V_P_2,c_List_Orev(T_a,V_xs_2))| -c_List_Olist__ex(T_a,V_P_2,V_xs_2).
% 5.94/6.00  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m)),c_Groups_Ozero__class_Ozero(T_a))).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|V_n_2=hAPP(c_Nat_OSuc,$f25(V_n_2)).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))|V_n_2!=hAPP(c_Nat_OSuc,B_m).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.00  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=hAPP(c_Nat_OSuc,$f26(V_n_2,V_m_2)).
% 5.94/6.00  0 [] -hBOOL(hAPP(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)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f26(V_n_2,V_m_2)),V_n_2)).
% 5.94/6.00  0 [] hBOOL(hAPP(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).
% 5.94/6.00  0 [] hBOOL(hAPP(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)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_n_2)).
% 5.94/6.00  0 [] -class_Rings_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(T_a).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 5.94/6.01  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)).
% 5.94/6.01  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 5.94/6.01  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m_2)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 5.94/6.01  0 [] -class_Rings_Olinordered__semidom(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m_2)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 5.94/6.01  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n))).
% 5.94/6.01  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Nat_Osemiring__1__class_Oof__nat(T_a,V_m)),c_Nat_Osemiring__1__class_Oof__nat(T_a,V_n)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)).
% 5.94/6.01  0 [] -class_Groups_Omonoid__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_zs_2))=hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_zs_2).
% 5.94/6.01  0 [] hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n))=hAPP(c_List_Onth(T_a,V_xs),V_n).
% 5.94/6.01  0 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n).
% 5.94/6.01  0 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs).
% 5.94/6.01  0 [] -class_Groups_Omonoid__add(T_a)|hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)).
% 5.94/6.01  0 [] c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n),V_x)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_n,V_x)).
% 5.94/6.01  0 [] -class_Groups_Omonoid__add(T_a)|hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_ys)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_b)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x))=c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x).
% 5.94/6.01  0 [] c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_x)=hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_m,V_x)).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)=hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Otl(T_a,V_xs)).
% 5.94/6.01  0 [] -class_Groups_Oab__semigroup__add(T_a)|c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,V_aa_2)=hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_xs_2).
% 5.94/6.01  0 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(T_a,V_xs,V_ys))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)).
% 5.94/6.01  0 [] hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))=hAPP(c_List_Onth(T_a,V_ys),V_n).
% 5.94/6.01  0 [] -class_Groups_Omonoid__add(T_a)|c_List_Omonoid__add__class_Olistsum(T_a)=c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)).
% 5.94/6.01  0 [] -class_Groups_Omonoid__add(T_a)|hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_xs_2)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a))).
% 5.94/6.01  0 [] -class_Groups_Omonoid__add(T_a)|hAPP(c_List_Ofoldl(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_xs_2)=c_List_Ofoldr(T_a,T_a,c_Groups_Oplus__class_Oplus(T_a),V_xs_2,c_Groups_Ozero__class_Ozero(T_a)).
% 5.94/6.01  0 [] -class_Rings_Olinordered__idom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))).
% 5.94/6.01  0 [] -class_Rings_Olinordered__idom(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)),c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))).
% 5.94/6.01  0 [] -class_Rings_Olinordered__semidom(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))|hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Ohd(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))),c_List_Olist_ONil(T_a)))=hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))|V_z_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,$f27(V_z_2,V_w_2)))).
% 5.94/6.01  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))|V_z_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,B_n))).
% 5.94/6.01  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n))=c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)).
% 5.94/6.01  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n)),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a).
% 5.94/6.01  0 [] -c_List_Odistinct(T_a,V_xs)|c_List_Odistinct(T_a,hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)| -c_List_Olinorder__class_Osorted(T_a,V_xs)|c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Otake(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs)=c_List_Olist_ONil(T_a).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2)!=c_List_Olist_ONil(T_a)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_xs_2=c_List_Olist_ONil(T_a).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2)=c_List_Olist_ONil(T_a)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2)=c_List_Olist_ONil(T_a)|V_xs_2!=c_List_Olist_ONil(T_a).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_n))|hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),V_i)=hAPP(c_List_Onth(T_a,V_xs),V_i).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs))=hAPP(hAPP(c_List_Odrop(T_a),V_m),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs)).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs))=hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))=V_xs.
% 5.94/6.01  0 [] c_List_OtakeWhile(T_a,V_P_2,V_xs_2)=hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))),V_xs_2).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Otl(T_a,V_xs))=c_List_Otl(T_a,hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys))=hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)!=V_zs_2|V_xs_2=hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)!=V_zs_2|V_ys_2=hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)=V_zs_2|V_xs_2!=hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2)|V_ys_2!=hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),V_zs_2).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))|hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Obutlast(T_a,V_xs))=hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs).
% 5.94/6.01  0 [] -class_Rings_Olinordered__idom(T_a)|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 5.94/6.01  0 [] c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.01  0 [] c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.01  0 [] c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m_2)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 5.94/6.01  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m_2)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Otake(T_a),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=c_Nat_Onat_Onat__case(tc_List_Olist(T_a),c_List_Olist_ONil(T_a),c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat,hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_a),tc_List_Olist(T_a),c_List_Otake(T_a)),V_xs_2)),V_n_2).
% 5.94/6.01  0 [] c_List_Orev(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))=hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),c_List_Orev(T_a,V_xs)).
% 5.94/6.01  0 [] c_List_Orev(T_a,hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))=hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),c_List_Orev(T_a,V_xs)).
% 5.94/6.01  0 [] V_xs=c_List_Olist_ONil(T_a)|hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)=hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Ohd(T_a,V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Otl(T_a,V_xs))).
% 5.94/6.01  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 5.94/6.01  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_aa_2),V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))|hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)=hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Onth(T_a,V_xs),V_i)),c_List_Olist_ONil(T_a))).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))|V_xs=hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Onth(T_a,V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 5.94/6.01  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))|hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_a)=hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z_2),V_x_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z_2),V_y_2)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z_2),V_x_2)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z_2),V_y_2)).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))).
% 5.94/6.01  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x),V_y))|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y),V_x)).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_l_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 5.94/6.01  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_l_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 5.94/6.01  0 [] -hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(tc_Int_Oint),V_k_2),V_l_2))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 5.94/6.01  0 [] hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(tc_Int_Oint),V_k_2),V_l_2))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 5.94/6.01  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)=V_z.
% 5.94/6.01  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))=V_z.
% 5.94/6.01  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z).
% 5.94/6.01  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)).
% 5.94/6.01  0 [] c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m_2)!=c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2)|V_m_2=V_n_2.
% 5.94/6.01  0 [] c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_m_2)=c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_n_2)|V_m_2!=V_n_2.
% 5.94/6.01  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)).
% 5.94/6.01  0 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2)!=c_List_Olist_ONil(T_a)|V_xs_2=c_List_Olist_ONil(T_a).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2)=c_List_Olist_ONil(T_a)|V_xs_2!=c_List_Olist_ONil(T_a).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_v)=c_List_Olist_ONil(T_a).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_y)=c_List_Olist_ONil(T_a).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_List_Onth(T_a,V_xs),V_i))=V_xs.
% 5.94/6.01  0 [] V_i=V_j|hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j)=hAPP(c_List_Onth(T_a,V_xs),V_j).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_i)),V_y)=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y)).
% 5.94/6.01  0 [] V_i=V_i_H|hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H)=hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y)=hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y).
% 5.94/6.01  0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_x)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|V_x_2=V_y_2|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|V_x_2!=V_y_2| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|V_x_2!=V_y_2| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))|V_x_2=V_y_2.
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|V_x_2=V_y_2.
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))|V_x_2!=V_y_2.
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 5.94/6.01  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x!=V_y.
% 5.94/6.01  0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 5.94/6.01  0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 5.94/6.01  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x!=V_y.
% 5.94/6.01  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_y!=V_x.
% 5.94/6.01  0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)).
% 5.94/6.01  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)).
% 5.94/6.01  0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)).
% 5.94/6.01  0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)).
% 5.94/6.01  0 [] -class_Orderings_Oord(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))|V_b!=V_c|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)).
% 5.94/6.01  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))|V_b!=V_c|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)).
% 5.94/6.01  0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)).
% 5.94/6.01  0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)).
% 5.94/6.01  0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))|V_x=V_y|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))|hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(c_List_Onth(tc_Nat_Onat,V_ns),V_k)).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))|hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_i),V_x)=hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_ys).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_y)=hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))|hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i)=V_x.
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))|hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2)!=V_xs_2|hAPP(c_List_Onth(T_a,V_xs_2),V_i_2)=V_x_2.
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))|hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2)=V_xs_2|hAPP(c_List_Onth(T_a,V_xs_2),V_i_2)!=V_x_2.
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))|V_i!=V_j|hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j)=V_x.
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))|V_i=V_j|hAPP(c_List_Onth(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j)=hAPP(c_List_Onth(T_a,V_xs),V_j).
% 5.94/6.01  0 [] hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)),V_i_2),V_v_2)=c_Nat_Onat_Onat__case(tc_List_Olist(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_v_2),V_xs_2),c_COMBB(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_Nat_Onat,hAPP(c_List_Olist_OCons(T_a),V_x_2),hAPP(c_COMBC(tc_Nat_Onat,T_a,tc_List_Olist(T_a),c_List_Olist__update(T_a,V_xs_2)),V_v_2)),V_i_2).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))|hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x)=hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_n),V_x)),V_ys).
% 5.94/6.01  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))|hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x)=hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist__update(T_a,V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_x)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_z_2)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_z_2)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2)),V_z_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_z_2))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_z_2)).
% 5.94/6.01  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_x)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_y))=c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y)).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_x_2)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_y_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2),V_y_2)).
% 5.94/6.01  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_x_2)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_y_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2),V_y_2)).
% 5.94/6.01  0 [] hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(tc_Int_Oint),V_k),V_k)).
% 5.94/6.01  0 [] c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_x_2)!=c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_y_2)|V_x_2=V_y_2.
% 5.94/6.01  0 [] c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_x_2)=c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,V_y_2)|V_x_2!=V_y_2.
% 5.94/6.01  0 [] c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_a))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_b))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))).
% 5.94/6.01  0 [] -class_Groups_Ominus(T_a)|hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a)=V_a.
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_a).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c))=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z))=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z)=hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)).
% 5.94/6.01  0 [] -class_Groups_Ominus(T_a)|hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a)),V_A_2),V_B_2),V_x_2)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)).
% 5.94/6.01  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 5.94/6.01  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 5.94/6.01  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)).
% 5.94/6.01  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b).
% 5.94/6.01  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)).
% 5.94/6.01  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d).
% 5.94/6.01  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)).
% 5.94/6.01  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a).
% 5.94/6.01  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_ba_2!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_aa_2)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 5.94/6.01  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_ba_2=hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ba_2),V_aa_2)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 5.94/6.01  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f28(V_P_2,V_xs_2,T_a,V_n_2)),V_n_2))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))|c_List_OtakeWhile(T_a,V_P_2,V_xs_2)=hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2).
% 5.94/6.01  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f28(V_P_2,V_xs_2,T_a,V_n_2)),V_n_2))|hBOOL(hAPP(V_P_2,hAPP(c_List_Onth(T_a,V_xs_2),V_n_2)))|c_List_OtakeWhile(T_a,V_P_2,V_xs_2)=hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2).
% 5.94/6.01  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f28(V_P_2,V_xs_2,T_a,V_n_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))|c_List_OtakeWhile(T_a,V_P_2,V_xs_2)=hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2).
% 5.94/6.01  0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f28(V_P_2,V_xs_2,T_a,V_n_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))|hBOOL(hAPP(V_P_2,hAPP(c_List_Onth(T_a,V_xs_2),V_n_2)))|c_List_OtakeWhile(T_a,V_P_2,V_xs_2)=hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2).
% 5.94/6.01  0 [] -hBOOL(hAPP(V_P_2,hAPP(c_List_Onth(T_a,V_xs_2),$f28(V_P_2,V_xs_2,T_a,V_n_2))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))|c_List_OtakeWhile(T_a,V_P_2,V_xs_2)=hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2).
% 5.94/6.01  0 [] -hBOOL(hAPP(V_P_2,hAPP(c_List_Onth(T_a,V_xs_2),$f28(V_P_2,V_xs_2,T_a,V_n_2))))|hBOOL(hAPP(V_P_2,hAPP(c_List_Onth(T_a,V_xs_2),V_n_2)))|c_List_OtakeWhile(T_a,V_P_2,V_xs_2)=hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2).
% 5.94/6.01  0 [] hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b),c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b),c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_Nat_Onat,c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b),c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_List_Ofilter(tc_List_Olist(T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b),c_fNot,hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool,c_fe_qual),c_List_Olist_ONil(T_b))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 5.94/6.01  0 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Ofilter(T_a,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Ofilter(T_a,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a,c_fNot,V_P_2),V_xs_2)))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2).
% 5.94/6.01  0 [] c_List_Oreplicate(T_a,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Ofilter(T_a,hAPP(c_fe_qual,V_x_2),V_xs_2)),V_x_2)=c_List_Ofilter(T_a,hAPP(c_fe_qual,V_x_2),V_xs_2).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_b)|hBOOL(hAPP(V_P_2,V_x_2))|c_List_Ofilter(T_a,V_P_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_a,T_b,V_f_2),V_x_2),V_xs_2))=c_List_Ofilter(T_a,V_P_2,V_xs_2).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_b)|c_List_Ofilter(T_a,V_P_2,c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))=c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,c_List_Ofilter(T_a,V_P_2,V_xs_2)).
% 5.94/6.01  0 [] -class_Orderings_Olinorder(T_a)|c_List_Olinorder__class_Osorted(T_a,c_List_Ofilter(T_a,hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool,c_fe_qual),hAPP(V_g_2,V_xs_2)),V_xs_2)).
% 5.94/6.01  0 [] -hBOOL(hAPP(V_P_2,V_x_2))|c_List_Ofilter(T_a,V_P_2,c_List_Oreplicate(T_a,V_n_2,V_x_2))=c_List_Oreplicate(T_a,V_n_2,V_x_2).
% 5.94/6.01  0 [] hBOOL(hAPP(V_P_2,V_x_2))|c_List_Ofilter(T_a,V_P_2,c_List_Oreplicate(T_a,V_n_2,V_x_2))=c_List_Olist_ONil(T_a).
% 5.94/6.01  0 [] c_List_Ofilter(T_a,V_P_2,c_List_Ofilter(T_a,V_Q_2,V_xs_2))=c_List_Ofilter(T_a,c_COMBS(T_a,tc_HOL_Obool,tc_HOL_Obool,c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_a,c_fconj,V_Q_2),V_P_2),V_xs_2).
% 5.94/6.01  0 [] c_List_Orev(T_a,c_List_Ofilter(T_a,V_P_2,V_xs_2))=c_List_Ofilter(T_a,V_P_2,c_List_Orev(T_a,V_xs_2)).
% 5.94/6.01  0 [] -c_List_Odistinct(T_a,V_xs_2)|c_List_Odistinct(T_a,c_List_Ofilter(T_a,V_P_2,V_xs_2)).
% 5.94/6.01  0 [] c_List_Ofilter(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))=hAPP(hAPP(c_List_Oappend(T_a),c_List_Ofilter(T_a,V_P_2,V_xs_2)),c_List_Ofilter(T_a,V_P_2,V_ys_2)).
% 5.94/6.01  0 [] c_List_Ofilter(T_a,V_P_2,c_List_Olist_ONil(T_a))=c_List_Olist_ONil(T_a).
% 5.94/6.01  0 [] -hBOOL(hAPP(V_P_2,V_x_2))|c_List_Ofilter(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Ofilter(T_a,V_P_2,V_xs_2)).
% 5.94/6.01  0 [] hBOOL(hAPP(V_P_2,V_x_2))|c_List_Ofilter(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))=c_List_Ofilter(T_a,V_P_2,V_xs_2).
% 5.94/6.01  0 [] c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a),c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Ofilter(tc_List_Olist(T_a),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_a),c_fNot,hAPP(c_COMBC(tc_List_Olist(T_a),tc_List_Olist(T_a),tc_HOL_Obool,c_fe_qual),c_List_Olist_ONil(T_a))),V_xs_2)).
% 5.94/6.01  0 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2))=c_List_Ofoldr(tc_List_Olist(T_a),tc_Nat_Onat,c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_a),c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.01  0 [] c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a)))=c_List_Olist_ONil(tc_List_Olist(T_a)).
% 5.94/6.01  0 [] c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss))=c_List_Otranspose(T_a,V_xss).
