%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SWV853-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n010.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 13:21:40 EDT 2022

% Result   : Unknown 187.43s 187.56s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SWV853-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n010.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Jul 27 05:58:54 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 187.43/187.52  ----- Otter 3.3f, August 2004 -----
% 187.43/187.52  The process was started by sandbox2 on n010.cluster.edu,
% 187.43/187.52  Wed Jul 27 05:58:55 2022
% 187.43/187.52  The command was "./otter".  The process ID is 6989.
% 187.43/187.52  
% 187.43/187.52  set(prolog_style_variables).
% 187.43/187.52  set(auto).
% 187.43/187.52     dependent: set(auto1).
% 187.43/187.52     dependent: set(process_input).
% 187.43/187.52     dependent: clear(print_kept).
% 187.43/187.52     dependent: clear(print_new_demod).
% 187.43/187.52     dependent: clear(print_back_demod).
% 187.43/187.52     dependent: clear(print_back_sub).
% 187.43/187.52     dependent: set(control_memory).
% 187.43/187.52     dependent: assign(max_mem, 12000).
% 187.43/187.52     dependent: assign(pick_given_ratio, 4).
% 187.43/187.52     dependent: assign(stats_level, 1).
% 187.43/187.52     dependent: assign(max_seconds, 10800).
% 187.43/187.52  clear(print_given).
% 187.43/187.52  
% 187.43/187.52  list(usable).
% 187.43/187.52  0 [] A=A.
% 187.43/187.52  0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a.
% 187.43/187.52  0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 187.43/187.52  0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 187.43/187.52  0 [] c_HOL_Ominus__class_Ominus(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))=V_A.
% 187.43/187.52  0 [] c_HOL_Ominus__class_Ominus(V_A,V_A,tc_fun(T_a,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] hAPP(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_x)=hAPP(V_f,hAPP(V_g,V_x)).
% 187.43/187.52  0 [] hAPP(V_a,hAPP(V_b,V_v))=hAPP(c_Fun_Ocomp(V_a,V_b,T_c,T_b,T_a),V_v).
% 187.43/187.52  0 [] c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool))=c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ouminus__class_Ouminus(V_a,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 187.43/187.52  0 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_C,V_D,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))| -c_lesse_quals(V_D,V_B,tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,V_C,tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] -class_Lattices_Oboolean__algebra(T_a)|c_HOL_Ouminus__class_Ouminus(V_x,T_a)!=c_HOL_Ouminus__class_Ouminus(V_y,T_a)|V_x=V_y.
% 187.43/187.52  0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ouminus__class_Ouminus(V_a,T_a)!=c_HOL_Ouminus__class_Ouminus(V_b,T_a)|V_a=V_b.
% 187.43/187.52  0 [] c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool))!=c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool))|V_A=V_B.
% 187.43/187.52  0 [] c_Natural_Oevalc(c_Com_Ocom_OSKIP,V_s,V_s).
% 187.43/187.52  0 [] c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s).
% 187.43/187.52  0 [] c_Com_OWT(V_c2)| -c_Com_OWT(c_Com_Ocom_OSemi(V_c1,V_c2)).
% 187.43/187.52  0 [] c_Com_OWT(V_c1)| -c_Com_OWT(c_Com_Ocom_OSemi(V_c1,V_c2)).
% 187.43/187.52  0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ozero__class_Ozero(T_a)=c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a).
% 187.43/187.52  0 [] c_Finite__Set_Ofold(V_f,V_z,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a)=V_z.
% 187.43/187.52  0 [] c_Fun_Ocomp(V_f,c_Fun_Ocomp(V_g,V_h,T_d,T_c,T_a),T_c,T_b,T_a)=c_Fun_Ocomp(c_Fun_Ocomp(V_f,V_g,T_c,T_b,T_d),V_h,T_d,T_b,T_a).
% 187.43/187.52  0 [] c_Com_Ocom_OSemi(V_com1_H,V_com2_H)!=c_Com_Ocom_OSKIP.
% 187.43/187.52  0 [] -class_HOL_Ouminus(T_b)|hAPP(c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(t_a,T_b)),v_x)=c_HOL_Ouminus__class_Ouminus(hAPP(V_A,v_x),T_b).
% 187.43/187.52  0 [] -class_OrderedGroup_Oordered__ab__group__add(T_a)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 187.43/187.52  0 [] c_Com_OWT(c_Com_Ocom_OSemi(V_c0,V_c1))| -c_Com_OWT(V_c1)| -c_Com_OWT(V_c0).
% 187.43/187.52  0 [] c_Finite__Set_Ofinite(c_List_Oset(V_xs,T_a),T_a).
% 187.43/187.52  0 [] hAPP(c_Set_Ovimage(V_f,T_a,T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_c,tc_fun(T_b,tc_bool)))=c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,hAPP(c_COMBB(c_Set_Ovimage(V_f,T_a,T_b),tc_fun(T_b,tc_bool),tc_fun(T_a,tc_bool),T_c),V_B),T_c,tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_Fun_Ocomp(V_a,V_b,T_c,T_b,T_a)!=c_Fun_Ocomp(V_c,V_d,T_d,T_b,T_a)|hAPP(V_a,hAPP(V_b,V_v))=hAPP(V_c,hAPP(V_d,V_v)).
% 187.43/187.52  0 [] hAPP(V_f,hAPP(V_g,V_x))!=hAPP(V_f_H,hAPP(V_g_H,V_x_H))|hAPP(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_x)=hAPP(c_Fun_Ocomp(V_f_H,V_g_H,T_d,T_a,T_e),V_x_H).
% 187.43/187.52  0 [] hBOOL(hAPP(V_A,hAPP(V_f,V_x)))| -hBOOL(hAPP(hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_A),V_x)).
% 187.43/187.52  0 [] hBOOL(hAPP(hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_A),V_x))| -hBOOL(hAPP(V_A,hAPP(V_f,V_x))).
% 187.43/187.52  0 [] c_HOL_Ominus__class_Ominus(V_B,c_HOL_Ominus__class_Ominus(V_C,V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))=V_A| -c_lesse_quals(V_B,V_C,tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|c_lesse_quals(V_y_H,V_x_H,T_a)| -c_lesse_quals(V_y,V_x,T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|c_lesse_quals(V_y,V_x,T_a)| -c_lesse_quals(V_y_H,V_x_H,T_a).
% 187.43/187.52  0 [] hAPP(c_Set_Ovimage(V_f,T_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_Com_Ocom_OSKIP!=c_Com_Ocom_OSemi(V_com1_H,V_com2_H).
% 187.43/187.52  0 [] hAPP(c_Fun_Othe__inv__into(V_A,c_Fun_Ocomp(V_f,V_g,T_a,T_b,T_c),T_c,T_b),V_x)=hAPP(c_Fun_Ocomp(c_Fun_Othe__inv__into(V_A,V_g,T_c,T_a),c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(V_g,T_c,T_a),V_A),V_f,T_a,T_b),T_a,T_c,T_b),V_x)| -hBOOL(hAPP(hAPP(c_in(T_b),V_x),hAPP(c_Set_Oimage(V_f,T_a,T_b),hAPP(c_Set_Oimage(V_g,T_c,T_a),V_A))))| -c_Fun_Oinj__on(V_g,V_A,T_c,T_a)| -c_Fun_Oinj__on(V_f,hAPP(c_Set_Oimage(V_g,T_c,T_a),V_A),T_a,T_b).
% 187.43/187.52  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Oordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Oordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Oordered__ab__group__add(T_a)|c_lesse_quals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Oordered__ab__group__add(T_a)|c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 187.43/187.52  0 [] c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(V_x,T_a),V_A),V_B,tc_fun(T_a,tc_bool))=hAPP(c_Set_Oinsert(V_x,T_a),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)))|hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)).
% 187.43/187.52  0 [] c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(V_x,T_a),V_A),V_B,tc_fun(T_a,tc_bool))=c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)).
% 187.43/187.52  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a))!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 187.43/187.52  0 [] c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(V_A,hAPP(c_Set_Oinsert(V_x,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)),T_a)=c_Finite__Set_Ocard(V_A,T_a)|hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.52  0 [] c_Finite__Set_Ocard(V_A,T_a)=c_HOL_Ozero__class_Ozero(tc_nat)|c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.52  0 [] c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)=c_HOL_Ozero__class_Ozero(tc_nat).
% 187.43/187.52  0 [] c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(V_x,T_a),V_A),T_a)=c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(V_A,hAPP(c_Set_Oinsert(V_x,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)),T_a))| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.52  0 [] c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)| -c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,hAPP(c_Set_Oinsert(V_a,T_a),V_B),tc_fun(T_a,tc_bool)),T_a).
% 187.43/187.52  0 [] c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,hAPP(c_Set_Oinsert(V_a,T_a),V_B),tc_fun(T_a,tc_bool)),T_a)| -c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a).
% 187.43/187.52  0 [] hAPP(c_Set_Oinsert(V_a,T_a),c_HOL_Ominus__class_Ominus(V_A,hAPP(c_Set_Oinsert(V_a,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)))=hAPP(c_Set_Oinsert(V_a,T_a),V_A).
% 187.43/187.52  0 [] -class_Orderings_Olinorder(T_a)|c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(V_a,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a)=V_a.
% 187.43/187.52  0 [] c_HOL_Ominus__class_Ominus(V_A,hAPP(c_Set_Oinsert(V_a,T_a),V_B),tc_fun(T_a,tc_bool))=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),hAPP(c_Set_Oinsert(V_a,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_HOL_Ominus__class_Ominus(V_A,hAPP(c_Set_Oinsert(V_a,T_a),V_B),tc_fun(T_a,tc_bool))=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,hAPP(c_Set_Oinsert(V_a,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] -class_Orderings_Olinorder(T_a)|c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(V_a,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a)=V_a.
% 187.43/187.52  0 [] c_lesse_quals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] V_A=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] hAPP(c_Fun_Othe__inv__into(V_A,V_f,T_a,T_b),hAPP(V_f,V_x))=V_x| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b).
% 187.43/187.52  0 [] -c_Fun_Oinj__on(V_f,V_A,T_aa,T_a)|hAPP(c_Fun_Othe__inv__into(V_A,V_f,T_aa,T_a),hAPP(V_f,V_x))=V_x| -hBOOL(hAPP(hAPP(c_in(T_aa),V_x),V_A)).
% 187.43/187.52  0 [] -class_Lattices_Oboolean__algebra(T_a)|c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(T_a),T_a)=c_Orderings_Obot__class_Obot(T_a).
% 187.43/187.52  0 [] -class_Lattices_Oboolean__algebra(T_a)|c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(T_a),T_a)=c_Orderings_Otop__class_Otop(T_a).
% 187.43/187.52  0 [] c_Finite__Set_Ocard(V_A,T_a)!=c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)| -c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)|V_A=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)| -c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),T_a)| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.52  0 [] c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),T_a)| -c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.52  0 [] c_HOL_Ominus__class_Ominus(V_A,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))=V_A.
% 187.43/187.52  0 [] c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_HOL_Ominus__class_Ominus(V_A,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_B),tc_fun(T_a,tc_bool)),hAPP(c_Set_Oimage(V_f,T_b,T_a),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_b,tc_bool))),tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_lesse_quals(hAPP(c_Set_Oimage(V_f,T_b,T_a),hAPP(c_Set_Ovimage(V_f,T_b,T_a),V_A)),V_A,tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_lesse_quals(V_A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool))| -c_lesse_quals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C),tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)))=V_B| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] -class_Lattices_Oboolean__algebra(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),c_HOL_Ouminus__class_Ouminus(V_x,T_a))=c_Orderings_Otop__class_Otop(T_a).