% 5.94/6.01  0 [] -c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Orev(tc_Nat_Onat,c_List_Omap(tc_List_Olist(T_a),tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Otranspose(T_a,V_xs_2))))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_List_Ofilter(tc_List_Olist(T_a),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_a),c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2),c_Nat_Osize__class_Osize(tc_List_Olist(T_a))),V_xs_2))))|hAPP(c_List_Onth(T_a,hAPP(c_List_Onth(tc_List_Olist(T_a),c_List_Otranspose(T_a,V_xs_2)),V_i_2)),V_j_2)=hAPP(c_List_Onth(T_a,hAPP(c_List_Onth(tc_List_Olist(T_a),V_xs_2),V_j_2)),V_i_2).
% 5.94/6.01  0 [] class_Enum_Oenum(tc_HOL_Obool).
% 5.94/6.01  0 [] -class_Enum_Oenum(T_2)| -class_Enum_Oenum(T_1)|class_Enum_Oenum(tc_fun(T_2,T_1)).
% 5.94/6.01  0 [] -class_Orderings_Opreorder(T_1)|class_Orderings_Opreorder(tc_fun(T_2,T_1)).
% 5.94/6.01  0 [] -class_Orderings_Oorder(T_1)|class_Orderings_Oorder(tc_fun(T_2,T_1)).
% 5.94/6.01  0 [] -class_Orderings_Oord(T_1)|class_Orderings_Oord(tc_fun(T_2,T_1)).
% 5.94/6.01  0 [] -class_Groups_Ominus(T_1)|class_Groups_Ominus(tc_fun(T_2,T_1)).
% 5.94/6.01  0 [] -class_Enum_Oenum(T_2)| -class_HOL_Oe_qual(T_1)|class_HOL_Oe_qual(tc_fun(T_2,T_1)).
% 5.94/6.01  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint).
% 5.94/6.01  0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint).
% 5.94/6.01  0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 5.94/6.01  0 [] class_Groups_Oordered__comm__monoid__add(tc_Int_Oint).
% 5.94/6.01  0 [] class_Groups_Olinordered__ab__group__add(tc_Int_Oint).
% 5.94/6.01  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 5.94/6.01  0 [] class_Groups_Oordered__ab__group__add(tc_Int_Oint).
% 5.94/6.01  0 [] class_Groups_Ocancel__semigroup__add(tc_Int_Oint).
% 5.94/6.01  0 [] class_Rings_Olinordered__semidom(tc_Int_Oint).
% 5.94/6.01  0 [] class_Groups_Oab__semigroup__add(tc_Int_Oint).
% 5.94/6.01  0 [] class_Groups_Ocomm__monoid__add(tc_Int_Oint).
% 5.94/6.01  0 [] class_Rings_Olinordered__idom(tc_Int_Oint).
% 5.94/6.01  0 [] class_Rings_Ocomm__semiring__1(tc_Int_Oint).
% 5.94/6.01  0 [] class_Groups_Osemigroup__add(tc_Int_Oint).
% 5.94/6.01  0 [] class_Nat_Osemiring__char__0(tc_Int_Oint).
% 5.94/6.01  0 [] class_Groups_Oab__group__add(tc_Int_Oint).
% 5.94/6.01  0 [] class_Orderings_Opreorder(tc_Int_Oint).
% 5.94/6.01  0 [] class_Orderings_Olinorder(tc_Int_Oint).
% 5.94/6.01  0 [] class_Groups_Omonoid__add(tc_Int_Oint).
% 5.94/6.01  0 [] class_Rings_Osemiring__1(tc_Int_Oint).
% 5.94/6.01  0 [] class_Groups_Ogroup__add(tc_Int_Oint).
% 5.94/6.01  0 [] class_Orderings_Oorder(tc_Int_Oint).
% 5.94/6.01  0 [] class_Orderings_Oord(tc_Int_Oint).
% 5.94/6.01  0 [] class_Groups_Ominus(tc_Int_Oint).
% 5.94/6.01  0 [] class_Groups_Ozero(tc_Int_Oint).
% 5.94/6.01  0 [] class_HOL_Oe_qual(tc_Int_Oint).
% 5.94/6.01  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Groups_Osemigroup__add(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Nat_Osemiring__char__0(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Orderings_Opreorder(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Orderings_Olinorder(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Groups_Omonoid__add(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Rings_Osemiring__1(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Orderings_Oorder(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Orderings_Oord(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Groups_Ominus(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Groups_Ozero(tc_Nat_Onat).
% 5.94/6.01  0 [] class_HOL_Oe_qual(tc_Nat_Onat).
% 5.94/6.01  0 [] class_Orderings_Opreorder(tc_HOL_Obool).
% 5.94/6.01  0 [] class_Orderings_Oorder(tc_HOL_Obool).
% 5.94/6.01  0 [] class_Orderings_Oord(tc_HOL_Obool).
% 5.94/6.01  0 [] class_Groups_Ominus(tc_HOL_Obool).
% 5.94/6.01  0 [] class_HOL_Oe_qual(tc_HOL_Obool).
% 5.94/6.01  0 [] class_HOL_Oe_qual(tc_List_Olist(T_1)).
% 5.94/6.01  0 [] hAPP(c_COMBI(T_a),V_P)=V_P.
% 5.94/6.01  0 [] hAPP(c_COMBK(T_a,T_b,V_P),V_Q)=V_P.
% 5.94/6.01  0 [] hAPP(c_COMBB(T_b,T_a,T_c,V_P_2,V_Q_2),V_R_2)=hAPP(V_P_2,hAPP(V_Q_2,V_R_2)).
% 5.94/6.01  0 [] hAPP(hAPP(c_COMBC(T_b,T_c,T_a,V_P_2),V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),V_Q_2).
% 5.94/6.01  0 [] hAPP(c_COMBS(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2)=hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)).
% 5.94/6.01  0 [] -hBOOL(hAPP(hAPP(c_fe_qual,V_x_2),V_y_2))|V_x_2=V_y_2.
% 5.94/6.01  0 [] V_x_2!=V_y_2|hBOOL(hAPP(hAPP(c_fe_qual,V_x_2),V_y_2)).
% 5.94/6.01  0 [] -hBOOL(hAPP(c_fNot,V_P_2))| -hBOOL(V_P_2).
% 5.94/6.01  0 [] hBOOL(V_P_2)|hBOOL(hAPP(c_fNot,V_P_2)).
% 5.94/6.01  0 [] -hBOOL(V_P_2)| -hBOOL(V_Q_2)|hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)).
% 5.94/6.01  0 [] -hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))|hBOOL(V_P_2).
% 5.94/6.01  0 [] -hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))|hBOOL(V_Q_2).
% 5.94/6.01  0 [] -hBOOL(V_P_2)|hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)).
% 5.94/6.01  0 [] -hBOOL(V_Q_2)|hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)).
% 5.94/6.01  0 [] -hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))|hBOOL(V_P_2)|hBOOL(V_Q_2).
% 5.94/6.01  0 [] v_a!=v_b.
% 5.94/6.01  0 [] -c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_a),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_b),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),B_c),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))).
% 5.94/6.01  end_of_list.
% 5.94/6.01  
% 5.94/6.01  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 5.94/6.01  
% 5.94/6.01  This ia a non-Horn set with equality.  The strategy will be
% 5.94/6.01  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 5.94/6.01  deletion, with positive clauses in sos and nonpositive
% 5.94/6.01  clauses in usable.
% 5.94/6.01  
% 5.94/6.01     dependent: set(knuth_bendix).
% 5.94/6.01     dependent: set(anl_eq).
% 5.94/6.01     dependent: set(para_from).
% 5.94/6.01     dependent: set(para_into).
% 5.94/6.01     dependent: clear(para_from_right).
% 5.94/6.01     dependent: clear(para_into_right).
% 5.94/6.01     dependent: set(para_from_vars).
% 5.94/6.01     dependent: set(eq_units_both_ways).
% 5.94/6.01     dependent: set(dynamic_demod_all).
% 5.94/6.01     dependent: set(dynamic_demod).
% 5.94/6.01     dependent: set(order_eq).
% 5.94/6.01     dependent: set(back_demod).
% 5.94/6.01     dependent: set(lrpo).
% 5.94/6.01     dependent: set(hyper_res).
% 5.94/6.01     dependent: set(unit_deletion).
% 5.94/6.01     dependent: set(factor).
% 5.94/6.01  
% 5.94/6.01  ------------> process usable:
% 5.94/6.01  ** KEPT (pick-wt=14): 1 [] hAPP(A,$f1(B,A))!=hAPP(B,$f1(B,A))|A=B.
% 5.94/6.01  ** KEPT (pick-wt=9): 2 [] c_List_Olist_ONil(A)!=hAPP(hAPP(c_List_Olist_OCons(A),B),C).
% 5.94/6.01  ** KEPT (pick-wt=9): 3 [] hAPP(hAPP(c_List_Olist_OCons(A),B),C)!=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=8): 5 [copy,4,flip.1] hAPP(hAPP(c_List_Olist_OCons(A),B),C)!=C.
% 5.94/6.01    Following clause subsumed by 5 during input processing: 0 [] hAPP(hAPP(c_List_Olist_OCons(A),B),C)!=C.
% 5.94/6.01  ** KEPT (pick-wt=16): 6 [] hAPP(hAPP(c_List_Olist_OCons(A),B),C)!=hAPP(hAPP(c_List_Olist_OCons(A),D),E)|B=D.
% 5.94/6.01  ** KEPT (pick-wt=16): 7 [] hAPP(hAPP(c_List_Olist_OCons(A),B),C)!=hAPP(hAPP(c_List_Olist_OCons(A),D),E)|C=E.
% 5.94/6.01  ** KEPT (pick-wt=19): 8 [] hAPP(hAPP(c_List_Olist_OCons(A),B),C)=hAPP(hAPP(c_List_Olist_OCons(A),D),E)|B!=D|C!=E.
% 5.94/6.01  ** KEPT (pick-wt=12): 9 [] A=c_List_Olist_ONil(B)| -c_List_Odistinct(B,A)|c_List_Odistinct(B,c_List_Obutlast(B,A)).
% 5.94/6.01  ** KEPT (pick-wt=11): 10 [] -class_Orderings_Olinorder(A)|c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olist_OCons(A),B),c_List_Olist_ONil(A))).
% 5.94/6.01  ** KEPT (pick-wt=14): 11 [] A!=c_List_Olist_ONil(B)|c_List_Olast(B,hAPP(hAPP(c_List_Olist_OCons(B),C),A))=C.
% 5.94/6.01  ** KEPT (pick-wt=6): 12 [] -class_Orderings_Olinorder(A)|c_List_Olinorder__class_Osorted(A,c_List_Olist_ONil(A)).
% 5.94/6.01  ** KEPT (pick-wt=14): 13 [] -class_Orderings_Olinorder(A)|B=c_List_Olist_ONil(A)| -c_List_Olinorder__class_Osorted(A,B)|c_List_Olinorder__class_Osorted(A,c_List_Obutlast(A,B)).
% 5.94/6.01    Following clause subsumed by 12 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_List_Olinorder__class_Osorted(A,c_List_Olist_ONil(A)).
% 5.94/6.01  ** KEPT (pick-wt=9): 14 [] -c_List_Odistinct(A,B)|c_List_Odistinct(A,c_List_Oinsert(A,C,B)).
% 5.94/6.01  ** KEPT (pick-wt=15): 15 [] A!=c_List_Olist_ONil(B)|c_List_Obutlast(B,hAPP(hAPP(c_List_Olist_OCons(B),C),A))=c_List_Olist_ONil(B).
% 5.94/6.01    Following clause subsumed by 11 during input processing: 0 [] A!=c_List_Olist_ONil(B)|c_List_Olast(B,hAPP(hAPP(c_List_Olist_OCons(B),C),A))=C.
% 5.94/6.01  ** KEPT (pick-wt=18): 16 [] hAPP(hAPP(c_List_Oappend(A),B),hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Olist_ONil(A)))!=D|D!=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=19): 17 [] hAPP(hAPP(c_List_Oappend(A),B),hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Olist_ONil(A)))!=D|c_List_Obutlast(A,D)=B.
% 5.94/6.01  ** KEPT (pick-wt=19): 18 [] hAPP(hAPP(c_List_Oappend(A),B),hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Olist_ONil(A)))!=D|c_List_Olast(A,D)=C.
% 5.94/6.01  ** KEPT (pick-wt=28): 19 [] hAPP(hAPP(c_List_Oappend(A),B),hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Olist_ONil(A)))=D|D=c_List_Olist_ONil(A)|c_List_Obutlast(A,D)!=B|c_List_Olast(A,D)!=C.
% 5.94/6.01  ** KEPT (pick-wt=7): 20 [] A!=c_List_Olist_ONil(B)|c_List_Onull(B,A).
% 5.94/6.01  ** KEPT (pick-wt=7): 21 [] A=c_List_Olist_ONil(B)| -c_List_Onull(B,A).
% 5.94/6.01    Following clause subsumed by 21 during input processing: 0 [] -c_List_Onull(A,B)|B=c_List_Olist_ONil(A).
% 5.94/6.01    Following clause subsumed by 20 during input processing: 0 [] c_List_Onull(A,B)|B!=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=8): 22 [] -c_List_Onull(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C)).
% 5.94/6.01  ** KEPT (pick-wt=39): 24 [copy,23,flip.2] hAPP(hAPP(c_List_Oappend(A),B),C)!=hAPP(hAPP(c_List_Oappend(A),D),E)|hAPP(hAPP(c_List_Oappend(A),D),$f2(E,D,C,B,A))=B|hAPP(hAPP(c_List_Oappend(A),B),$f2(E,D,C,B,A))=D.
% 5.94/6.01  ** KEPT (pick-wt=39): 26 [copy,25,flip.2,flip.3] hAPP(hAPP(c_List_Oappend(A),B),C)!=hAPP(hAPP(c_List_Oappend(A),D),E)|hAPP(hAPP(c_List_Oappend(A),D),$f2(E,D,C,B,A))=B|hAPP(hAPP(c_List_Oappend(A),$f2(E,D,C,B,A)),E)=C.
% 5.94/6.01  ** KEPT (pick-wt=39): 27 [] hAPP(hAPP(c_List_Oappend(A),B),C)!=hAPP(hAPP(c_List_Oappend(A),D),E)|hAPP(hAPP(c_List_Oappend(A),$f2(E,D,C,B,A)),C)=E|hAPP(hAPP(c_List_Oappend(A),B),$f2(E,D,C,B,A))=D.
% 5.94/6.01  ** KEPT (pick-wt=39): 29 [copy,28,flip.3] hAPP(hAPP(c_List_Oappend(A),B),C)!=hAPP(hAPP(c_List_Oappend(A),D),E)|hAPP(hAPP(c_List_Oappend(A),$f2(E,D,C,B,A)),C)=E|hAPP(hAPP(c_List_Oappend(A),$f2(E,D,C,B,A)),E)=C.
% 5.94/6.01  ** KEPT (pick-wt=29): 30 [] hAPP(hAPP(c_List_Oappend(A),B),C)=hAPP(hAPP(c_List_Oappend(A),D),E)|B!=hAPP(hAPP(c_List_Oappend(A),D),F)|hAPP(hAPP(c_List_Oappend(A),F),C)!=E.
% 5.94/6.01  ** KEPT (pick-wt=29): 31 [] hAPP(hAPP(c_List_Oappend(A),B),C)=hAPP(hAPP(c_List_Oappend(A),D),E)|hAPP(hAPP(c_List_Oappend(A),B),F)!=D|C!=hAPP(hAPP(c_List_Oappend(A),F),E).
% 5.94/6.01  ** KEPT (pick-wt=16): 32 [] hAPP(hAPP(c_List_Oappend(A),B),C)!=hAPP(hAPP(c_List_Oappend(A),B),D)|C=D.
% 5.94/6.01  ** KEPT (pick-wt=16): 33 [] hAPP(hAPP(c_List_Oappend(A),B),C)=hAPP(hAPP(c_List_Oappend(A),B),D)|C!=D.
% 5.94/6.01  ** KEPT (pick-wt=16): 34 [] hAPP(hAPP(c_List_Oappend(A),B),C)!=hAPP(hAPP(c_List_Oappend(A),D),C)|B=D.
% 5.94/6.01  ** KEPT (pick-wt=16): 35 [] hAPP(hAPP(c_List_Oappend(A),B),C)=hAPP(hAPP(c_List_Oappend(A),D),C)|B!=D.
% 5.94/6.01    Following clause subsumed by 31 during input processing: 0 [] hAPP(hAPP(c_List_Oappend(A),B),C)!=D|E!=hAPP(hAPP(c_List_Oappend(A),C),F)|hAPP(hAPP(c_List_Oappend(A),B),E)=hAPP(hAPP(c_List_Oappend(A),D),F).
% 5.94/6.01  ** KEPT (pick-wt=29): 36 [] hAPP(hAPP(c_List_Olist_OCons(A),B),C)!=D|E!=hAPP(hAPP(c_List_Oappend(A),C),F)|hAPP(hAPP(c_List_Olist_OCons(A),B),E)=hAPP(hAPP(c_List_Oappend(A),D),F).