% 187.43/187.52  0 [] -class_Lattices_Oboolean__algebra(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),c_HOL_Ouminus__class_Ouminus(V_x,T_a)),V_x)=c_Orderings_Otop__class_Otop(T_a).
% 187.43/187.52  0 [] c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,hAPP(c_COMBB(V_B,T_c,tc_fun(T_a,tc_bool),T_b),V_f),T_b,tc_fun(T_a,tc_bool))=c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(V_f,T_b,T_c),V_A),V_B,T_c,tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] hAPP(c_Set_Oimage(V_f,T_b,T_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_c,tc_fun(T_b,tc_bool)))=c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,hAPP(c_COMBB(c_Set_Oimage(V_f,T_b,T_a),tc_fun(T_b,tc_bool),tc_fun(T_a,tc_bool),T_c),V_B),T_c,tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(V_f,T_c,T_b),V_A),V_B,T_b,tc_fun(T_a,tc_bool))=c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,hAPP(c_COMBB(V_B,T_b,tc_fun(T_a,tc_bool),T_c),V_f),T_c,tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)))=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool))),V_A)=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_Fun_Oinj__on(c_Fun_Ocomp(V_g,V_f,T_b,T_c,T_a),V_A,T_a,T_c)| -c_Fun_Oinj__on(V_g,hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),T_b,T_c)| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b).
% 187.43/187.52  0 [] c_Fun_Oinj__on(V_g,hAPP(c_Set_Oimage(V_f,T_a,T_c),V_A),T_c,T_b)| -c_Fun_Oinj__on(c_Fun_Ocomp(V_g,V_f,T_c,T_b,T_a),V_A,T_a,T_b).
% 187.43/187.52  0 [] c_Fun_Oinj__on(c_Fun_Othe__inv__into(V_A,V_f,T_a,T_b),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),T_b,T_a)| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b).
% 187.43/187.52  0 [] hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(V_A,V_f,T_a,T_b),T_b,T_a),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A))=V_A| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b).
% 187.43/187.52  0 [] c_Finite__Set_Ocard(hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),T_b)=c_Finite__Set_Ocard(V_A,T_a)| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b).
% 187.43/187.52  0 [] hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),hAPP(V_f,V_x))=V_x| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b).
% 187.43/187.52  0 [] hAPP(c_Fun_Ocomp(c_COMBK(V_c,T_b,T_c),V_f,T_c,T_b,t_a),v_x)=V_c.
% 187.43/187.52  0 [] c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(V_A,hAPP(c_Set_Oinsert(V_x,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)),T_a))=c_Finite__Set_Ocard(V_A,T_a)| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.52  0 [] c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)| -c_Finite__Set_Ofinite(V_A,T_a)| -c_Finite__Set_Ofinite(V_B,T_a).
% 187.43/187.52  0 [] c_Finite__Set_Ofinite(V_A,T_a)| -c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)| -c_Finite__Set_Ofinite(V_B,T_a).
% 187.43/187.52  0 [] c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool))),V_B).
% 187.43/187.52  0 [] hAPP(c_Set_Ovimage(V_f,T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)))=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_Com_Ocom_OSemi(V_com1,V_com2)!=c_Com_Ocom_OSemi(V_com1_H,V_com2_H)|V_com1=V_com1_H.
% 187.43/187.52  0 [] c_Com_Ocom_OSemi(V_com1,V_com2)!=c_Com_Ocom_OSemi(V_com1_H,V_com2_H)|V_com2=V_com2_H.
% 187.43/187.52  0 [] c_lesse_quals(c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))| -c_lesse_quals(V_B,V_A,tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_lesse_quals(V_B,V_A,tc_fun(T_a,tc_bool))| -c_lesse_quals(c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_lesse_quals(c_HOL_Ouminus__class_Ouminus(V_B,tc_fun(T_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a).
% 187.43/187.52  0 [] hAPP(c_Set_Ovimage(V_f,T_a,T_b),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_b,tc_bool)))=c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_A),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_B),tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_Fun_Oinj__on(V_f,c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b)| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b).
% 187.43/187.52  0 [] c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),T_a)| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.52  0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ozero__class_Ozero(T_a)!=c_HOL_Ouminus__class_Ouminus(V_a,T_a)|c_HOL_Ozero__class_Ozero(T_a)=V_a.
% 187.43/187.52  0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))=c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.52  0 [] c_Fun_Ocomp(V_f,c_Fun_Ofun__upd(V_g,V_x,V_y,T_a,T_c),T_c,T_b,T_a)=c_Fun_Ofun__upd(c_Fun_Ocomp(V_f,V_g,T_c,T_b,T_a),V_x,hAPP(V_f,V_y),T_a,T_b).
% 187.43/187.52  0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)|V_xa=V_y.
% 187.43/187.52  0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|V_x_H=V_y_H.
% 187.43/187.52  0 [] c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_n,V_s2)| -c_Natural_Oevaln(V_c1,V_s1,V_n,V_s2)| -c_Natural_Oevaln(V_c0,V_s0,V_n,V_s1).
% 187.43/187.53  0 [] c_Com_OWT(c_Com_Ocom_OSKIP).
% 187.43/187.53  0 [] c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_s2)| -c_Natural_Oevalc(V_c1,V_s1,V_s2)| -c_Natural_Oevalc(V_c0,V_s0,V_s1).
% 187.43/187.53  0 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_x=V_y.
% 187.43/187.53  0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=V_b.
% 187.43/187.53  0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=V_b.
% 187.43/187.53  0 [] hAPP(c_Set_Ovimage(V_f,T_a,T_b),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_b,tc_bool)))=c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_A),tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_lesse_quals(hAPP(c_Set_Ovimage(V_f,T_b,T_a),V_A),hAPP(c_Set_Ovimage(V_f,T_b,T_a),V_B),tc_fun(T_b,tc_bool))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] -class_HOL_Ominus(T_b)|hAPP(c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(t_a,T_b)),v_x)=c_HOL_Ominus__class_Ominus(hAPP(V_A,v_x),hAPP(V_B,v_x),T_b).
% 187.43/187.53  0 [] hAPP(c_Set_Ovimage(c_Fun_Ocomp(V_g,V_f,T_c,T_b,T_a),T_a,T_b),V_x)=hAPP(c_Set_Ovimage(V_f,T_a,T_c),hAPP(c_Set_Ovimage(V_g,T_c,T_b),V_x)).
% 187.43/187.53  0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ouminus__class_Ouminus(V_a,T_a).
% 187.43/187.53  0 [] V_t=V_s| -c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t).
% 187.43/187.53  0 [] -class_OrderedGroup_Oordered__ab__group__add(T_a)|c_HOL_Ouminus__class_Ouminus(V_a,T_a)!=V_a|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 187.43/187.53  0 [] c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))=V_A.
% 187.43/187.53  0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)=V_a.
% 187.43/187.53  0 [] -class_Lattices_Oboolean__algebra(T_a)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a)=V_x.
% 187.43/187.53  0 [] -class_OrderedGroup_Ogroup__add(T_a)|V_b=c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a).
% 187.43/187.53  0 [] -class_OrderedGroup_Ogroup__add(T_a)|V_a=c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a).
% 187.43/187.53  0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)=V_b.
% 187.43/187.53  0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a)=c_HOL_Ominus__class_Ominus(V_b,V_a,T_a).
% 187.43/187.53  0 [] V_t=V_s| -c_Natural_Oevalc(c_Com_Ocom_OSKIP,V_s,V_t).
% 187.43/187.53  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a).
% 187.43/187.53  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)| -c_lesse_quals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a).
% 187.43/187.53  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a)| -c_lesse_quals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a).
% 187.43/187.53  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)| -c_lesse_quals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a).
% 187.43/187.53  0 [] -hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))| -hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))| -hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool))))|hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)).
% 187.43/187.53  0 [] -hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))| -hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool)))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))))|hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))| -hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool))))|hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))| -hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_a),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_B)))| -hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),V_B)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_b),V_a),hAPP(c_Set_Ovimage(V_f,T_b,T_a),V_A)))| -hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_a)),V_A)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_b),V_a),hAPP(c_Set_Ovimage(V_f,T_b,T_a),V_B)))| -hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_a)),V_B)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),V_B))| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_B))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),V_A))| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_A))).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(c_Fun_Ocomp(V_f,V_g,T_c,T_a,T_b),T_b,T_a),V_r)=hAPP(c_Set_Oimage(V_f,T_c,T_a),hAPP(c_Set_Oimage(V_g,T_b,T_c),V_r)).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool))),V_A)=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_HOL_Ominus__class_Ominus(V_B,V_A,tc_fun(T_a,tc_bool)))=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B).
% 187.43/187.53  0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool))=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_HOL_Ominus__class_Ominus(V_A,V_C,tc_fun(T_a,tc_bool))),c_HOL_Ominus__class_Ominus(V_B,V_C,tc_fun(T_a,tc_bool))).
% 187.43/187.53  0 [] hAPP(c_Set_Ovimage(V_f,T_a,T_b),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),V_A),V_B))=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_A)),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_B)).
% 187.43/187.53  0 [] hAPP(c_Fun_Ocomp(V_f,V_g,T_c,T_b,t_a),v_x)=hAPP(V_f,hAPP(V_g,v_x)).
% 187.43/187.53  0 [] hAPP(c_Com_Ocom_OBODY,V_pname_H)!=c_Com_Ocom_OSKIP.
% 187.43/187.53  0 [] hAPP(c_Com_Ocom_OBODY,V_pname_H)!=c_Com_Ocom_OSemi(V_com1,V_com2).
% 187.43/187.53  0 [] c_Com_Ocom_OSemi(V_com1,V_com2)!=hAPP(c_Com_Ocom_OBODY,V_pname_H).
% 187.43/187.53  0 [] c_Com_Ocom_OSKIP!=hAPP(c_Com_Ocom_OBODY,V_pname_H).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Ohoare__valids(V_G,V_ts,t_a)|hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(V_G,V_ts)),V_ts)).
% 187.43/187.53  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_x,c_Finite__Set_Olinorder__class_OMax(V_A,T_a),T_a)| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.53  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(c_Finite__Set_Olinorder__class_OMin(V_A,T_a),V_x,T_a)| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.53  0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(hAPP(c_in(T_a),c_Finite__Set_Olinorder__class_OMin(V_A,T_a)),V_A))|V_A=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.53  0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(hAPP(c_in(T_a),c_Finite__Set_Olinorder__class_OMax(V_A,T_a)),V_A))|V_A=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.53  0 [] c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(V_x,T_a),V_A),T_a)=c_Finite__Set_Ocard(V_A,T_a)| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.53  0 [] hAPP(c_Set_Oinsert(V_a,T_a),c_HOL_Ominus__class_Ominus(V_A,hAPP(c_Set_Oinsert(V_a,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)))=V_A| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)).
% 187.43/187.53  0 [] hAPP(V_f,V_a)=V_b| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),hAPP(c_Set_Ovimage(V_f,T_a,T_b),hAPP(c_Set_Oinsert(V_b,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)))))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_aa),V_a),hAPP(c_Set_Ovimage(V_f,T_aa,T_a),hAPP(c_Set_Oinsert(hAPP(V_f,V_a),T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))))).
% 187.43/187.53  0 [] c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(V_x,T_a),V_A),hAPP(c_Set_Oinsert(V_x,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool))=V_A|hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)).