% 5.94/6.01  ** KEPT (pick-wt=13): 37 [] c_List_Olist_ONil(A)!=hAPP(hAPP(c_List_Oappend(A),B),C)|B=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=13): 38 [] c_List_Olist_ONil(A)!=hAPP(hAPP(c_List_Oappend(A),B),C)|C=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=17): 39 [] c_List_Olist_ONil(A)=hAPP(hAPP(c_List_Oappend(A),B),C)|B!=c_List_Olist_ONil(A)|C!=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=12): 41 [copy,40,flip.1] hAPP(hAPP(c_List_Oappend(A),B),C)!=B|C=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=12): 43 [copy,42,flip.1] hAPP(hAPP(c_List_Oappend(A),B),C)=B|C!=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=12): 45 [copy,44,flip.1] hAPP(hAPP(c_List_Oappend(A),B),C)!=C|B=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=12): 47 [copy,46,flip.1] hAPP(hAPP(c_List_Oappend(A),B),C)=C|B!=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=13): 48 [] hAPP(hAPP(c_List_Oappend(A),B),C)!=c_List_Olist_ONil(A)|B=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=13): 49 [] hAPP(hAPP(c_List_Oappend(A),B),C)!=c_List_Olist_ONil(A)|C=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=17): 50 [] hAPP(hAPP(c_List_Oappend(A),B),C)=c_List_Olist_ONil(A)|B!=c_List_Olist_ONil(A)|C!=c_List_Olist_ONil(A).
% 5.94/6.01    Following clause subsumed by 41 during input processing: 0 [] hAPP(hAPP(c_List_Oappend(A),B),C)!=B|C=c_List_Olist_ONil(A).
% 5.94/6.01    Following clause subsumed by 43 during input processing: 0 [] hAPP(hAPP(c_List_Oappend(A),B),C)=B|C!=c_List_Olist_ONil(A).
% 5.94/6.01    Following clause subsumed by 45 during input processing: 0 [] hAPP(hAPP(c_List_Oappend(A),B),C)!=C|B=c_List_Olist_ONil(A).
% 5.94/6.01    Following clause subsumed by 47 during input processing: 0 [] hAPP(hAPP(c_List_Oappend(A),B),C)=C|B!=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=12): 51 [] A!=B|A=hAPP(hAPP(c_List_Oappend(C),c_List_Olist_ONil(C)),B).
% 5.94/6.01  ** KEPT (pick-wt=30): 53 [copy,52,flip.3] hAPP(hAPP(c_List_Oappend(A),B),C)!=hAPP(hAPP(c_List_Olist_OCons(A),D),E)|B=c_List_Olist_ONil(A)|hAPP(hAPP(c_List_Olist_OCons(A),D),$f3(E,D,C,B,A))=B.
% 5.94/6.01  ** KEPT (pick-wt=30): 54 [] hAPP(hAPP(c_List_Oappend(A),B),C)!=hAPP(hAPP(c_List_Olist_OCons(A),D),E)|B=c_List_Olist_ONil(A)|hAPP(hAPP(c_List_Oappend(A),$f3(E,D,C,B,A)),C)=E.
% 5.94/6.01  ** KEPT (pick-wt=34): 56 [copy,55,flip.3] hAPP(hAPP(c_List_Oappend(A),B),C)!=hAPP(hAPP(c_List_Olist_OCons(A),D),E)|C=hAPP(hAPP(c_List_Olist_OCons(A),D),E)|hAPP(hAPP(c_List_Olist_OCons(A),D),$f3(E,D,C,B,A))=B.
% 5.94/6.01  ** KEPT (pick-wt=34): 57 [] hAPP(hAPP(c_List_Oappend(A),B),C)!=hAPP(hAPP(c_List_Olist_OCons(A),D),E)|C=hAPP(hAPP(c_List_Olist_OCons(A),D),E)|hAPP(hAPP(c_List_Oappend(A),$f3(E,D,C,B,A)),C)=E.
% 5.94/6.01  ** KEPT (pick-wt=25): 58 [] hAPP(hAPP(c_List_Oappend(A),B),C)=hAPP(hAPP(c_List_Olist_OCons(A),D),E)|B!=c_List_Olist_ONil(A)|C!=hAPP(hAPP(c_List_Olist_OCons(A),D),E).
% 5.94/6.01  ** KEPT (pick-wt=29): 59 [] hAPP(hAPP(c_List_Oappend(A),B),C)=hAPP(hAPP(c_List_Olist_OCons(A),D),E)|B!=hAPP(hAPP(c_List_Olist_OCons(A),D),F)|hAPP(hAPP(c_List_Oappend(A),F),C)!=E.
% 5.94/6.01  ** KEPT (pick-wt=30): 60 [] hAPP(hAPP(c_List_Olist_OCons(A),B),C)!=hAPP(hAPP(c_List_Oappend(A),D),E)|D=c_List_Olist_ONil(A)|hAPP(hAPP(c_List_Olist_OCons(A),B),$f4(E,D,C,B,A))=D.
% 5.94/6.01  ** KEPT (pick-wt=30): 62 [copy,61,flip.3] hAPP(hAPP(c_List_Olist_OCons(A),B),C)!=hAPP(hAPP(c_List_Oappend(A),D),E)|D=c_List_Olist_ONil(A)|hAPP(hAPP(c_List_Oappend(A),$f4(E,D,C,B,A)),E)=C.
% 5.94/6.01  ** KEPT (pick-wt=34): 63 [] hAPP(hAPP(c_List_Olist_OCons(A),B),C)!=hAPP(hAPP(c_List_Oappend(A),D),E)|hAPP(hAPP(c_List_Olist_OCons(A),B),C)=E|hAPP(hAPP(c_List_Olist_OCons(A),B),$f4(E,D,C,B,A))=D.
% 5.94/6.01  ** KEPT (pick-wt=34): 65 [copy,64,flip.3] hAPP(hAPP(c_List_Olist_OCons(A),B),C)!=hAPP(hAPP(c_List_Oappend(A),D),E)|hAPP(hAPP(c_List_Olist_OCons(A),B),C)=E|hAPP(hAPP(c_List_Oappend(A),$f4(E,D,C,B,A)),E)=C.
% 5.94/6.01  ** KEPT (pick-wt=25): 66 [] hAPP(hAPP(c_List_Olist_OCons(A),B),C)=hAPP(hAPP(c_List_Oappend(A),D),E)|D!=c_List_Olist_ONil(A)|hAPP(hAPP(c_List_Olist_OCons(A),B),C)!=E.
% 5.94/6.01    Following clause subsumed by 36 during input processing: 0 [] hAPP(hAPP(c_List_Olist_OCons(A),B),C)=hAPP(hAPP(c_List_Oappend(A),D),E)|hAPP(hAPP(c_List_Olist_OCons(A),B),F)!=D|C!=hAPP(hAPP(c_List_Oappend(A),F),E).
% 5.94/6.01  ** KEPT (pick-wt=28): 67 [] hAPP(hAPP(c_List_Oappend(A),B),hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Olist_ONil(A)))!=hAPP(hAPP(c_List_Oappend(A),D),hAPP(hAPP(c_List_Olist_OCons(A),E),c_List_Olist_ONil(A)))|B=D.
% 5.94/6.01  ** KEPT (pick-wt=28): 68 [] hAPP(hAPP(c_List_Oappend(A),B),hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Olist_ONil(A)))!=hAPP(hAPP(c_List_Oappend(A),D),hAPP(hAPP(c_List_Olist_OCons(A),E),c_List_Olist_ONil(A)))|C=E.
% 5.94/6.01  ** KEPT (pick-wt=31): 69 [] hAPP(hAPP(c_List_Oappend(A),B),hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Olist_ONil(A)))=hAPP(hAPP(c_List_Oappend(A),D),hAPP(hAPP(c_List_Olist_OCons(A),E),c_List_Olist_ONil(A)))|B!=D|C!=E.
% 5.94/6.01  ** KEPT (pick-wt=16): 70 [] A!=c_List_Olist_ONil(B)|c_List_Obutlast(B,hAPP(hAPP(c_List_Oappend(B),C),A))=c_List_Obutlast(B,C).
% 5.94/6.01  ** KEPT (pick-wt=16): 71 [] A!=c_List_Olist_ONil(B)|c_List_Olast(B,hAPP(hAPP(c_List_Oappend(B),C),A))=c_List_Olast(B,C).
% 5.94/6.01    Following clause subsumed by 71 during input processing: 0 [] A!=c_List_Olist_ONil(B)|c_List_Olast(B,hAPP(hAPP(c_List_Oappend(B),C),A))=c_List_Olast(B,C).
% 5.94/6.01  ** KEPT (pick-wt=12): 72 [] -hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(tc_List_Olist(A)),B),c_List_Olist_ONil(A)))|c_List_Onull(A,B).
% 5.94/6.01  ** KEPT (pick-wt=12): 73 [] hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(tc_List_Olist(A)),B),c_List_Olist_ONil(A)))| -c_List_Onull(A,B).
% 5.94/6.01  ** KEPT (pick-wt=16): 74 [] -hBOOL(hAPP(A,c_List_Olist_ONil(B)))|hBOOL(hAPP(A,$f5(C,B,A)))|hBOOL(hAPP(A,C)).
% 5.94/6.01  ** KEPT (pick-wt=30): 75 [] -hBOOL(hAPP(A,c_List_Olist_ONil(B)))| -hBOOL(hAPP(A,hAPP(hAPP(c_List_Oappend(B),$f5(C,B,A)),hAPP(hAPP(c_List_Olist_OCons(B),$f6(C,B,A)),c_List_Olist_ONil(B)))))|hBOOL(hAPP(A,C)).
% 5.94/6.01  ** KEPT (pick-wt=26): 76 [] c_List_Orev(A,B)!=hAPP(hAPP(c_List_Olist_OCons(A),C),D)|B=hAPP(hAPP(c_List_Oappend(A),c_List_Orev(A,D)),hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Olist_ONil(A))).
% 5.94/6.01  ** KEPT (pick-wt=26): 77 [] c_List_Orev(A,B)=hAPP(hAPP(c_List_Olist_OCons(A),C),D)|B!=hAPP(hAPP(c_List_Oappend(A),c_List_Orev(A,D)),hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Olist_ONil(A))).
% 5.94/6.01  ** KEPT (pick-wt=16): 78 [] A!=c_List_Olist_ONil(B)|c_List_Ohd(B,hAPP(hAPP(c_List_Oappend(B),A),C))=c_List_Ohd(B,C).
% 5.94/6.01  ** KEPT (pick-wt=10): 79 [] c_List_Orev(A,B)!=c_List_Orev(A,C)|B=C.
% 5.94/6.01  ** KEPT (pick-wt=10): 80 [] c_List_Orev(A,B)=c_List_Orev(A,C)|B!=C.
% 5.94/6.01  ** KEPT (pick-wt=10): 81 [] c_List_Orev(A,B)!=C|B=c_List_Orev(A,C).
% 5.94/6.01  ** KEPT (pick-wt=10): 82 [] c_List_Orev(A,B)=C|B!=c_List_Orev(A,C).
% 5.94/6.01  ** KEPT (pick-wt=11): 83 [] -hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(tc_List_Olist(A)),B),C))|B=C.
% 5.94/6.01  ** KEPT (pick-wt=11): 84 [] hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(tc_List_Olist(A)),B),C))|B!=C.
% 5.94/6.01  ** KEPT (pick-wt=10): 85 [] c_List_Orev(A,B)!=c_List_Olist_ONil(A)|B=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=10): 86 [] c_List_Orev(A,B)=c_List_Olist_ONil(A)|B!=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=10): 87 [] c_List_Olist_ONil(A)!=c_List_Orev(A,B)|B=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=10): 88 [] c_List_Olist_ONil(A)=c_List_Orev(A,B)|B!=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=8): 89 [] -c_List_Odistinct(A,c_List_Orev(A,B))|c_List_Odistinct(A,B).
% 5.94/6.01  ** KEPT (pick-wt=8): 90 [] c_List_Odistinct(A,c_List_Orev(A,B))| -c_List_Odistinct(A,B).
% 5.94/6.01  ** KEPT (pick-wt=10): 91 [] c_List_Orotate1(A,B)!=c_List_Olist_ONil(A)|B=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=10): 92 [] c_List_Orotate1(A,B)=c_List_Olist_ONil(A)|B!=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=8): 93 [] -c_List_Odistinct(A,c_List_Orotate1(A,B))|c_List_Odistinct(A,B).
% 5.94/6.01  ** KEPT (pick-wt=8): 94 [] c_List_Odistinct(A,c_List_Orotate1(A,B))| -c_List_Odistinct(A,B).
% 5.94/6.01  ** KEPT (pick-wt=20): 95 [] hAPP(hAPP(c_List_Olist_OCons(A),B),c_List_Olist_ONil(A))!=c_List_Orev(A,C)|C=hAPP(hAPP(c_List_Olist_OCons(A),B),c_List_Olist_ONil(A)).
% 5.94/6.01  ** KEPT (pick-wt=20): 96 [] hAPP(hAPP(c_List_Olist_OCons(A),B),c_List_Olist_ONil(A))=c_List_Orev(A,C)|C!=hAPP(hAPP(c_List_Olist_OCons(A),B),c_List_Olist_ONil(A)).
% 5.94/6.01  ** KEPT (pick-wt=20): 97 [] c_List_Orev(A,B)!=hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Olist_ONil(A))|B=hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Olist_ONil(A)).
% 5.94/6.01  ** KEPT (pick-wt=20): 98 [] c_List_Orev(A,B)=hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Olist_ONil(A))|B!=hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Olist_ONil(A)).
% 5.94/6.01  ** KEPT (pick-wt=6): 99 [] -class_HOL_Oe_qual(A)|c_HOL_Oe_qual__class_Oe_qual(A)=c_fe_qual.
% 5.94/6.01  ** KEPT (pick-wt=9): 100 [] -class_HOL_Oe_qual(A)|hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(A),B),B)).
% 5.94/6.01  ** KEPT (pick-wt=12): 101 [] -class_HOL_Oe_qual(A)| -hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(A),B),C))|B=C.
% 5.94/6.01  ** KEPT (pick-wt=12): 102 [] -class_HOL_Oe_qual(A)|hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(A),B),C))|B!=C.
% 5.94/6.01    Following clause subsumed by 99 during input processing: 0 [flip.2] -class_HOL_Oe_qual(A)|c_HOL_Oe_qual__class_Oe_qual(A)=c_fe_qual.
% 5.94/6.01  ** KEPT (pick-wt=16): 103 [] c_List_OdropWhile(A,B,C)=c_List_Olist_ONil(A)| -hBOOL(hAPP(B,c_List_Ohd(A,c_List_OdropWhile(A,B,C)))).
% 5.94/6.01  ** KEPT (pick-wt=5): 104 [] -c_List_Olist__ex1(A,B,c_List_Olist_ONil(A)).
% 5.94/6.01  ** KEPT (pick-wt=5): 105 [] -c_List_Omember(A,c_List_Olist_ONil(A),B).
% 5.94/6.01  ** KEPT (pick-wt=18): 106 [] -hBOOL(hAPP(A,B))|c_List_OdropWhile(C,A,hAPP(hAPP(c_List_Olist_OCons(C),B),D))=c_List_OdropWhile(C,A,D).
% 5.94/6.01  ** KEPT (pick-wt=8): 107 [] -c_List_Odistinct(A,B)|c_List_Odistinct(A,c_List_Otl(A,B)).
% 5.94/6.01  ** KEPT (pick-wt=9): 108 [] -c_List_Odistinct(A,B)|c_List_Odistinct(A,c_List_OdropWhile(A,C,B)).
% 5.94/6.01  ** KEPT (pick-wt=10): 109 [] -class_Orderings_Olinorder(A)| -c_List_Olinorder__class_Osorted(A,B)|c_List_Olinorder__class_Osorted(A,c_List_Otl(A,B)).
% 5.94/6.01  ** KEPT (pick-wt=11): 110 [] -class_Orderings_Olinorder(A)| -c_List_Olinorder__class_Osorted(A,B)|c_List_Olinorder__class_Osorted(A,c_List_OdropWhile(A,C,B)).
% 5.94/6.01  ** KEPT (pick-wt=16): 111 [] -c_List_Omember(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C),D)|B=D|c_List_Omember(A,C,D).
% 5.94/6.01  ** KEPT (pick-wt=12): 112 [] c_List_Omember(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C),D)|B!=D.
% 5.94/6.01  ** KEPT (pick-wt=13): 113 [] c_List_Omember(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C),D)| -c_List_Omember(A,C,D).