% 187.43/187.53  0 [] c_Finite__Set_Ocard(V_A,T_a)!=c_HOL_Ozero__class_Ozero(tc_nat)| -c_Finite__Set_Ofinite(V_A,T_a)|V_A=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,hAPP(c_COMBB(c_Set_Oinsert(V_a,T_b),tc_fun(T_b,tc_bool),tc_fun(T_b,tc_bool),T_a),V_B),T_a,tc_fun(T_b,tc_bool))=hAPP(c_Set_Oinsert(V_a,T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)))| -hBOOL(hAPP(hAPP(c_in(T_a),V_u),V_A)).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_b,hAPP(c_Set_Oinsert(V_a,T_a),V_A),T_a,T_a)=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_b,V_A,T_a,T_a))| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.53  0 [] hAPP(c_Set_Ovimage(c_COMBK(V_c,T_b,T_a),T_a,T_b),V_A)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))|hBOOL(hAPP(hAPP(c_in(T_b),V_c),V_A)).
% 187.43/187.53  0 [] c_lesse_quals(V_A,hAPP(c_Set_Oinsert(V_x,T_a),V_B),tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool))| -c_lesse_quals(c_HOL_Ominus__class_Ominus(V_A,hAPP(c_Set_Oinsert(V_x,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hAPP(c_Set_Ovimage(V_f,T_a,T_b),hAPP(c_Set_Oinsert(V_a,T_b),V_B))=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(c_Set_Ovimage(V_f,T_a,T_b),hAPP(c_Set_Oinsert(V_a,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))))),hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_B)).
% 187.43/187.53  0 [] hAPP(V_f,hAPP(c_Fun_Othe__inv__into(V_A,V_f,T_a,T_b),V_y))=V_y| -hBOOL(hAPP(hAPP(c_in(T_b),V_y),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)))| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b).
% 187.43/187.53  0 [] c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),hAPP(c_COMBB(c_Set_Oinsert(V_a,T_a),tc_fun(T_a,tc_bool),tc_fun(T_a,tc_bool),T_b),V_B),T_b,tc_fun(T_a,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,hAPP(c_COMBB(c_Set_Oinsert(V_a,T_a),tc_fun(T_a,tc_bool),tc_fun(T_a,tc_bool),T_b),V_B),T_b,tc_fun(T_a,tc_bool))=hAPP(c_Set_Oinsert(V_a,T_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,V_B,T_b,tc_fun(T_a,tc_bool)))|V_C=c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)).
% 187.43/187.53  0 [] hAPP(c_Set_Oinsert(V_a,T_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,V_B,T_b,tc_fun(T_a,tc_bool)))=c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,hAPP(c_COMBB(c_Set_Oinsert(V_a,T_a),tc_fun(T_a,tc_bool),tc_fun(T_a,tc_bool),T_b),V_B),T_b,tc_fun(T_a,tc_bool))|V_C=c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)).
% 187.43/187.53  0 [] hAPP(c_Set_Ovimage(c_COMBK(V_c,T_b,T_a),T_a,T_b),V_A)=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))| -hBOOL(hAPP(hAPP(c_in(T_b),V_c),V_A)).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,V_B,T_b,tc_fun(T_a,tc_bool)))=c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,hAPP(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),tc_fun(T_a,tc_bool),tc_fun(T_a,tc_bool),T_b),V_B),T_b,tc_fun(T_a,tc_bool))|V_C=c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)).
% 187.43/187.53  0 [] c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,hAPP(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),tc_fun(T_a,tc_bool),tc_fun(T_a,tc_bool),T_b),V_B),T_b,tc_fun(T_a,tc_bool))=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_C,V_B,T_b,tc_fun(T_a,tc_bool)))|V_C=c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)).
% 187.43/187.53  0 [] c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),hAPP(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),tc_fun(T_a,tc_bool),tc_fun(T_a,tc_bool),T_b),V_B),T_b,tc_fun(T_a,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_Finite__Set_Ocard(hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),T_b)=c_Finite__Set_Ocard(V_A,T_a)| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b)| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.53  0 [] c_Finite__Set_Ocard(hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),T_b)!=c_Finite__Set_Ocard(V_A,T_a)| -c_Finite__Set_Ofinite(V_A,T_a)|c_Fun_Oinj__on(V_f,V_A,T_a,T_b).
% 187.43/187.53  0 [] c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(V_h,T_b,T_a),V_F),T_b)| -c_Fun_Oinj__on(V_h,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_b,T_a)| -c_Finite__Set_Ofinite(V_F,T_a).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(V_f,T_a,T_b),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)))=c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_B),tc_fun(T_b,tc_bool))| -c_lesse_quals(V_B,V_C,tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,V_C,tc_fun(T_a,tc_bool))| -c_Fun_Oinj__on(V_f,V_C,T_a,T_b).
% 187.43/187.53  0 [] hAPP(c_Set_Ovimage(V_f,T_a,T_b),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A))=V_A| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(V_f,T_a,T_b),c_HOL_Ominus__class_Ominus(V_A,V_B,tc_fun(T_a,tc_bool)))=c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_B),tc_fun(T_b,tc_bool))| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b).
% 187.43/187.53  0 [] c_Fun_Ocomp(c_Fun_Ocomp(V_g,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),T_a,T_c,T_b),V_f,T_b,T_c,T_a)=V_g| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b).
% 187.43/187.53  0 [] hBOOL(hAPP(V_P,V_x))| -hBOOL(hAPP(V_P,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(V_P,V_f,T_a,T_b))))| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b).
% 187.43/187.53  0 [] hAPP(c_Fun_Ocomp(v_f,v_g,t_a,t_b,t_c),v_x)=hAPP(v_f,hAPP(v_g,v_x)).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_b,V_A,T_a,T_a),T_a)| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.53  0 [] c_Fun_Oinj__on(V_f,V_A,T_a,T_a)| -c_lesse_quals(V_A,hAPP(c_Set_Oimage(V_f,T_a,T_a),V_A),tc_fun(T_a,tc_bool))| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.53  0 [] c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b)!=V_f|hAPP(V_f,V_x)=V_y.
% 187.43/187.53  0 [] -class_Finite__Set_Ofinite_Ofinite(T_a)|c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),T_b,T_a),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A))=V_A| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),T_b,T_a),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_X))=V_X| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b).
% 187.43/187.53  0 [] hAPP(c_Set_Oinsert(V_a,T_a),V_A)=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(c_Set_Oinsert(V_a,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))),V_A).
% 187.43/187.53  0 [] c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,hAPP(c_Set_Oinsert(V_x,T_a),V_B),tc_fun(T_a,tc_bool))|hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)).
% 187.43/187.53  0 [] c_lesse_quals(V_A,hAPP(c_Set_Oinsert(V_x,T_a),V_B),tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool))|hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)).
% 187.43/187.53  0 [] c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool))|hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -c_lesse_quals(V_A,hAPP(c_Set_Oinsert(V_x,T_a),V_B),tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_lesse_quals(V_A,hAPP(c_Set_Oinsert(V_x,T_a),V_B),tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool))|hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_Set_Oinsert(V_y,T_a),V_A),V_x))| -hBOOL(hAPP(V_A,V_x)).
% 187.43/187.53  0 [] -class_Complete__Lattice_Ocomplete__lattice(T_b)|c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,c_COMBK(V_M,T_b,T_a),T_a,T_b)=V_M|V_A=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))| -c_lesse_quals(hAPP(c_Set_Oinsert(V_x,T_a),V_A),V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oinsert(V_t,tc_Hoare__Mirabelle_Otriple(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a)| -c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oinsert(V_t,tc_Hoare__Mirabelle_Otriple(T_a)),V_ts),T_a).
% 187.43/187.53  0 [] hAPP(c_Set_Oinsert(V_x,T_a),V_xa)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))|hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_xa)).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(c_COMBK(V_c,T_a,T_b),T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hAPP(c_Set_Oinsert(V_a,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))!=hAPP(c_Set_Oinsert(V_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))|V_a=V_b.
% 187.43/187.53  0 [] c_Fun_Oinj__on(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a,T_b).
% 187.43/187.53  0 [] hAPP(c_Set_Oinsert(V_xa,T_a),hAPP(c_Set_Oinsert(V_x,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))=hAPP(c_Set_Oinsert(V_x,T_a),hAPP(c_Set_Oinsert(V_xa,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))).
% 187.43/187.53  0 [] -class_Complete__Lattice_Ocomplete__lattice(T_a)|c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(V_xs,T_b),V_f,T_b,T_a)=c_List_Ofoldl(c_COMBC(hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(T_a),T_a,tc_fun(T_a,T_a),T_b),V_f),T_b,T_a,T_a),c_Orderings_Obot__class_Obot(T_a),V_xs,T_a,T_b).
% 187.43/187.53  0 [] hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),hAPP(c_COMBB(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool),T_b),V_r),T_b,tc_fun(t_a,tc_bool)),v_x)=hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),V_r,T_b,tc_fun(t_a,tc_bool))).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),T_b,T_a),V_A)=hAPP(c_Set_Oinsert(V_y,T_a),hAPP(c_Set_Oimage(V_f,T_b,T_a),c_HOL_Ominus__class_Ominus(V_A,hAPP(c_Set_Oinsert(V_x,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))),tc_fun(T_b,tc_bool))))| -hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)).
% 187.43/187.53  0 [] -hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),hAPP(c_Set_Oimage(V_f,T_a,T_b),c_HOL_Ominus__class_Ominus(V_A,hAPP(c_Set_Oinsert(V_a,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)))))| -c_Fun_Oinj__on(V_f,hAPP(c_Set_Oinsert(V_a,T_a),V_A),T_a,T_b).
% 187.43/187.53  0 [] c_Fun_Oinj__on(V_f,hAPP(c_Set_Oinsert(V_a,T_a),V_A),T_a,T_b)|hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),hAPP(c_Set_Oimage(V_f,T_a,T_b),c_HOL_Ominus__class_Ominus(V_A,hAPP(c_Set_Oinsert(V_a,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)))))| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b).
% 187.43/187.53  0 [] -class_Complete__Lattice_Ocomplete__lattice(T_b)|c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_f,T_a,T_b)=c_Finite__Set_Ofold(hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(T_b),T_b,tc_fun(T_b,T_b),T_a),V_f),c_Orderings_Obot__class_Obot(T_b),V_A,T_a,T_b)| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Ohoare__valids(V_G,V_ts,t_a)| -c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(V_G,V_ts),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(V_G,V_ts),t_a).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),c_Com_Ocom_OSemi(V_c,V_d)),V_R),tc_Hoare__Mirabelle_Otriple(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a)| -c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_Q),V_d),V_R),tc_Hoare__Mirabelle_Otriple(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a)| -c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),V_c),V_Q),tc_Hoare__Mirabelle_Otriple(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),c_Com_Ocom_OSKIP),V_P),tc_Hoare__Mirabelle_Otriple(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a).
% 187.43/187.53  0 [] hAPP(c_Hilbert__Choice_Oinv__into(V_A,c_Fun_Ocomp(V_f,V_g,T_a,T_b,T_c),T_c,T_b),V_x)=hAPP(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(V_A,V_g,T_c,T_a),c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(V_g,T_c,T_a),V_A),V_f,T_a,T_b),T_a,T_c,T_b),V_x)| -hBOOL(hAPP(hAPP(c_in(T_b),V_x),hAPP(c_Set_Oimage(V_f,T_a,T_b),hAPP(c_Set_Oimage(V_g,T_c,T_a),V_A))))| -c_Fun_Oinj__on(V_g,V_A,T_c,T_a)| -c_Fun_Oinj__on(V_f,hAPP(c_Set_Oimage(V_g,T_c,T_a),V_A),T_a,T_b).
% 187.43/187.53  0 [] c_lesse_quals(hAPP(c_Set_Ovimage(V_f,T_a,T_b),V_B),V_A,tc_fun(T_a,tc_bool))| -c_lesse_quals(V_B,hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),tc_fun(T_b,tc_bool))| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b).
% 187.43/187.53  0 [] c_lesse_quals(hAPP(c_Set_Oimage(V_f,T_a,T_b),c_HOL_Ouminus__class_Ouminus(V_A,tc_fun(T_a,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),tc_fun(T_b,tc_bool)),tc_fun(T_b,tc_bool))| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b).