% 5.94/6.01  ** KEPT (pick-wt=27): 115 [copy,114,flip.2] c_List_OdropWhile(A,B,C)!=hAPP(hAPP(c_List_Olist_OCons(A),D),E)|hAPP(hAPP(c_List_Oappend(A),c_List_OtakeWhile(A,B,C)),hAPP(hAPP(c_List_Olist_OCons(A),D),E))=C.
% 5.94/6.01  ** KEPT (pick-wt=15): 116 [] c_List_OdropWhile(A,B,C)!=hAPP(hAPP(c_List_Olist_OCons(A),D),E)| -hBOOL(hAPP(B,D)).
% 5.94/6.01  ** KEPT (pick-wt=31): 118 [copy,117,flip.2] c_List_OdropWhile(A,B,C)=hAPP(hAPP(c_List_Olist_OCons(A),D),E)|hAPP(hAPP(c_List_Oappend(A),c_List_OtakeWhile(A,B,C)),hAPP(hAPP(c_List_Olist_OCons(A),D),E))!=C|hBOOL(hAPP(B,D)).
% 5.94/6.01  ** KEPT (pick-wt=12): 119 [] A!=c_List_Olist_ONil(B)|A!=hAPP(hAPP(c_List_Olist_OCons(B),C),D).
% 5.94/6.01  ** KEPT (pick-wt=12): 120 [] c_List_Oreplicate(A,B,C)!=c_List_Oreplicate(A,D,E)|B=D.
% 5.94/6.01  ** KEPT (pick-wt=16): 121 [] c_List_Oreplicate(A,B,C)!=c_List_Oreplicate(A,D,E)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|C=E.
% 5.94/6.01  ** KEPT (pick-wt=16): 122 [] c_List_Oreplicate(A,B,C)=c_List_Oreplicate(A,D,E)|B!=D|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.01  ** KEPT (pick-wt=15): 123 [] c_List_Oreplicate(A,B,C)=c_List_Oreplicate(A,D,E)|B!=D|C!=E.
% 5.94/6.01  ** KEPT (pick-wt=9): 124 [] -c_List_Odistinct(A,B)|c_List_Odistinct(A,c_List_OtakeWhile(A,C,B)).
% 5.94/6.01  ** KEPT (pick-wt=11): 125 [] -class_Orderings_Olinorder(A)| -c_List_Olinorder__class_Osorted(A,B)|c_List_Olinorder__class_Osorted(A,c_List_OtakeWhile(A,C,B)).
% 5.94/6.01  ** KEPT (pick-wt=11): 126 [] c_List_Olist_ONil(A)!=c_List_Oreplicate(A,B,C)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.01  ** KEPT (pick-wt=11): 127 [] c_List_Olist_ONil(A)=c_List_Oreplicate(A,B,C)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.01  ** KEPT (pick-wt=11): 128 [] c_List_Oreplicate(A,B,C)!=c_List_Olist_ONil(A)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.01  ** KEPT (pick-wt=11): 129 [] c_List_Oreplicate(A,B,C)=c_List_Olist_ONil(A)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.01  ** KEPT (pick-wt=23): 131 [copy,130,flip.2] -hBOOL(hAPP(A,B))|hAPP(hAPP(c_List_Olist_OCons(C),B),c_List_OtakeWhile(C,A,D))=c_List_OtakeWhile(C,A,hAPP(hAPP(c_List_Olist_OCons(C),B),D)).
% 5.94/6.01  ** KEPT (pick-wt=10): 132 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 5.94/6.01  ** KEPT (pick-wt=10): 133 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 5.94/6.01  ** KEPT (pick-wt=19): 134 [] -class_Orderings_Olinorder(A)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,C),D),c_List_Olist_ONil(B))=hAPP(hAPP(c_List_Olist_OCons(B),D),c_List_Olist_ONil(B)).
% 5.94/6.01  ** KEPT (pick-wt=28): 135 [] A=c_List_Olist_ONil(B)| -c_List_Odistinct(B,A)|c_List_OtakeWhile(B,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,B,c_fNot,hAPP(c_COMBC(B,B,tc_HOL_Obool,c_fe_qual),c_List_Olast(B,A))),A)=c_List_Obutlast(B,A).
% 5.94/6.01  ** KEPT (pick-wt=10): 136 [] -class_Groups_Omonoid__add(A)|hAPP(c_List_Omonoid__add__class_Olistsum(A),c_List_Olist_ONil(A))=c_Groups_Ozero__class_Ozero(A).
% 5.94/6.01  ** KEPT (pick-wt=16): 137 [] -class_Orderings_Olinorder(A)| -c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A)),B),C))|c_List_Olinorder__class_Osorted(A,C).
% 5.94/6.01  ** KEPT (pick-wt=16): 138 [] -class_Orderings_Olinorder(A)|c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A)),B),C))| -c_List_Olinorder__class_Osorted(A,C).
% 5.94/6.01  ** KEPT (pick-wt=37): 139 [] -class_Orderings_Olinorder(A)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A)),B),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A)),C),D))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A)),C),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A)),B),D)).
% 5.94/6.01  ** KEPT (pick-wt=40): 140 [] -class_Orderings_Olinorder(A)|hAPP(B,C)=hAPP(B,D)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(E,A,B),D),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(E,A,B),C),F))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(E,A,B),C),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(E,A,B),D),F)).
% 5.94/6.01  ** KEPT (pick-wt=13): 141 [] -class_Orderings_Olinorder(A)|hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,C),D),E)!=c_List_Olist_ONil(B).
% 5.94/6.01  ** KEPT (pick-wt=13): 142 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(c_List_Omonoid__add__class_Olistsum(A),c_List_Orev(A,B))=hAPP(c_List_Omonoid__add__class_Olistsum(A),B).
% 5.94/6.01  ** KEPT (pick-wt=36): 143 [] -c_List_Olist__ex1(A,B,hAPP(hAPP(c_List_Olist_OCons(A),C),D))| -hBOOL(hAPP(B,C))|c_List_Olist__all(A,c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool,c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A,c_fdisj,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,A,c_fNot,B)),hAPP(c_fe_qual,C)),D).
% 5.94/6.01  ** KEPT (pick-wt=17): 144 [] -c_List_Olist__ex1(A,B,hAPP(hAPP(c_List_Olist_OCons(A),C),D))|hBOOL(hAPP(B,C))|c_List_Olist__ex1(A,B,D).
% 5.94/6.01  ** KEPT (pick-wt=17): 145 [] c_List_Olist__ex1(A,B,hAPP(hAPP(c_List_Olist_OCons(A),C),D))|hBOOL(hAPP(B,C))| -c_List_Olist__ex1(A,B,D).
% 5.94/6.01  ** KEPT (pick-wt=36): 146 [] c_List_Olist__ex1(A,B,hAPP(hAPP(c_List_Olist_OCons(A),C),D))| -c_List_Olist__all(A,c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool,c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A,c_fdisj,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,A,c_fNot,B)),hAPP(c_fe_qual,C)),D)| -hBOOL(hAPP(B,C)).
% 5.94/6.01  ** KEPT (pick-wt=36): 147 [] c_List_Olist__ex1(A,B,hAPP(hAPP(c_List_Olist_OCons(A),C),D))| -c_List_Olist__all(A,c_COMBS(A,tc_HOL_Obool,tc_HOL_Obool,c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),A,c_fdisj,c_COMBB(tc_HOL_Obool,tc_HOL_Obool,A,c_fNot,B)),hAPP(c_fe_qual,C)),D)| -c_List_Olist__ex1(A,B,D).
% 5.94/6.01  ** KEPT (pick-wt=25): 148 [] -class_Orderings_Olinorder(A)|c_List_Olinorder__class_Osort__key(B,A,C,hAPP(hAPP(c_List_Olist_OCons(B),D),E))=hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,C),D),c_List_Olinorder__class_Osort__key(B,A,C,E)).
% 5.94/6.01  ** KEPT (pick-wt=14): 149 [] -class_Orderings_Olinorder(A)| -c_List_Olinorder__class_Osorted(A,B)|c_List_Olinorder__class_Osorted(A,c_List_Olinorder__class_Oinsort__insert__key(A,A,c_COMBI(A),C,B)).
% 5.94/6.01  ** KEPT (pick-wt=14): 150 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),C)|B!=C.
% 5.94/6.01  ** KEPT (pick-wt=17): 151 [] -class_Orderings_Olinorder(A)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),c_List_Olinorder__class_Osort__key(B,A,C,D))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),D).
% 5.94/6.01  ** KEPT (pick-wt=28): 153 [copy,152,flip.2] -class_Orderings_Olinorder(A)|hAPP(c_List_Ofoldl(tc_List_Olist(A),A,c_COMBC(A,tc_List_Olist(A),tc_List_Olist(A),c_List_Olinorder__class_Oinsort__key(A,A,c_COMBI(A))),c_List_Olist_ONil(A)),B)=c_List_Olinorder__class_Osort__key(A,A,c_COMBI(A),B).
% 5.94/6.01  ** KEPT (pick-wt=13): 154 [] -c_List_Olist__all(A,B,hAPP(hAPP(c_List_Olist_OCons(A),C),D))|hBOOL(hAPP(B,C)).
% 5.94/6.01  ** KEPT (pick-wt=13): 155 [] -c_List_Olist__all(A,B,hAPP(hAPP(c_List_Olist_OCons(A),C),D))|c_List_Olist__all(A,B,D).
% 5.94/6.01  ** KEPT (pick-wt=17): 156 [] c_List_Olist__all(A,B,hAPP(hAPP(c_List_Olist_OCons(A),C),D))| -hBOOL(hAPP(B,C))| -c_List_Olist__all(A,B,D).
% 5.94/6.01  ** KEPT (pick-wt=13): 157 [] -c_List_Olist__all(A,B,hAPP(hAPP(c_List_Oappend(A),C),D))|c_List_Olist__all(A,B,C).
% 5.94/6.01  ** KEPT (pick-wt=13): 158 [] -c_List_Olist__all(A,B,hAPP(hAPP(c_List_Oappend(A),C),D))|c_List_Olist__all(A,B,D).
% 5.94/6.01  ** KEPT (pick-wt=17): 159 [] c_List_Olist__all(A,B,hAPP(hAPP(c_List_Oappend(A),C),D))| -c_List_Olist__all(A,B,C)| -c_List_Olist__all(A,B,D).
% 5.94/6.01  ** KEPT (pick-wt=11): 160 [] -class_Orderings_Olinorder(A)|c_List_Olinorder__class_Osort__key(B,A,C,c_List_Olist_ONil(B))=c_List_Olist_ONil(B).
% 5.94/6.01  ** KEPT (pick-wt=10): 161 [] -c_List_Olist__all(A,B,c_List_Orev(A,C))|c_List_Olist__all(A,B,C).
% 5.94/6.01  ** KEPT (pick-wt=10): 162 [] c_List_Olist__all(A,B,c_List_Orev(A,C))| -c_List_Olist__all(A,B,C).
% 5.94/6.01  ** KEPT (pick-wt=12): 163 [] -class_Orderings_Olinorder(A)| -c_List_Odistinct(B,c_List_Olinorder__class_Osort__key(B,A,C,D))|c_List_Odistinct(B,D).
% 5.94/6.01  ** KEPT (pick-wt=12): 164 [] -class_Orderings_Olinorder(A)|c_List_Odistinct(B,c_List_Olinorder__class_Osort__key(B,A,C,D))| -c_List_Odistinct(B,D).
% 5.94/6.01  ** KEPT (pick-wt=12): 165 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=12): 166 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=13): 167 [] -class_Orderings_Olinorder(A)| -c_List_Odistinct(B,C)|c_List_Odistinct(B,c_List_Olinorder__class_Oinsort__insert__key(B,A,D,E,C)).
% 5.94/6.01  ** KEPT (pick-wt=10): 168 [] -class_Orderings_Olinorder(A)|c_List_Olinorder__class_Osorted(A,c_List_Olinorder__class_Osort__key(A,A,c_COMBI(A),B)).
% 5.94/6.01  ** KEPT (pick-wt=46): 169 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(C)),D)| -hBOOL(hAPP(hAPP(E,c_List_Olist_ONil(A)),c_List_Olist_ONil(C)))|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),$f15(E,D,C,B,A))=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(C)),$f13(E,D,C,B,A))|hBOOL(hAPP(hAPP(E,B),D)).
% 5.94/6.01  ** KEPT (pick-wt=41): 170 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(C)),D)| -hBOOL(hAPP(hAPP(E,c_List_Olist_ONil(A)),c_List_Olist_ONil(C)))|hBOOL(hAPP(hAPP(E,$f15(E,D,C,B,A)),$f13(E,D,C,B,A)))|hBOOL(hAPP(hAPP(E,B),D)).
% 5.94/6.01  ** KEPT (pick-wt=61): 171 [] hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(C)),D)| -hBOOL(hAPP(hAPP(E,c_List_Olist_ONil(A)),c_List_Olist_ONil(C)))| -hBOOL(hAPP(hAPP(E,hAPP(hAPP(c_List_Olist_OCons(A),$f16(E,D,C,B,A)),$f15(E,D,C,B,A))),hAPP(hAPP(c_List_Olist_OCons(C),$f14(E,D,C,B,A)),$f13(E,D,C,B,A))))|hBOOL(hAPP(hAPP(E,B),D)).
% 5.94/6.01  ** KEPT (pick-wt=22): 172 [] -c_List_Olist__all(A,B,C)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,D),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),C)))|hBOOL(hAPP(B,hAPP(c_List_Onth(A,C),D))).
% 5.94/6.01  ** KEPT (pick-wt=15): 173 [] c_List_Olist__all(A,B,C)| -hBOOL(hAPP(B,hAPP(c_List_Onth(A,C),$f17(C,B,A)))).
% 5.94/6.01  ** KEPT (pick-wt=7): 174 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.94/6.01  ** KEPT (pick-wt=9): 175 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|A!=B.
% 5.94/6.01  ** KEPT (pick-wt=9): 176 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|B!=A.
% 5.94/6.01  ** KEPT (pick-wt=6): 177 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),A)).
% 5.94/6.01    Following clause subsumed by 175 during input processing: 0 [] A!=B| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 5.94/6.01    Following clause subsumed by 176 during input processing: 0 [] A!=B| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),A)).
% 5.94/6.01    Following clause subsumed by 177 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),A)).
% 5.94/6.01  ** KEPT (pick-wt=10): 178 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.01    Following clause subsumed by 174 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.94/6.01    Following clause subsumed by 178 during input processing: 0 [] A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 5.94/6.01    Following clause subsumed by 174 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.94/6.01  ** KEPT (pick-wt=22): 179 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)))|c_List_Olast(B,hAPP(hAPP(c_List_Odrop(B),A),C))=c_List_Olast(B,C).
% 5.94/6.01  ** KEPT (pick-wt=11): 180 [] -c_List_Odistinct(A,B)|c_List_Odistinct(A,hAPP(hAPP(c_List_Odrop(A),C),B)).
% 5.94/6.01  ** KEPT (pick-wt=13): 181 [] -class_Orderings_Olinorder(A)| -c_List_Olinorder__class_Osorted(A,B)|c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Odrop(A),C),B)).
% 5.94/6.01  ** KEPT (pick-wt=28): 182 [] A=c_List_Olist_ONil(B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),A)))|c_List_Ohd(B,hAPP(hAPP(c_List_Odrop(B),C),A))=hAPP(c_List_Onth(B,A),C).
% 5.94/6.01  ** KEPT (pick-wt=20): 183 [] hAPP(hAPP(c_List_Odrop(A),B),C)!=hAPP(hAPP(c_List_Olist_OCons(A),D),E)|hAPP(c_List_Onth(A,C),B)=D.
% 5.94/6.01    Following clause subsumed by 150 during input processing: 0 [] A!=B|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(C)),A)=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(C)),B).
% 5.94/6.01  ** KEPT (pick-wt=24): 184 [] A!=B| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(D)),A)))|hAPP(c_List_Onth(D,A),C)=hAPP(c_List_Onth(D,B),C).
% 5.94/6.01  ** KEPT (pick-wt=27): 185 [] A=B|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(C)),A)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(C)),B)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f18(C,B,A)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(C)),A))).
% 5.94/6.01  ** KEPT (pick-wt=31): 186 [] A=B|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(C)),A)!=hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(C)),B)|hAPP(c_List_Onth(C,A),$f18(C,B,A))!=hAPP(c_List_Onth(C,B),$f18(C,B,A)).
% 5.94/6.01  ** KEPT (pick-wt=16): 187 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hAPP(c_List_Onth(C,c_List_Oreplicate(C,B,D)),A)=D.
% 5.94/6.01  ** KEPT (pick-wt=15): 188 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)))|B!=c_List_Olist_ONil(A).
% 5.94/6.01  ** KEPT (pick-wt=37): 189 [] -c_List_Odistinct(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,D),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)))|C=D|hAPP(c_List_Onth(A,B),C)!=hAPP(c_List_Onth(A,B),D).