% 187.43/187.53  0 [] c_Finite__Set_Ocard(V_A,T_a)=c_Finite__Set_Ocard(V_B,T_b)| -c_Finite__Set_Ofinite(V_B,T_b)| -c_Finite__Set_Ofinite(V_A,T_a)| -c_lesse_quals(hAPP(c_Set_Oimage(V_g,T_b,T_a),V_B),V_A,tc_fun(T_a,tc_bool))| -c_Fun_Oinj__on(V_g,V_B,T_b,T_a)| -c_lesse_quals(hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),V_B,tc_fun(T_b,tc_bool))| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b).
% 187.43/187.53  0 [] -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a)|hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),hAPP(c_Set_Oimage(V_f,T_aa,T_a),c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)))))|hAPP(V_f,V_x)=hAPP(V_f,c_ATP__Linkup_Osko__Fun__Xrange__ex1__e_q__1__2(hAPP(V_f,V_x),V_f,V_x,T_a,T_aa)).
% 187.43/187.53  0 [] hBOOL(hAPP(V_P,V_x))|hBOOL(hAPP(hAPP(c_in(T_b),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(V_P,V_f,T_a,T_b)),hAPP(c_Set_Oimage(V_f,T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)))))| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b).
% 187.43/187.53  0 [] c_ATP__Linkup_Osko__Fun__Xrange__ex1__e_q__1__2(hAPP(V_f,V_x),V_f,V_x,T_a,T_aa)!=V_x| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a)|hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),hAPP(c_Set_Oimage(V_f,T_aa,T_a),c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool))))).
% 187.43/187.53  0 [] V_b=hAPP(V_f,c_ATP__Linkup_Osko__Fun__Xrange__ex1__e_q__1__1(V_b,V_f,T_b,T_a))| -hBOOL(hAPP(hAPP(c_in(T_b),V_b),hAPP(c_Set_Oimage(V_f,T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)))))| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b).
% 187.43/187.53  0 [] -hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_y)),hAPP(c_Set_Oimage(V_f,T_aa,T_a),c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)))))| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a)|V_y=c_ATP__Linkup_Osko__Fun__Xrange__ex1__e_q__1__1(hAPP(V_f,V_y),V_f,T_a,T_aa).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),hAPP(c_Fun_Othe__inv__into(V_A,V_f,T_a,T_b),V_x)),V_B))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool))| -hBOOL(hAPP(hAPP(c_in(T_b),V_x),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)))| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b).
% 187.43/187.53  0 [] -class_Complete__Lattice_Ocomplete__lattice(T_b)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_b),V_B),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_f,T_a,T_b))=c_Finite__Set_Ofold(hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(T_b),T_b,tc_fun(T_b,T_b),T_a),V_f),V_B,V_A,T_a,T_b)| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.53  0 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(V_A,hAPP(c_Set_Oinsert(V_x,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -c_lesse_quals(V_A,hAPP(c_Set_Oinsert(V_x,T_a),V_B),tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_lesse_quals(V_A,hAPP(c_Set_Oinsert(V_x,T_a),V_B),tc_fun(T_a,tc_bool))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -c_lesse_quals(c_HOL_Ominus__class_Ominus(V_A,hAPP(c_Set_Oinsert(V_x,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_lesse_quals(V_A,hAPP(c_Set_Oinsert(V_x,T_a),V_B),tc_fun(T_a,tc_bool))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -c_lesse_quals(c_HOL_Ominus__class_Ominus(V_A,hAPP(c_Set_Oinsert(V_x,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_xa))|c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(V_x,T_a),V_xa),T_a)=c_Suc(c_Finite__Set_Ocard(V_xa,T_a))|c_Finite__Set_Ocard(V_xa,T_a)=c_HOL_Ozero__class_Ozero(tc_nat).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))|c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(V_x,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),T_a)=c_Suc(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)).
% 187.43/187.53  0 [] c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(V_x,T_a),V_A),T_a)=c_Suc(c_Finite__Set_Ocard(V_A,T_a))|hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.53  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(c_Finite__Set_Olinorder__class_OMax(V_M,T_a),c_Finite__Set_Olinorder__class_OMax(V_N,T_a),T_a)| -c_Finite__Set_Ofinite(V_N,T_a)|V_M=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))| -c_lesse_quals(V_M,V_N,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(c_Finite__Set_Olinorder__class_OMin(V_N,T_a),c_Finite__Set_Olinorder__class_OMin(V_M,T_a),T_a)| -c_Finite__Set_Ofinite(V_N,T_a)|V_M=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))| -c_lesse_quals(V_M,V_N,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_Natural_Oevalc(V_c,V_s,V_t)| -c_Natural_Oevaln(V_c,V_s,V_n,V_t).
% 187.43/187.53  0 [] c_Natural_Oevalc(V_c,V_s,V_t)| -c_Natural_Oevaln(V_c,V_s,V_x,V_t).
% 187.43/187.53  0 [] -class_HOL_Oord(T_b)|c_lesse_quals(hAPP(V_f,V_x),hAPP(V_g,V_x),T_b)| -c_lesse_quals(V_f,V_g,tc_fun(T_a,T_b)).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Otriple__valid(V_n,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),t_a)|c_Natural_Oevaln(V_c,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(V_P,V_Q,V_c,V_n),V_n,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(V_P,V_Q,V_c,V_n)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_a),hAPP(c_Set_Oinsert(V_b,T_a),V_A)))| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_a),hAPP(c_Set_Oinsert(V_b,T_a),V_B)))| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_B)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_B))| -hBOOL(hAPP(hAPP(c_in(T_a),V_t),V_A))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))| -hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] -hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))).
% 187.43/187.53  0 [] hBOOL(hAPP(V_P,V_x))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))).
% 187.43/187.53  0 [] -hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))).