% 5.94/6.01  ** KEPT (pick-wt=10): 190 [] c_List_Odistinct(A,B)|$f20(B,A)!=$f19(B,A).
% 5.94/6.01    Following clause subsumed by 189 during input processing: 0 [] -c_List_Odistinct(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,D),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)))|hAPP(c_List_Onth(A,B),C)!=hAPP(c_List_Onth(A,B),D)|C=D.
% 5.94/6.01  ** KEPT (pick-wt=37): 191 [] -c_List_Odistinct(A,B)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,D),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)))|hAPP(c_List_Onth(A,B),C)=hAPP(c_List_Onth(A,B),D)|C!=D.
% 5.94/6.01  ** KEPT (pick-wt=32): 192 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),c_List_OtakeWhile(A,B,C))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),C)))| -hBOOL(hAPP(B,hAPP(c_List_Onth(A,C),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),c_List_OtakeWhile(A,B,C))))).
% 5.94/6.01  ** KEPT (pick-wt=27): 193 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),c_List_OtakeWhile(B,C,D))))|hAPP(c_List_Onth(B,c_List_OtakeWhile(B,C,D)),A)=hAPP(c_List_Onth(B,D),A).
% 5.94/6.01  ** KEPT (pick-wt=20): 194 [] -class_Orderings_Olinorder(A)| -c_List_Olinorder__class_Osorted(A,c_List_Orev(A,B))|B!=c_List_Olist_ONil(A)|c_List_Ofoldr(A,A,c_Orderings_Oord__class_Omax(A),B,C)=C.
% 5.94/6.01  ** KEPT (pick-wt=30): 196 [copy,195,flip.4] -class_Orderings_Olinorder(A)| -c_List_Olinorder__class_Osorted(A,c_List_Orev(A,B))|B=c_List_Olist_ONil(A)|hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(c_List_Onth(A,B),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),C)=c_List_Ofoldr(A,A,c_Orderings_Oord__class_Omax(A),B,C).
% 5.94/6.01  ** KEPT (pick-wt=39): 197 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),c_List_OdropWhile(B,C,D))))|hAPP(c_List_Onth(B,c_List_OdropWhile(B,C,D)),A)=hAPP(c_List_Onth(B,D),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),c_List_OtakeWhile(B,C,D)))).
% 5.94/6.01  ** KEPT (pick-wt=34): 198 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)))|hAPP(hAPP(c_List_Olist_OCons(B),hAPP(c_List_Onth(B,C),A)),hAPP(hAPP(c_List_Odrop(B),hAPP(c_Nat_OSuc,A)),C))=hAPP(hAPP(c_List_Odrop(B),A),C).
% 5.94/6.01  ** KEPT (pick-wt=17): 199 [] -c_List_Olist__ex(A,B,C)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f21(C,B,A)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),C))).
% 5.94/6.01  ** KEPT (pick-wt=15): 200 [] -c_List_Olist__ex(A,B,C)|hBOOL(hAPP(B,hAPP(c_List_Onth(A,C),$f21(C,B,A)))).
% 5.94/6.01  ** KEPT (pick-wt=22): 201 [] c_List_Olist__ex(A,B,C)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,D),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),C)))| -hBOOL(hAPP(B,hAPP(c_List_Onth(A,C),D))).
% 5.94/6.01  ** KEPT (pick-wt=18): 202 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(A,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)).
% 5.94/6.01  ** KEPT (pick-wt=18): 203 [] -class_Rings_Olinordered__semidom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(A,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)).
% 5.94/6.01  ** KEPT (pick-wt=26): 204 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)))|hAPP(c_List_Onth(B,hAPP(hAPP(c_List_Oappend(B),C),D)),A)=hAPP(c_List_Onth(B,C),A).
% 5.94/6.01  ** KEPT (pick-wt=16): 205 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),hAPP(c_Nat_OSuc,B))).
% 5.94/6.01  ** KEPT (pick-wt=10): 206 [] hAPP(c_Nat_OSuc,A)!=hAPP(c_Nat_OSuc,B)|A=B.
% 5.94/6.01  ** KEPT (pick-wt=16): 207 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)|A=C.
% 5.94/6.01  ** KEPT (pick-wt=16): 208 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)|A!=C.
% 5.94/6.01  ** KEPT (pick-wt=16): 209 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)|B=C.
% 5.94/6.01  ** KEPT (pick-wt=16): 210 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)|B!=C.
% 5.94/6.01  ** KEPT (pick-wt=12): 211 [] -class_Nat_Osemiring__char__0(A)|c_Nat_Osemiring__1__class_Oof__nat(A,B)!=c_Nat_Osemiring__1__class_Oof__nat(A,C)|B=C.
% 5.94/6.01  ** KEPT (pick-wt=12): 212 [] -class_Nat_Osemiring__char__0(A)|c_Nat_Osemiring__1__class_Oof__nat(A,B)=c_Nat_Osemiring__1__class_Oof__nat(A,C)|B!=C.
% 5.94/6.01    Following clause subsumed by 206 during input processing: 0 [] hAPP(c_Nat_OSuc,A)!=hAPP(c_Nat_OSuc,B)|A=B.
% 5.94/6.01  ** KEPT (pick-wt=10): 213 [] hAPP(c_Nat_OSuc,A)=hAPP(c_Nat_OSuc,B)|A!=B.
% 5.94/6.01  ** KEPT (pick-wt=22): 214 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),B)).
% 5.94/6.01  ** KEPT (pick-wt=22): 215 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),B)).
% 5.94/6.01  ** KEPT (pick-wt=18): 217 [copy,216,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),$f22(B,A)))=B.
% 5.94/6.01  ** KEPT (pick-wt=16): 218 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|B!=hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)).
% 5.94/6.01  ** KEPT (pick-wt=21): 219 [] -class_Rings_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(A,B)),c_Nat_Osemiring__1__class_Oof__nat(A,C)).
% 5.94/6.01  ** KEPT (pick-wt=5): 220 [] hAPP(c_Nat_OSuc,A)!=A.
% 5.94/6.01    Following clause subsumed by 220 during input processing: 0 [flip.1] hAPP(c_Nat_OSuc,A)!=A.
% 5.94/6.01  ** KEPT (pick-wt=27): 221 [] -class_Groups_Oordered__ab__group__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E)).
% 5.94/6.01  ** KEPT (pick-wt=27): 222 [] -class_Groups_Oordered__ab__group__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E)).
% 5.94/6.02  ** KEPT (pick-wt=20): 223 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,B))),A)).
% 5.94/6.02  ** KEPT (pick-wt=20): 224 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),A),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=A.
% 5.94/6.02  ** KEPT (pick-wt=21): 225 [] hAPP(hAPP(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).
% 5.94/6.02  ** KEPT (pick-wt=23): 226 [] hAPP(hAPP(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)).
% 5.94/6.02  ** KEPT (pick-wt=19): 227 [] hAPP(hAPP(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).
% 5.94/6.02  ** KEPT (pick-wt=21): 228 [] hAPP(hAPP(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)).
% 5.94/6.02  ** KEPT (pick-wt=21): 229 [] hAPP(hAPP(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).
% 5.94/6.02  ** KEPT (pick-wt=21): 230 [] hAPP(hAPP(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)).
% 5.94/6.02  ** KEPT (pick-wt=21): 231 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(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).
% 5.94/6.02  ** KEPT (pick-wt=23): 232 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(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)).
% 5.94/6.02  ** KEPT (pick-wt=19): 233 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.02  ** KEPT (pick-wt=21): 234 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.02  ** KEPT (pick-wt=21): 235 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(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).
% 5.94/6.02  ** KEPT (pick-wt=21): 236 [] hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 5.94/6.02  ** KEPT (pick-wt=20): 237 [] -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C))|hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.94/6.02  ** KEPT (pick-wt=21): 238 [] -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),C)))|B!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)|hBOOL(hAPP(A,D)).
% 5.94/6.02  ** KEPT (pick-wt=22): 239 [] hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C))| -hBOOL(hAPP(A,$f23(C,B,A))).
% 5.94/6.02  ** KEPT (pick-wt=25): 241 [copy,240,flip.3] hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),C)))| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),$f23(C,B,A))=B.
% 5.94/6.02  ** KEPT (pick-wt=21): 242 [] hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),C)))| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,$f23(C,B,A))).
% 5.94/6.02    Following clause subsumed by 237 during input processing: 0 [] -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C))|hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 5.94/6.02    Following clause subsumed by 238 during input processing: 0 [] -hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),C)))|B!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),D)|hBOOL(hAPP(A,D)).
% 5.94/6.02  ** KEPT (pick-wt=22): 243 [] hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C))| -hBOOL(hAPP(A,$f24(C,B,A))).
% 5.94/6.02  ** KEPT (pick-wt=25): 245 [copy,244,flip.3] hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),C)))| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),$f24(C,B,A))=B.
% 5.94/6.02  ** KEPT (pick-wt=21): 246 [] hBOOL(hAPP(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),C)))| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,$f24(C,B,A))).
% 5.94/6.02  ** KEPT (pick-wt=11): 247 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),c_Groups_Ozero__class_Ozero(A))=B.
% 5.94/6.02  ** KEPT (pick-wt=11): 248 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),B)=c_Groups_Ozero__class_Ozero(A).
% 5.94/6.02  ** KEPT (pick-wt=14): 249 [] -class_Groups_Oab__group__add(A)|B!=C|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)=c_Groups_Ozero__class_Ozero(A).
% 5.94/6.02  ** KEPT (pick-wt=14): 250 [] -class_Groups_Oab__group__add(A)|B=C|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)!=c_Groups_Ozero__class_Ozero(A).
% 5.94/6.02  ** KEPT (pick-wt=14): 251 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)!=c_Groups_Ozero__class_Ozero(A)|B=C.
% 5.94/6.02  ** KEPT (pick-wt=14): 252 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)=c_Groups_Ozero__class_Ozero(A)|B!=C.
% 5.94/6.02  ** KEPT (pick-wt=21): 253 [] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E)|B!=C|D=E.
% 5.94/6.02  ** KEPT (pick-wt=21): 254 [] -class_Groups_Oab__group__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)!=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),D),E)|B=C|D!=E.
% 5.94/6.02  ** KEPT (pick-wt=18): 255 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)|B=D.
% 5.94/6.02  ** KEPT (pick-wt=18): 256 [] -class_Groups_Ocancel__ab__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)|C=D.
% 5.94/6.02  ** KEPT (pick-wt=18): 257 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)|C=D.
% 5.94/6.02    Following clause subsumed by 255 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)|B=D.
% 5.94/6.02  ** KEPT (pick-wt=18): 258 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)|B!=D.
% 5.94/6.02    Following clause subsumed by 257 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)|C=D.
% 5.94/6.02  ** KEPT (pick-wt=18): 259 [] -class_Groups_Ocancel__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)|C!=D.
% 5.94/6.02  ** KEPT (pick-wt=30): 260 [] -class_Groups_Oordered__ab__group__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)=hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),D)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),C),D)).
% 5.94/6.02  ** KEPT (pick-wt=30): 261 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)=hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 5.94/6.02  ** KEPT (pick-wt=25): 262 [] -class_Groups_Oab__semigroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 5.94/6.02  ** KEPT (pick-wt=15): 263 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),C)=B.
% 5.94/6.02  ** KEPT (pick-wt=15): 264 [] -class_Groups_Ogroup__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),C)=B.
% 5.94/6.02  ** KEPT (pick-wt=11): 265 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A))=B.
% 5.94/6.02  ** KEPT (pick-wt=11): 266 [] -class_Groups_Omonoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A))=B.
% 5.94/6.02  ** KEPT (pick-wt=15): 267 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)|B=c_Groups_Ozero__class_Ozero(A).
% 5.94/6.02  ** KEPT (pick-wt=15): 268 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)|B!=c_Groups_Ozero__class_Ozero(A).
% 5.94/6.02  ** KEPT (pick-wt=11): 269 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B)=B.
% 5.94/6.02  ** KEPT (pick-wt=11): 270 [] -class_Groups_Omonoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B)=B.
% 5.94/6.02  ** KEPT (pick-wt=24): 271 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 5.94/6.02  ** KEPT (pick-wt=24): 272 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 5.94/6.02  ** KEPT (pick-wt=30): 273 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),E))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E))).
% 5.94/6.02  ** KEPT (pick-wt=24): 274 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C))).
% 5.94/6.02  ** KEPT (pick-wt=24): 275 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D))).
% 5.94/6.02    Following clause subsumed by 271 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 5.94/6.02  ** KEPT (pick-wt=24): 276 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 5.94/6.02    Following clause subsumed by 272 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 5.94/6.02  ** KEPT (pick-wt=24): 277 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 5.94/6.02  ** KEPT (pick-wt=21): 278 [] hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),A),B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=B.
% 5.94/6.02  ** KEPT (pick-wt=17): 279 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),A),C)),B)).
% 5.94/6.02  ** KEPT (pick-wt=28): 280 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),C),B)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),C),A))).
% 5.94/6.02  ** KEPT (pick-wt=6): 281 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,A).
% 5.94/6.02    Following clause subsumed by 281 during input processing: 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,A).
% 5.94/6.02  ** KEPT (pick-wt=6): 282 [] hAPP(c_Nat_OSuc,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.02    Following clause subsumed by 282 during input processing: 0 [] hAPP(c_Nat_OSuc,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.02    Following clause subsumed by 281 during input processing: 0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,A).
% 5.94/6.02    Following clause subsumed by 282 during input processing: 0 [] hAPP(c_Nat_OSuc,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.02  ** KEPT (pick-wt=14): 283 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),hAPP(c_Nat_OSuc,A))).
% 5.94/6.02  ** KEPT (pick-wt=17): 284 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|A=B.
% 5.94/6.02  ** KEPT (pick-wt=14): 285 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 5.94/6.02  ** KEPT (pick-wt=11): 286 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|A!=B.
% 5.94/6.02  ** KEPT (pick-wt=16): 287 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),hAPP(c_Nat_OSuc,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 5.94/6.02    Following clause subsumed by 205 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),hAPP(c_Nat_OSuc,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 5.94/6.02    Following clause subsumed by 284 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|A=B.
% 5.94/6.02    Following clause subsumed by 286 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|A!=B.
% 5.94/6.02  ** KEPT (pick-wt=17): 288 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|B=A.
% 5.94/6.02    Following clause subsumed by 285 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B))).
% 5.94/6.02  ** KEPT (pick-wt=19): 289 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hAPP(c_Nat_OSuc,A)=B|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),B)).
% 5.94/6.02  ** KEPT (pick-wt=20): 290 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),C)).
% 5.94/6.02    Following clause subsumed by 284 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|A=B.
% 5.94/6.02  ** KEPT (pick-wt=14): 291 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 5.94/6.02    Following clause subsumed by 287 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,A)),hAPP(c_Nat_OSuc,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 5.94/6.02  ** KEPT (pick-wt=13): 292 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.02  ** KEPT (pick-wt=13): 293 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.02  ** KEPT (pick-wt=17): 294 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.02  ** KEPT (pick-wt=12): 295 [] hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)!=A|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.02  ** KEPT (pick-wt=11): 296 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),A)).
% 5.94/6.02  ** KEPT (pick-wt=11): 297 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),B)).
% 5.94/6.02  ** KEPT (pick-wt=22): 298 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 5.94/6.02  ** KEPT (pick-wt=22): 299 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 5.94/6.02  ** KEPT (pick-wt=17): 300 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C))).
% 5.94/6.02  ** KEPT (pick-wt=17): 301 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))).
% 5.94/6.02  ** KEPT (pick-wt=22): 302 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C))).
% 5.94/6.02  ** KEPT (pick-wt=28): 303 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),D))).
% 5.94/6.02  ** KEPT (pick-wt=25): 304 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B)!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),D)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),D)).
% 5.94/6.02  ** KEPT (pick-wt=17): 305 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),C)).
% 5.94/6.02  ** KEPT (pick-wt=29): 306 [] -class_Groups_Osemigroup__add(A)|hAPP(c_List_Ofoldl(A,A,c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_List_Ofoldl(A,A,c_Groups_Oplus__class_Oplus(A),C),D)).
% 5.94/6.02  ** KEPT (pick-wt=20): 307 [] -class_Groups_Oordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 5.94/6.02  ** KEPT (pick-wt=20): 308 [] -class_Groups_Oordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 5.94/6.02  ** KEPT (pick-wt=17): 309 [] -c_List_Olist__ex(A,B,hAPP(hAPP(c_List_Olist_OCons(A),C),D))|hBOOL(hAPP(B,C))|c_List_Olist__ex(A,B,D).
% 5.94/6.02  ** KEPT (pick-wt=13): 310 [] c_List_Olist__ex(A,B,hAPP(hAPP(c_List_Olist_OCons(A),C),D))| -hBOOL(hAPP(B,C)).
% 5.94/6.02  ** KEPT (pick-wt=13): 311 [] c_List_Olist__ex(A,B,hAPP(hAPP(c_List_Olist_OCons(A),C),D))| -c_List_Olist__ex(A,B,D).
% 5.94/6.02  ** KEPT (pick-wt=5): 312 [] -c_List_Olist__ex(A,B,c_List_Olist_ONil(A)).
% 5.94/6.02  ** KEPT (pick-wt=17): 313 [] -c_List_Olist__ex(A,B,hAPP(hAPP(c_List_Oappend(A),C),D))|c_List_Olist__ex(A,B,C)|c_List_Olist__ex(A,B,D).
% 5.94/6.02  ** KEPT (pick-wt=13): 314 [] c_List_Olist__ex(A,B,hAPP(hAPP(c_List_Oappend(A),C),D))| -c_List_Olist__ex(A,B,C).
% 5.94/6.02  ** KEPT (pick-wt=13): 315 [] c_List_Olist__ex(A,B,hAPP(hAPP(c_List_Oappend(A),C),D))| -c_List_Olist__ex(A,B,D).
% 5.94/6.02  ** KEPT (pick-wt=34): 317 [copy,316,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)))|hAPP(c_List_Onth(B,C),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)),hAPP(c_Nat_OSuc,A)))=hAPP(c_List_Onth(B,c_List_Orev(B,C)),A).
% 5.94/6.02  ** KEPT (pick-wt=21): 318 [] -class_Groups_Olinordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 5.94/6.02  ** KEPT (pick-wt=21): 319 [] -class_Groups_Olinordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B)).
% 5.94/6.02  ** KEPT (pick-wt=21): 320 [] -class_Groups_Olinordered__ab__group__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 5.94/6.02  ** KEPT (pick-wt=21): 321 [] -class_Groups_Olinordered__ab__group__add(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 5.94/6.02  ** KEPT (pick-wt=28): 322 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C))).
% 5.94/6.02  ** KEPT (pick-wt=28): 323 [] -class_Groups_Oordered__comm__monoid__add(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),c_Groups_Ozero__class_Ozero(A))).
% 5.94/6.02  ** KEPT (pick-wt=18): 324 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),A),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),A)).
% 5.94/6.02  ** KEPT (pick-wt=18): 325 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),A),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),A)).
% 5.94/6.02  ** KEPT (pick-wt=25): 326 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),B),A)),B)).
% 5.94/6.02  ** KEPT (pick-wt=10): 327 [] -c_List_Olist__ex(A,B,c_List_Orev(A,C))|c_List_Olist__ex(A,B,C).
% 5.94/6.02  ** KEPT (pick-wt=10): 328 [] c_List_Olist__ex(A,B,c_List_Orev(A,C))| -c_List_Olist__ex(A,B,C).
% 5.94/6.02  ** KEPT (pick-wt=11): 329 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Nat_Osemiring__1__class_Oof__nat(A,B)),c_Groups_Ozero__class_Ozero(A))).
% 5.94/6.02  ** KEPT (pick-wt=13): 331 [copy,330,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hAPP(c_Nat_OSuc,$f25(A))=A.
% 5.94/6.02  ** KEPT (pick-wt=12): 332 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|A!=hAPP(c_Nat_OSuc,B).
% 5.94/6.02  ** KEPT (pick-wt=13): 333 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.02    Following clause subsumed by 286 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.02  ** KEPT (pick-wt=19): 335 [copy,334,flip.3] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Nat_OSuc,$f26(B,A))=A.
% 5.94/6.02  ** KEPT (pick-wt=20): 336 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f26(B,A)),B)).
% 5.94/6.02  ** KEPT (pick-wt=12): 337 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.02  ** KEPT (pick-wt=19): 338 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_OSuc,B)))|A!=hAPP(c_Nat_OSuc,C)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),B)).
% 5.94/6.02  ** KEPT (pick-wt=9): 339 [] -class_Rings_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(A).
% 5.94/6.02  ** KEPT (pick-wt=26): 340 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)).
% 5.94/6.02    Following clause subsumed by 300 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 5.94/6.02    Following clause subsumed by 301 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),A),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)).
% 5.94/6.02  ** KEPT (pick-wt=18): 341 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Nat_Osemiring__1__class_Oof__nat(A,B)),c_Nat_Osemiring__1__class_Oof__nat(A,C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 5.94/6.02  ** KEPT (pick-wt=18): 342 [] -class_Rings_Olinordered__semidom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Nat_Osemiring__1__class_Oof__nat(A,B)),c_Nat_Osemiring__1__class_Oof__nat(A,C)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 5.94/6.02    Following clause subsumed by 342 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Nat_Osemiring__1__class_Oof__nat(A,B)),c_Nat_Osemiring__1__class_Oof__nat(A,C))).
% 5.94/6.02    Following clause subsumed by 341 during input processing: 0 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Nat_Osemiring__1__class_Oof__nat(A,B)),c_Nat_Osemiring__1__class_Oof__nat(A,C)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B),C)).
% 5.94/6.02  ** KEPT (pick-wt=25): 343 [] -class_Groups_Omonoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_List_Ofoldl(A,A,c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),C))=hAPP(c_List_Ofoldl(A,A,c_Groups_Oplus__class_Oplus(A),B),C).
% 5.94/6.02  ** KEPT (pick-wt=21): 344 [] -class_Groups_Omonoid__add(A)|hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Olist_OCons(A),B),C))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(c_List_Omonoid__add__class_Olistsum(A),C)).
% 5.94/6.02  ** KEPT (pick-wt=24): 346 [copy,345,flip.2] -class_Groups_Omonoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(c_List_Omonoid__add__class_Olistsum(A),B)),hAPP(c_List_Omonoid__add__class_Olistsum(A),C))=hAPP(c_List_Omonoid__add__class_Olistsum(A),hAPP(hAPP(c_List_Oappend(A),B),C)).
% 5.94/6.02  ** KEPT (pick-wt=22): 347 [] -class_Orderings_Olinorder(A)|hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(B,A,C),D),E))=hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),E)).
% 5.94/6.02  ** KEPT (pick-wt=18): 349 [copy,348,flip.2] -class_Groups_Oab__semigroup__add(A)|hAPP(c_List_Ofoldl(A,A,c_Groups_Oplus__class_Oplus(A),B),C)=c_List_Ofoldr(A,A,c_Groups_Oplus__class_Oplus(A),C,B).
% 5.94/6.02  ** KEPT (pick-wt=12): 350 [] -class_Groups_Omonoid__add(A)|c_List_Omonoid__add__class_Olistsum(A)=c_List_Ofoldl(A,A,c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)).
% 5.94/6.02  ** KEPT (pick-wt=24): 352 [copy,351,flip.2] -class_Groups_Omonoid__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_List_Ofoldr(A,A,c_Groups_Oplus__class_Oplus(A),C,c_Groups_Ozero__class_Ozero(A)))=hAPP(c_List_Ofoldl(A,A,c_Groups_Oplus__class_Oplus(A),B),C).
% 5.94/6.02  ** KEPT (pick-wt=20): 353 [] -class_Groups_Omonoid__add(A)|hAPP(c_List_Ofoldl(A,A,c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B)=c_List_Ofoldr(A,A,c_Groups_Oplus__class_Oplus(A),B,c_Groups_Ozero__class_Ozero(A)).
% 5.94/6.02  ** KEPT (pick-wt=21): 354 [] -class_Rings_Olinordered__idom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 5.94/6.02  ** KEPT (pick-wt=21): 355 [] -class_Rings_Olinordered__idom(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)),c_Groups_Ozero__class_Ozero(A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),c_Groups_Ozero__class_Ozero(A))).
% 5.94/6.02  ** KEPT (pick-wt=26): 356 [] -class_Rings_Olinordered__semidom(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D))).
% 5.94/6.02  ** KEPT (pick-wt=43): 357 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)))|hAPP(hAPP(c_List_Oappend(B),hAPP(hAPP(c_List_Otake(B),A),C)),hAPP(hAPP(c_List_Olist_OCons(B),c_List_Ohd(B,hAPP(hAPP(c_List_Odrop(B),A),C))),c_List_Olist_ONil(B)))=hAPP(hAPP(c_List_Otake(B),hAPP(c_Nat_OSuc,A)),C).
% 5.94/6.02    Following clause subsumed by 301 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),C),B))).
% 5.94/6.02  ** KEPT (pick-wt=20): 359 [copy,358,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))|hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,$f27(B,A))))=B.
% 5.94/6.02  ** KEPT (pick-wt=18): 360 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))|B!=hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,hAPP(c_Nat_OSuc,C))).
% 5.94/6.02  ** KEPT (pick-wt=11): 361 [] -c_List_Odistinct(A,B)|c_List_Odistinct(A,hAPP(hAPP(c_List_Otake(A),C),B)).
% 5.94/6.02  ** KEPT (pick-wt=13): 362 [] -class_Orderings_Olinorder(A)| -c_List_Olinorder__class_Osorted(A,B)|c_List_Olinorder__class_Osorted(A,hAPP(hAPP(c_List_Otake(A),C),B)).
% 5.94/6.02  ** KEPT (pick-wt=17): 363 [] hAPP(hAPP(c_List_Otake(A),B),C)!=c_List_Olist_ONil(A)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|C=c_List_Olist_ONil(A).
% 5.94/6.02  ** KEPT (pick-wt=13): 364 [] hAPP(hAPP(c_List_Otake(A),B),C)=c_List_Olist_ONil(A)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.02  ** KEPT (pick-wt=13): 365 [] hAPP(hAPP(c_List_Otake(A),B),C)=c_List_Olist_ONil(A)|C!=c_List_Olist_ONil(A).
% 5.94/6.02  ** KEPT (pick-wt=22): 366 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hAPP(c_List_Onth(C,hAPP(hAPP(c_List_Otake(C),B),D)),A)=hAPP(c_List_Onth(C,D),A).
% 5.94/6.02  ** KEPT (pick-wt=20): 368 [copy,367,flip.2] hAPP(hAPP(c_List_Oappend(A),B),C)!=D|hAPP(hAPP(c_List_Otake(A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)),D)=B.
% 5.94/6.02  ** KEPT (pick-wt=20): 369 [] hAPP(hAPP(c_List_Oappend(A),B),C)!=D|C=hAPP(hAPP(c_List_Odrop(A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)),D).
% 5.94/6.02  ** KEPT (pick-wt=32): 371 [copy,370,flip.2] hAPP(hAPP(c_List_Oappend(A),B),C)=D|hAPP(hAPP(c_List_Otake(A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)),D)!=B|C!=hAPP(hAPP(c_List_Odrop(A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)),D).
% 5.94/6.02  ** KEPT (pick-wt=25): 372 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)))|hAPP(hAPP(c_List_Otake(B),A),c_List_Obutlast(B,C))=hAPP(hAPP(c_List_Otake(B),A),C).
% 5.94/6.02  ** KEPT (pick-wt=17): 373 [] -class_Rings_Olinordered__idom(A)|B=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 5.94/6.02  ** KEPT (pick-wt=10): 374 [] c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.02  ** KEPT (pick-wt=10): 375 [] c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.02  ** KEPT (pick-wt=16): 376 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 5.94/6.02  ** KEPT (pick-wt=16): 377 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 5.94/6.02  ** KEPT (pick-wt=15): 378 [] -class_Groups_Olinordered__ab__group__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 5.94/6.02  ** KEPT (pick-wt=15): 379 [] -class_Groups_Olinordered__ab__group__add(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 5.94/6.02  ** KEPT (pick-wt=40): 381 [copy,380,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)))|hAPP(hAPP(c_List_Oappend(B),hAPP(hAPP(c_List_Otake(B),A),C)),hAPP(hAPP(c_List_Olist_OCons(B),hAPP(c_List_Onth(B,C),A)),c_List_Olist_ONil(B)))=hAPP(hAPP(c_List_Otake(B),hAPP(c_Nat_OSuc,A)),C).
% 5.94/6.02  ** KEPT (pick-wt=39): 383 [copy,382,flip.2] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)))|hAPP(hAPP(c_List_Oappend(B),hAPP(hAPP(c_List_Otake(B),A),C)),hAPP(hAPP(c_List_Olist_OCons(B),hAPP(c_List_Onth(B,C),A)),hAPP(hAPP(c_List_Odrop(B),hAPP(c_Nat_OSuc,A)),C)))=C.
% 5.94/6.02  ** KEPT (pick-wt=16): 384 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 5.94/6.02  ** KEPT (pick-wt=16): 385 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)).
% 5.94/6.02    Following clause subsumed by 300 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B),C))).
% 5.94/6.02  ** KEPT (pick-wt=41): 386 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)))|hAPP(hAPP(c_List_Olist__update(B,C),A),D)=hAPP(hAPP(c_List_Oappend(B),hAPP(hAPP(c_List_Otake(B),A),C)),hAPP(hAPP(c_List_Olist_OCons(B),D),hAPP(hAPP(c_List_Odrop(B),hAPP(c_Nat_OSuc,A)),C))).
% 5.94/6.02  ** KEPT (pick-wt=25): 387 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 5.94/6.02  ** KEPT (pick-wt=19): 388 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)).
% 5.94/6.02  ** KEPT (pick-wt=19): 389 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 5.94/6.02  ** KEPT (pick-wt=22): 390 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),A),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B),C))).
% 5.94/6.02  ** KEPT (pick-wt=18): 391 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 5.94/6.02  ** KEPT (pick-wt=18): 392 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,A),B))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 5.94/6.02  ** KEPT (pick-wt=9): 393 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))).
% 5.94/6.02  ** KEPT (pick-wt=16): 394 [] -hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(tc_Int_Oint),A),B))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 5.94/6.02  ** KEPT (pick-wt=16): 395 [] hBOOL(hAPP(hAPP(c_HOL_Oe_qual__class_Oe_qual(tc_Int_Oint),A),B))|hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),A),B)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 5.94/6.02  ** KEPT (pick-wt=10): 396 [] c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)!=c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B)|A=B.
% 5.94/6.02  ** KEPT (pick-wt=10): 397 [] c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)=c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B)|A!=B.
% 5.94/6.02  ** KEPT (pick-wt=14): 398 [] hAPP(hAPP(c_List_Olist__update(A,B),C),D)!=c_List_Olist_ONil(A)|B=c_List_Olist_ONil(A).
% 5.94/6.02  ** KEPT (pick-wt=14): 399 [] hAPP(hAPP(c_List_Olist__update(A,B),C),D)=c_List_Olist_ONil(A)|B!=c_List_Olist_ONil(A).
% 5.94/6.02  ** KEPT (pick-wt=8): 400 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),B)).
% 5.94/6.02  ** KEPT (pick-wt=17): 401 [] -class_Orderings_Olinorder(A)|B=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 5.94/6.02  ** KEPT (pick-wt=11): 402 [] -class_Orderings_Olinorder(A)|B!=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C)).
% 5.94/6.02  ** KEPT (pick-wt=11): 403 [] -class_Orderings_Olinorder(A)|B!=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 5.94/6.02    Following clause subsumed by 401 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B))|B=C.
% 5.94/6.02  ** KEPT (pick-wt=14): 404 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 5.94/6.02    Following clause subsumed by 402 during input processing: 0 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B!=C.
% 5.94/6.02    Following clause subsumed by 401 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 5.94/6.02    Following clause subsumed by 401 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B))|C=B.
% 5.94/6.02    Following clause subsumed by 402 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B))|C!=B.
% 5.94/6.02    Following clause subsumed by 401 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 5.94/6.02  ** KEPT (pick-wt=11): 405 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B!=C.
% 5.94/6.02  ** KEPT (pick-wt=14): 406 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 5.94/6.02    Following clause subsumed by 406 during input processing: 0 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 5.94/6.02    Following clause subsumed by 405 during input processing: 0 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B!=C.
% 5.94/6.02  ** KEPT (pick-wt=11): 407 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|C!=B.
% 5.94/6.02    Following clause subsumed by 406 during input processing: 0 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 5.94/6.02  ** KEPT (pick-wt=14): 408 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 5.94/6.02  ** KEPT (pick-wt=17): 409 [] -class_Orderings_Oord(A)|B!=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 5.94/6.02  ** KEPT (pick-wt=17): 410 [] -class_Orderings_Oorder(A)|B!=C| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),B)).
% 5.94/6.02  ** KEPT (pick-wt=17): 411 [] -class_Orderings_Oord(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|C!=D|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 5.94/6.02  ** KEPT (pick-wt=17): 412 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B!=D|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 5.94/6.02  ** KEPT (pick-wt=20): 413 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 5.94/6.02  ** KEPT (pick-wt=20): 414 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),B))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,D),C)).
% 5.94/6.02    Following clause subsumed by 406 during input processing: 0 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 5.94/6.02    Following clause subsumed by 401 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|B=C|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),B)).
% 5.94/6.02  ** KEPT (pick-wt=39): 415 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),B)))|hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,B),A),C))=hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),B)),C)),hAPP(c_List_Onth(tc_Nat_Onat,B),A)).
% 5.94/6.02  ** KEPT (pick-wt=35): 416 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)))|hAPP(hAPP(c_List_Olist__update(B,hAPP(hAPP(c_List_Oappend(B),C),D)),A),E)=hAPP(hAPP(c_List_Oappend(B),hAPP(hAPP(c_List_Olist__update(B,C),A),E)),D).
% 5.94/6.02  ** KEPT (pick-wt=23): 417 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)))|hAPP(c_List_Onth(B,hAPP(hAPP(c_List_Olist__update(B,C),A),D)),A)=D.
% 5.94/6.02  ** KEPT (pick-wt=26): 418 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)))|hAPP(hAPP(c_List_Olist__update(B,C),A),D)!=C|hAPP(c_List_Onth(B,C),A)=D.
% 5.94/6.02  ** KEPT (pick-wt=26): 419 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)))|hAPP(hAPP(c_List_Olist__update(B,C),A),D)=C|hAPP(c_List_Onth(B,C),A)!=D.
% 5.94/6.02  ** KEPT (pick-wt=26): 420 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)))|A!=D|hAPP(c_List_Onth(B,hAPP(hAPP(c_List_Olist__update(B,C),A),E)),D)=E.
% 5.94/6.02  ** KEPT (pick-wt=30): 421 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)))|A=D|hAPP(c_List_Onth(B,hAPP(hAPP(c_List_Olist__update(B,C),A),E)),D)=hAPP(c_List_Onth(B,C),D).
% 5.94/6.02    Following clause subsumed by 416 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)))|hAPP(hAPP(c_List_Olist__update(B,hAPP(hAPP(c_List_Oappend(B),C),D)),A),E)=hAPP(hAPP(c_List_Oappend(B),hAPP(hAPP(c_List_Olist__update(B,C),A),E)),D).
% 5.94/6.02  ** KEPT (pick-wt=19): 422 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D)).
% 5.94/6.02  ** KEPT (pick-wt=19): 423 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 5.94/6.02  ** KEPT (pick-wt=25): 424 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),D))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,C),D)).
% 5.94/6.02    Following clause subsumed by 376 during input processing: 0 [] -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B)))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 5.94/6.02    Following clause subsumed by 377 during input processing: 0 [] hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,A),B)).
% 5.94/6.02    Following clause subsumed by 396 during input processing: 0 [] c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)!=c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B)|A=B.
% 5.94/6.02    Following clause subsumed by 397 during input processing: 0 [] c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,A)=c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint,B)|A!=B.
% 5.94/6.02    Following clause subsumed by 388 during input processing: 0 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))).
% 5.94/6.02    Following clause subsumed by 389 during input processing: 0 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),C))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(A,B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),D),C))).
% 5.94/6.02  ** KEPT (pick-wt=23): 425 [] -class_Groups_Ominus(A)|hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(B,A)),C),D),E)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(C,E)),hAPP(D,E)).
% 5.94/6.02  ** KEPT (pick-wt=10): 426 [] -class_Orderings_Olinorder(A)|hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),B)=B.
% 5.94/6.02  ** KEPT (pick-wt=15): 427 [] -class_Orderings_Olinorder(A)|hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)=hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),B).
% 5.94/6.02    Following clause subsumed by 427 during input processing: 0 [] -class_Orderings_Olinorder(A)|hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)=hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),B).
% 5.94/6.02  ** KEPT (pick-wt=20): 428 [] -class_Orderings_Olinorder(A)|hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C))=hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C).
% 5.94/6.02    Following clause subsumed by 428 during input processing: 0 [] -class_Orderings_Olinorder(A)|hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C))=hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C).
% 5.94/6.02  ** KEPT (pick-wt=25): 429 [] -class_Orderings_Olinorder(A)|hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))=hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)).
% 5.94/6.02    Following clause subsumed by 429 during input processing: 0 [] -class_Orderings_Olinorder(A)|hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D))=hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),D)).
% 5.94/6.02  ** KEPT (pick-wt=25): 430 [] -class_Orderings_Olinorder(A)|hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)=hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)).
% 5.94/6.02    Following clause subsumed by 430 during input processing: 0 [] -class_Orderings_Olinorder(A)|hAPP(hAPP(c_Orderings_Oord__class_Omax(A),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),C)),D)=hAPP(hAPP(c_Orderings_Oord__class_Omax(A),B),hAPP(hAPP(c_Orderings_Oord__class_Omax(A),C),D)).
% 5.94/6.02    Following clause subsumed by 425 during input processing: 0 [] -class_Groups_Ominus(A)|hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(B,A)),C),D),E)=hAPP(hAPP(c_Groups_Ominus__class_Ominus(A),hAPP(C,E)),hAPP(D,E)).
% 5.94/6.02  ** KEPT (pick-wt=11): 431 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),c_Groups_Ozero__class_Ozero(A)),B)=B.
% 5.94/6.02  ** KEPT (pick-wt=11): 432 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),c_Groups_Ozero__class_Ozero(A))=B.
% 5.94/6.02  ** KEPT (pick-wt=35): 433 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),D),E))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),E)).
% 5.94/6.02  ** KEPT (pick-wt=25): 434 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)),C).
% 5.94/6.02  ** KEPT (pick-wt=25): 435 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 5.94/6.02    Following clause subsumed by 435 during input processing: 0 [flip.2] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D)).
% 5.94/6.02  ** KEPT (pick-wt=25): 436 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),D))=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),D)).
% 5.94/6.02  ** KEPT (pick-wt=15): 437 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),C),B).
% 5.94/6.02  ** KEPT (pick-wt=14): 439 [copy,438,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)!=B|C=c_Groups_Ozero__class_Ozero(A).
% 5.94/6.02  ** KEPT (pick-wt=14): 441 [copy,440,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|hAPP(hAPP(c_Groups_Oplus__class_Oplus(A),B),C)=B|C!=c_Groups_Ozero__class_Ozero(A).
% 5.94/6.03  ** KEPT (pick-wt=33): 442 [] -hBOOL(hAPP(A,hAPP(c_List_Onth(B,C),$f28(A,C,B,D))))|hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,D),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(B)),C)))|c_List_OtakeWhile(B,A,C)=hAPP(hAPP(c_List_Otake(B),D),C).
% 5.94/6.03  ** KEPT (pick-wt=31): 443 [] -hBOOL(hAPP(A,hAPP(c_List_Onth(B,C),$f28(A,C,B,D))))|hBOOL(hAPP(A,hAPP(c_List_Onth(B,C),D)))|c_List_OtakeWhile(B,A,C)=hAPP(hAPP(c_List_Otake(B),D),C).
% 5.94/6.03  ** KEPT (pick-wt=22): 444 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(B,C))|c_List_Ofilter(D,B,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(D,A,E),C),F))=c_List_Ofilter(D,B,F).
% 5.94/6.03  ** KEPT (pick-wt=19): 445 [] -class_Orderings_Olinorder(A)|c_List_Ofilter(B,C,c_List_Olinorder__class_Osort__key(B,A,D,E))=c_List_Olinorder__class_Osort__key(B,A,D,c_List_Ofilter(B,C,E)).
% 5.94/6.03  ** KEPT (pick-wt=16): 446 [] -class_Orderings_Olinorder(A)|c_List_Olinorder__class_Osorted(A,c_List_Ofilter(A,hAPP(c_COMBC(A,A,tc_HOL_Obool,c_fe_qual),hAPP(B,C)),C)).
% 5.94/6.03  ** KEPT (pick-wt=16): 447 [] -hBOOL(hAPP(A,B))|c_List_Ofilter(C,A,c_List_Oreplicate(C,D,B))=c_List_Oreplicate(C,D,B).
% 5.94/6.03  ** KEPT (pick-wt=9): 448 [] -c_List_Odistinct(A,B)|c_List_Odistinct(A,c_List_Ofilter(A,C,B)).
% 5.94/6.03  ** KEPT (pick-wt=23): 450 [copy,449,flip.2] -hBOOL(hAPP(A,B))|hAPP(hAPP(c_List_Olist_OCons(C),B),c_List_Ofilter(C,A,D))=c_List_Ofilter(C,A,hAPP(hAPP(c_List_Olist_OCons(C),B),D)).
% 5.94/6.03  ** KEPT (pick-wt=73): 451 [] -c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Orev(tc_Nat_Onat,c_List_Omap(tc_List_Olist(A),tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_List_Olist(A)),B)))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(A))),c_List_Otranspose(A,B))))| -hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,D),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(A))),c_List_Ofilter(tc_List_Olist(A),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(A),c_Orderings_Oord__class_Oless(tc_Nat_Onat,C),c_Nat_Osize__class_Osize(tc_List_Olist(A))),B))))|hAPP(c_List_Onth(A,hAPP(c_List_Onth(tc_List_Olist(A),c_List_Otranspose(A,B)),C)),D)=hAPP(c_List_Onth(A,hAPP(c_List_Onth(tc_List_Olist(A),B),D)),C).
% 5.94/6.03  ** KEPT (pick-wt=8): 452 [] -class_Enum_Oenum(A)| -class_Enum_Oenum(B)|class_Enum_Oenum(tc_fun(A,B)).
% 5.94/6.03  ** KEPT (pick-wt=6): 453 [] -class_Orderings_Opreorder(A)|class_Orderings_Opreorder(tc_fun(B,A)).
% 5.94/6.03  ** KEPT (pick-wt=6): 454 [] -class_Orderings_Oorder(A)|class_Orderings_Oorder(tc_fun(B,A)).
% 5.94/6.03  ** KEPT (pick-wt=6): 455 [] -class_Orderings_Oord(A)|class_Orderings_Oord(tc_fun(B,A)).
% 5.94/6.03  ** KEPT (pick-wt=6): 456 [] -class_Groups_Ominus(A)|class_Groups_Ominus(tc_fun(B,A)).
% 5.94/6.03  ** KEPT (pick-wt=8): 457 [] -class_Enum_Oenum(A)| -class_HOL_Oe_qual(B)|class_HOL_Oe_qual(tc_fun(A,B)).
% 5.94/6.03  ** KEPT (pick-wt=9): 458 [] -hBOOL(hAPP(hAPP(c_fe_qual,A),B))|A=B.
% 5.94/6.03  ** KEPT (pick-wt=9): 459 [] A!=B|hBOOL(hAPP(hAPP(c_fe_qual,A),B)).
% 5.94/6.03  ** KEPT (pick-wt=6): 460 [] -hBOOL(hAPP(c_fNot,A))| -hBOOL(A).
% 5.94/6.03  ** KEPT (pick-wt=10): 461 [] -hBOOL(A)| -hBOOL(B)|hBOOL(hAPP(hAPP(c_fconj,A),B)).
% 5.94/6.03  ** KEPT (pick-wt=8): 462 [] -hBOOL(hAPP(hAPP(c_fconj,A),B))|hBOOL(A).
% 5.94/6.03  ** KEPT (pick-wt=8): 463 [] -hBOOL(hAPP(hAPP(c_fconj,A),B))|hBOOL(B).
% 5.94/6.03  ** KEPT (pick-wt=8): 464 [] -hBOOL(A)|hBOOL(hAPP(hAPP(c_fdisj,A),B)).
% 5.94/6.03  ** KEPT (pick-wt=8): 465 [] -hBOOL(A)|hBOOL(hAPP(hAPP(c_fdisj,B),A)).
% 5.94/6.03  ** KEPT (pick-wt=10): 466 [] -hBOOL(hAPP(hAPP(c_fdisj,A),B))|hBOOL(A)|hBOOL(B).
% 5.94/6.03  ** KEPT (pick-wt=3): 468 [copy,467,flip.1] v_b!=v_a.
% 5.94/6.03  ** KEPT (pick-wt=19): 469 [] -c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_a),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),v_b),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),A),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))).
% 5.94/6.03    Following clause subsumed by 3 during input processing: 0 [copy,2,flip.1] hAPP(hAPP(c_List_Olist_OCons(A),B),C)!=c_List_Olist_ONil(A).
% 5.94/6.03    Following clause subsumed by 2 during input processing: 0 [copy,3,flip.1] c_List_Olist_ONil(A)!=hAPP(hAPP(c_List_Olist_OCons(A),B),C).
% 5.94/6.03    Following clause subsumed by 282 during input processing: 0 [copy,281,flip.1] hAPP(c_Nat_OSuc,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.03    Following clause subsumed by 281 during input processing: 0 [copy,282,flip.1] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=hAPP(c_Nat_OSuc,A).
% 5.94/6.03  
% 5.94/6.03  ------------> process sos:
% 5.94/6.03  ** KEPT (pick-wt=3): 510 [] A=A.
% 5.94/6.03  ** KEPT (pick-wt=19): 511 [] c_List_Odistinct(tc_Arrow__Order__Mirabelle_Oalt,hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),$c3),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),$c2),hAPP(hAPP(c_List_Olist_OCons(tc_Arrow__Order__Mirabelle_Oalt),$c1),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt))))).
% 5.94/6.03  ** KEPT (pick-wt=4): 512 [] c_List_Odistinct(A,c_List_Olist_ONil(A)).
% 5.94/6.03  ** KEPT (pick-wt=17): 513 [] c_List_Osplice(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C),c_List_Olist_ONil(A))=hAPP(hAPP(c_List_Olist_OCons(A),B),C).
% 5.94/6.03  ---> New Demodulator: 514 [new_demod,513] c_List_Osplice(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C),c_List_Olist_ONil(A))=hAPP(hAPP(c_List_Olist_OCons(A),B),C).
% 5.94/6.03  ** KEPT (pick-wt=13): 516 [copy,515,flip.1] hAPP(hAPP(c_List_Olist_OCons(A),B),c_List_Olist_ONil(A))=c_List_Oinsert(A,B,c_List_Olist_ONil(A)).
% 5.94/6.03  ---> New Demodulator: 517 [new_demod,516] hAPP(hAPP(c_List_Olist_OCons(A),B),c_List_Olist_ONil(A))=c_List_Oinsert(A,B,c_List_Olist_ONil(A)).
% 5.94/6.03  ** KEPT (pick-wt=16): 518 [] A=c_List_Olist_ONil(B)|c_List_Olast(B,hAPP(hAPP(c_List_Olist_OCons(B),C),A))=c_List_Olast(B,A).
% 5.94/6.03  ** KEPT (pick-wt=7): 519 [] c_List_Obutlast(A,c_List_Olist_ONil(A))=c_List_Olist_ONil(A).
% 5.94/6.03  ---> New Demodulator: 520 [new_demod,519] c_List_Obutlast(A,c_List_Olist_ONil(A))=c_List_Olist_ONil(A).
% 5.94/6.03  ** KEPT (pick-wt=29): 522 [copy,521,flip.1] hAPP(hAPP(c_List_Olist_OCons(A),B),hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Osplice(A,D,E)))=c_List_Osplice(A,hAPP(hAPP(c_List_Olist_OCons(A),B),D),hAPP(hAPP(c_List_Olist_OCons(A),C),E)).
% 5.94/6.03  ---> New Demodulator: 523 [new_demod,522] hAPP(hAPP(c_List_Olist_OCons(A),B),hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Osplice(A,D,E)))=c_List_Osplice(A,hAPP(hAPP(c_List_Olist_OCons(A),B),D),hAPP(hAPP(c_List_Olist_OCons(A),C),E)).
% 5.94/6.03  ** KEPT (pick-wt=7): 524 [] c_List_Osplice(A,B,c_List_Olist_ONil(A))=B.
% 5.94/6.03  ---> New Demodulator: 525 [new_demod,524] c_List_Osplice(A,B,c_List_Olist_ONil(A))=B.
% 5.94/6.03  ** KEPT (pick-wt=7): 526 [] c_List_Osplice(A,c_List_Olist_ONil(A),B)=B.
% 5.94/6.03  ---> New Demodulator: 527 [new_demod,526] c_List_Osplice(A,c_List_Olist_ONil(A),B)=B.
% 5.94/6.03  ** KEPT (pick-wt=21): 529 [copy,528,flip.2] A=c_List_Olist_ONil(B)|hAPP(hAPP(c_List_Olist_OCons(B),C),c_List_Obutlast(B,A))=c_List_Obutlast(B,hAPP(hAPP(c_List_Olist_OCons(B),C),A)).
% 5.94/6.03    Following clause subsumed by 518 during input processing: 0 [] A=c_List_Olist_ONil(B)|c_List_Olast(B,hAPP(hAPP(c_List_Olist_OCons(B),C),A))=c_List_Olast(B,A).
% 5.94/6.03  ** KEPT (pick-wt=9): 530 [] c_List_Olist_Olist__case(A,B,C,D,c_List_Olist_ONil(B))=C.
% 5.94/6.03  ---> New Demodulator: 531 [new_demod,530] c_List_Olist_Olist__case(A,B,C,D,c_List_Olist_ONil(B))=C.
% 5.94/6.03  ** KEPT (pick-wt=17): 532 [] c_List_Olist_Olist__case(A,B,C,D,hAPP(hAPP(c_List_Olist_OCons(B),E),F))=hAPP(hAPP(D,E),F).
% 5.94/6.03  ** KEPT (pick-wt=20): 534 [copy,533,demod,517] A=c_List_Olist_ONil(B)|hAPP(hAPP(c_List_Oappend(B),c_List_Obutlast(B,A)),c_List_Oinsert(B,c_List_Olast(B,A),c_List_Olist_ONil(B)))=A.
% 5.94/6.03  ** KEPT (pick-wt=9): 535 [] c_List_Olist_Olist__rec(A,B,C,D,c_List_Olist_ONil(B))=C.
% 5.94/6.03  ---> New Demodulator: 536 [new_demod,535] c_List_Olist_Olist__rec(A,B,C,D,c_List_Olist_ONil(B))=C.
% 5.94/6.03  ** KEPT (pick-wt=24): 537 [] c_List_Olist_Olist__rec(A,B,C,D,hAPP(hAPP(c_List_Olist_OCons(B),E),F))=hAPP(hAPP(hAPP(D,E),F),c_List_Olist_Olist__rec(A,B,C,D,F)).
% 5.94/6.03  ** KEPT (pick-wt=4): 538 [] c_List_Onull(A,c_List_Olist_ONil(A)).
% 5.94/6.03  ** KEPT (pick-wt=14): 540 [copy,539,demod,517] c_List_Olast(A,hAPP(hAPP(c_List_Oappend(A),B),c_List_Oinsert(A,C,c_List_Olist_ONil(A))))=C.
% 5.94/6.03  ---> New Demodulator: 541 [new_demod,540] c_List_Olast(A,hAPP(hAPP(c_List_Oappend(A),B),c_List_Oinsert(A,C,c_List_Olist_ONil(A))))=C.
% 5.94/6.03  ** KEPT (pick-wt=23): 542 [] hAPP(hAPP(c_List_Oappend(A),hAPP(hAPP(c_List_Oappend(A),B),C)),D)=hAPP(hAPP(c_List_Oappend(A),B),hAPP(hAPP(c_List_Oappend(A),C),D)).
% 5.94/6.03  ---> New Demodulator: 543 [new_demod,542] hAPP(hAPP(c_List_Oappend(A),hAPP(hAPP(c_List_Oappend(A),B),C)),D)=hAPP(hAPP(c_List_Oappend(A),B),hAPP(hAPP(c_List_Oappend(A),C),D)).
% 5.94/6.03  ** KEPT (pick-wt=23): 544 [] hAPP(hAPP(c_List_Oappend(A),hAPP(hAPP(c_List_Olist_OCons(A),B),C)),D)=hAPP(hAPP(c_List_Olist_OCons(A),B),hAPP(hAPP(c_List_Oappend(A),C),D)).
% 5.94/6.03  ---> New Demodulator: 545 [new_demod,544] hAPP(hAPP(c_List_Oappend(A),hAPP(hAPP(c_List_Olist_OCons(A),B),C)),D)=hAPP(hAPP(c_List_Olist_OCons(A),B),hAPP(hAPP(c_List_Oappend(A),C),D)).
% 5.94/6.03  ** KEPT (pick-wt=9): 546 [] hAPP(hAPP(c_List_Oappend(A),c_List_Olist_ONil(A)),B)=B.
% 5.94/6.03  ---> New Demodulator: 547 [new_demod,546] hAPP(hAPP(c_List_Oappend(A),c_List_Olist_ONil(A)),B)=B.
% 5.94/6.03  ** KEPT (pick-wt=9): 548 [] hAPP(hAPP(c_List_Oappend(A),B),c_List_Olist_ONil(A))=B.
% 5.94/6.03  ---> New Demodulator: 549 [new_demod,548] hAPP(hAPP(c_List_Oappend(A),B),c_List_Olist_ONil(A))=B.
% 5.94/6.03  ** KEPT (pick-wt=21): 551 [copy,550,flip.2] A=c_List_Olist_ONil(B)|hAPP(hAPP(c_List_Oappend(B),C),c_List_Obutlast(B,A))=c_List_Obutlast(B,hAPP(hAPP(c_List_Oappend(B),C),A)).
% 5.94/6.03  ** KEPT (pick-wt=16): 552 [] A=c_List_Olist_ONil(B)|c_List_Olast(B,hAPP(hAPP(c_List_Oappend(B),C),A))=c_List_Olast(B,A).
% 5.94/6.03    Following clause subsumed by 552 during input processing: 0 [] A=c_List_Olist_ONil(B)|c_List_Olast(B,hAPP(hAPP(c_List_Oappend(B),C),A))=c_List_Olast(B,A).
% 5.94/6.03  ** KEPT (pick-wt=14): 554 [copy,553,demod,517] c_List_Obutlast(A,hAPP(hAPP(c_List_Oappend(A),B),c_List_Oinsert(A,C,c_List_Olist_ONil(A))))=B.
% 5.94/6.03  ---> New Demodulator: 555 [new_demod,554] c_List_Obutlast(A,hAPP(hAPP(c_List_Oappend(A),B),c_List_Oinsert(A,C,c_List_Olist_ONil(A))))=B.
% 5.94/6.03  ** KEPT (pick-wt=7): 556 [] c_List_Orotate1(A,c_List_Olist_ONil(A))=c_List_Olist_ONil(A).
% 5.94/6.03  ---> New Demodulator: 557 [new_demod,556] c_List_Orotate1(A,c_List_Olist_ONil(A))=c_List_Olist_ONil(A).
% 5.94/6.03  ** KEPT (pick-wt=19): 559 [copy,558,demod,517] c_List_Orotate1(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C))=hAPP(hAPP(c_List_Oappend(A),C),c_List_Oinsert(A,B,c_List_Olist_ONil(A))).
% 5.94/6.03  ** KEPT (pick-wt=23): 560 [] c_List_Omaps(A,B,C,hAPP(hAPP(c_List_Olist_OCons(A),D),E))=hAPP(hAPP(c_List_Oappend(B),hAPP(C,D)),c_List_Omaps(A,B,C,E)).
% 5.94/6.03  ** KEPT (pick-wt=20): 562 [copy,561,demod,517,flip.2] A=c_List_Olist_ONil(B)|hAPP(hAPP(c_List_Oappend(B),$f8(B,A)),c_List_Oinsert(B,$f7(B,A),c_List_Olist_ONil(B)))=A.
% 5.94/6.03  ** KEPT (pick-wt=23): 564 [copy,563,demod,517] hAPP(hAPP(c_List_Oappend(A),c_List_Oreplicate(A,B,C)),c_List_Oinsert(A,C,c_List_Olist_ONil(A)))=hAPP(hAPP(c_List_Olist_OCons(A),C),c_List_Oreplicate(A,B,C)).
% 5.94/6.03  ** KEPT (pick-wt=21): 566 [copy,565,demod,517] c_List_Orev(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C))=hAPP(hAPP(c_List_Oappend(A),c_List_Orev(A,C)),c_List_Oinsert(A,B,c_List_Olist_ONil(A))).
% 5.94/6.03  ** KEPT (pick-wt=16): 567 [] A=c_List_Olist_ONil(B)|c_List_Ohd(B,hAPP(hAPP(c_List_Oappend(B),A),C))=c_List_Ohd(B,A).
% 5.94/6.03    Following clause subsumed by 567 during input processing: 0 [] A=c_List_Olist_ONil(B)|c_List_Ohd(B,hAPP(hAPP(c_List_Oappend(B),A),C))=c_List_Ohd(B,A).
% 5.94/6.03  ** KEPT (pick-wt=11): 568 [] c_List_Orev(A,c_List_Oreplicate(A,B,C))=c_List_Oreplicate(A,B,C).
% 5.94/6.03  ---> New Demodulator: 569 [new_demod,568] c_List_Orev(A,c_List_Oreplicate(A,B,C))=c_List_Oreplicate(A,B,C).
% 5.94/6.03  ** KEPT (pick-wt=7): 570 [] c_List_Orev(A,c_List_Orev(A,B))=B.
% 5.94/6.03  ---> New Demodulator: 571 [new_demod,570] c_List_Orev(A,c_List_Orev(A,B))=B.
% 5.94/6.03  ** KEPT (pick-wt=7): 572 [] c_List_Orev(A,c_List_Olist_ONil(A))=c_List_Olist_ONil(A).
% 5.94/6.03  ---> New Demodulator: 573 [new_demod,572] c_List_Orev(A,c_List_Olist_ONil(A))=c_List_Olist_ONil(A).
% 5.94/6.03  ** KEPT (pick-wt=19): 574 [] c_List_Orev(A,hAPP(hAPP(c_List_Oappend(A),B),C))=hAPP(hAPP(c_List_Oappend(A),c_List_Orev(A,C)),c_List_Orev(A,B)).
% 5.94/6.03  ** KEPT (pick-wt=13): 575 [] A=c_List_Olist_ONil(B)|c_List_Ohd(B,c_List_Orev(B,A))=c_List_Olast(B,A).
% 5.94/6.03  ** KEPT (pick-wt=13): 576 [] A=c_List_Olist_ONil(B)|c_List_Olast(B,c_List_Orev(B,A))=c_List_Ohd(B,A).
% 5.94/6.03  ** KEPT (pick-wt=25): 577 [] hAPP(hAPP(c_List_Oappend(A),c_List_Oreplicate(A,B,C)),c_List_Oreplicate(A,D,C))=hAPP(hAPP(c_List_Oappend(A),c_List_Oreplicate(A,D,C)),c_List_Oreplicate(A,B,C)).
% 5.94/6.03  ** KEPT (pick-wt=10): 578 [] c_List_Ohd(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C))=B.
% 5.94/6.03  ---> New Demodulator: 579 [new_demod,57
% 5.94/6.03  Search stopped in tp_alloc by max_mem option.
% 5.94/6.03  8] c_List_Ohd(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C))=B.
% 5.94/6.03  ** KEPT (pick-wt=29): 580 [] hAPP(hAPP(c_List_Oappend(A),c_List_Oreplicate(A,B,C)),hAPP(hAPP(c_List_Olist_OCons(A),C),D))=hAPP(hAPP(c_List_Olist_OCons(A),C),hAPP(hAPP(c_List_Oappend(A),c_List_Oreplicate(A,B,C)),D)).
% 5.94/6.03  ** KEPT (pick-wt=9): 581 [] c_List_Omaps(A,B,C,c_List_Olist_ONil(A))=c_List_Olist_ONil(B).
% 5.94/6.03  ** KEPT (pick-wt=22): 583 [copy,582,demod,517,flip.2] A=c_List_Olist_ONil(B)|hAPP(hAPP(c_List_Oappend(B),c_List_Otl(B,A)),c_List_Oinsert(B,c_List_Ohd(B,A),c_List_Olist_ONil(B)))=c_List_Orotate1(B,A).
% 5.94/6.03  ** KEPT (pick-wt=21): 585 [copy,584,flip.2] A=c_List_Olist_ONil(B)|hAPP(hAPP(c_List_Oappend(B),c_List_Otl(B,A)),C)=c_List_Otl(B,hAPP(hAPP(c_List_Oappend(B),A),C)).
% 5.94/6.03  ** KEPT (pick-wt=10): 586 [] c_List_Otl(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C))=C.
% 5.94/6.03  ---> New Demodulator: 587 [new_demod,586] c_List_Otl(A,hAPP(hAPP(c_List_Olist_OCons(A),B),C))=C.
% 5.94/6.03  ** KEPT (pick-wt=7): 588 [] c_List_Otl(A,c_List_Olist_ONil(A))=c_List_Olist_ONil(A).
% 5.94/6.03  ---> New Demodulator: 589 [new_demod,588] c_List_Otl(A,c_List_Olist_ONil(A))=c_List_Olist_ONil(A).
% 5.94/6.03  ** KEPT (pick-wt=20): 590 [] hBOOL(hAPP(A,B))|c_List_OdropWhile(C,A,hAPP(hAPP(c_List_Olist_OCons(C),B),D))=hAPP(hAPP(c_List_Olist_OCons(C),B),D).
% 5.94/6.03  ** KEPT (pick-wt=8): 591 [] c_List_OdropWhile(A,B,c_List_Olist_ONil(A))=c_List_Olist_ONil(A).
% 5.94/6.03  ---> New Demodulator: 592 [new_demod,591] c_List_OdropWhile(A,B,c_List_Olist_ONil(A))=c_List_Olist_ONil(A).
% 5.94/6.03  ** KEPT (pick-wt=14): 593 [] hAPP(hAPP(c_List_Oappend(A),c_List_OtakeWhile(A,B,C)),c_List_OdropWhile(A,B,C))=C.
% 5.94/6.03  ---> New Demodulator: 594 [new_demod,593] hAPP(hAPP(c_List_Oappend(A),c_List_OtakeWhile(A,B,C)),c_List_OdropWhile(A,B,C))=C.
% 5.94/6.03  ** KEPT (pick-wt=12): 595 [] A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Ohd(B,c_List_Oreplicate(B,A,C))=C.
% 5.94/6.03  ** KEPT (pick-wt=12): 596 [] A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_List_Olast(B,c_List_Oreplicate(B,A,C))=C.
% 5.94/6.03  ** KEPT (pick-wt=16): 598 [copy,597,flip.2] A=c_List_Olist_ONil(B)|hAPP(hAPP(c_List_Olist_OCons(B),$f10(B,A)),$f9(B,A))=A.
% 5.94/6.03  ** KEPT (pick-wt=16): 600 [copy,599,flip.2] A=c_List_Olist_ONil(B)|hAPP(hAPP(c_List_Olist_OCons(B),$f12(B,A)),$f11(B,A))=A.
% 5.94/6.03  ** KEPT (pick-wt=9): 601 [] c_List_Omap__filter(A,B,C,c_List_Olist_ONil(A))=c_List_Olist_ONil(B).
% 5.94/6.03  ** KEPT (pick-wt=23): 602 [] hBOOL(hAPP(A,B))|c_List_OtakeWhile(C,A,hAPP(hAPP(c_List_Oappend(C),D),hAPP(hAPP(c_List_Olist_OCons(C),B),E)))=c_List_OtakeWhile(C,A,D).
% 5.94/6.03  ** KEPT (pick-wt=8): 603 [] c_List_OtakeWhile(A,B,c_List_Olist_ONil(A))=c_List_Olist_ONil(A).
% 5.94/6.03  ---> New Demodulator: 604 [new_demod,603] c_List_OtakeWhile(A,B,c_List_Olist_ONil(A))=c_List_Olist_ONil(A).
% 5.94/6.03  ** KEPT (pick-wt=8): 605 [] c_List_Oreplicate(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)=c_List_Olist_ONil(A).
% 5.94/6.03  ** KEPT (pick-wt=16): 606 [] hBOOL(hAPP(A,B))|c_List_OtakeWhile(C,A,hAPP(hAPP(c_List_Olist_OCons(C),B),D))=c_List_Olist_ONil(C).
% 5.94/6.03  ** KEPT (pick-wt=8): 607 [] c_List_Olist_Olist__size(A,B,c_List_Olist_ONil(A))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.03  ---> New Demodulator: 608 [new_demod,607] c_List_Olist_Olist__size(A,B,c_List_Olist_ONil(A))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 5.94/6.03  ** KEPT (pick-wt=14): 610 [copy,609,flip.2] A=c_List_Olist_ONil(B)|hAPP(c_List_Onth(B,A),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_List_Ohd(B,A).
% 5.94/6.03  
% 5.94/6.03  Search stopped in tp_alloc by max_mem option.
% 5.94/6.03  
% 5.94/6.03  ============ end of search ============
% 5.94/6.03  
% 5.94/6.03  -------------- statistics -------------
% 5.94/6.03  clauses given                  0
% 5.94/6.03  clauses generated             45
% 5.94/6.03  clauses kept                 534
% 5.94/6.03  clauses forward subsumed      80
% 5.94/6.03  clauses back subsumed          0
% 5.94/6.03  Kbytes malloced            11718
% 5.94/6.03  
% 5.94/6.03  ----------- times (seconds) -----------
% 5.94/6.03  user CPU time          0.05          (0 hr, 0 min, 0 sec)
% 5.94/6.03  system CPU time        0.00          (0 hr, 0 min, 0 sec)
% 5.94/6.03  wall-clock time        5             (0 hr, 0 min, 5 sec)
% 5.94/6.03  
% 5.94/6.03  Process 18625 finished Wed Jul 27 08:49:36 2022
% 5.94/6.03  Otter interrupted
% 5.94/6.03  PROOF NOT FOUND
%------------------------------------------------------------------------------