% 187.43/187.53  0 [] -hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))|V_a=V_b| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),hAPP(c_Set_Oinsert(V_b,T_a),V_A))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_x),hAPP(c_Set_Oinsert(V_x,T_a),V_A))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_a),hAPP(c_Set_Oinsert(V_a,T_a),V_B))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_x),hAPP(c_Set_Oinsert(V_x,T_a),V_B))).
% 187.43/187.53  0 [] hAPP(V_f,V_x)!=hAPP(V_f,V_y)| -hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))|V_x=V_y| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b).
% 187.43/187.53  0 [] hAPP(V_f,V_x)!=hAPP(V_f,V_y)| -hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b)|V_x=V_y.
% 187.43/187.53  0 [] hAPP(V_f,V_x)!=hAPP(V_f,V_xa)| -hBOOL(hAPP(hAPP(c_in(T_a),V_xa),V_A))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b)|V_x=V_xa.
% 187.43/187.53  0 [] hAPP(V_f,V_x)!=hAPP(V_f,V_y)| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b)|V_x=V_y| -hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)).
% 187.43/187.53  0 [] -hBOOL(hAPP(V_P,V_x))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))).
% 187.43/187.53  0 [] hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_R)!=hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_S)|V_R=V_S.
% 187.43/187.53  0 [] hAPP(c_Set_Oinsert(V_x,T_a),V_A)!=hAPP(c_Set_Oinsert(V_x,T_a),V_B)|hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))|hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))|V_A=V_B.
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool))))| -hBOOL(hAPP(hAPP(c_in(T_a),V_b),hAPP(V_B,V_x)))| -hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_b),V_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool))))| -hBOOL(hAPP(hAPP(c_in(T_b),V_b),hAPP(V_B,V_a)))| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)).
% 187.43/187.53  0 [] hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a)))| -hBOOL(hAPP(V_P,V_x))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)).
% 187.43/187.53  0 [] hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a)))| -hBOOL(hAPP(V_P,V_xa))| -hBOOL(hAPP(hAPP(c_in(T_a),V_xa),V_A)).
% 187.43/187.53  0 [] hAPP(c_Set_Oinsert(V_a,T_a),V_A)=V_A| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)).
% 187.43/187.53  0 [] hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),V_b))| -hBOOL(hAPP(hAPP(V_B,V_x),V_b))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)).
% 187.43/187.53  0 [] hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),V_b))| -hBOOL(hAPP(hAPP(V_B,V_a),V_b))| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)).
% 187.43/187.53  0 [] c_Fun_Oinj__on(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_A,T_a,T_b)|hBOOL(hAPP(hAPP(c_in(T_b),V_y),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)))| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)))| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))| -hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)))| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b).
% 187.43/187.53  0 [] c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(hAPP(c_COMBB(V_f,T_a,T_c,T_b),V_g),T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool))),T_c)| -c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(V_g,T_b,T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool))),T_a).
% 187.43/187.53  0 [] c_Suc(V_m)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 187.43/187.53  0 [] c_Suc(V_nat_H)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 187.43/187.53  0 [] c_Natural_Oevaln(V_c,V_s,c_Suc(V_n),V_s_H)| -c_Natural_Oevaln(V_c,V_s,V_n,V_s_H).
% 187.43/187.53  0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_m).
% 187.43/187.53  0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_nat_H).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|c_lesse_quals(V_a,V_x,T_a)| -c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b),V_x,T_a).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|c_lesse_quals(V_b,V_x,T_a)| -c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b),V_x,T_a).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|c_lesse_quals(V_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b),T_a)| -c_lesse_quals(V_x,V_a,T_a).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|c_lesse_quals(V_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b),T_a)| -c_lesse_quals(V_x,V_b,T_a).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|c_lesse_quals(V_x,V_z,T_a)| -c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y),V_z,T_a).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|c_lesse_quals(V_y,V_z,T_a)| -c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y),V_z,T_a).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)=V_y| -c_lesse_quals(V_x,V_y,T_a).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)!=V_y|c_lesse_quals(V_x,V_y,T_a).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)=V_x| -c_lesse_quals(V_y,V_x,T_a).
% 187.43/187.53  0 [] -class_Lattices_Obounded__lattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)=V_x.
% 187.43/187.53  0 [] -class_Lattices_Obounded__lattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a))=V_x.
% 187.43/187.53  0 [] -class_Lattices_Obounded__lattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x)=c_Orderings_Otop__class_Otop(T_a).
% 187.43/187.53  0 [] -class_Lattices_Obounded__lattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))=c_Orderings_Otop__class_Otop(T_a).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_a),V_b),V_x,T_a)| -c_lesse_quals(V_b,V_x,T_a)| -c_lesse_quals(V_a,V_x,T_a).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|c_lesse_quals(V_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y),T_a).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|c_lesse_quals(V_y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y),T_a).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z),V_x,T_a)| -c_lesse_quals(V_z,V_x,T_a)| -c_lesse_quals(V_y,V_x,T_a).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y),V_z,T_a)| -c_lesse_quals(V_y,V_z,T_a)| -c_lesse_quals(V_x,V_z,T_a).
% 187.43/187.53  0 [] -class_Lattices_Olattice(T_a)|c_lesse_quals(V_y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y),T_a).
% 187.43/187.53  0 [] -class_Lattices_Olattice(T_a)|c_lesse_quals(V_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y),T_a).
% 187.43/187.53  0 [] -class_Lattices_Obounded__lattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_A),V_B)!=c_Orderings_Obot__class_Obot(T_a)|V_A=c_Orderings_Obot__class_Obot(T_a).
% 187.43/187.53  0 [] -class_Lattices_Obounded__lattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_A),V_B)!=c_Orderings_Obot__class_Obot(T_a)|V_B=c_Orderings_Obot__class_Obot(T_a).
% 187.43/187.53  0 [] -c_lesse_quals(V_x,V_A,tc_fun(T_b,tc_bool))|c_lesse_quals(hAPP(c_Set_Oimage(V_f,T_b,T_a),V_x),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A),tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_lesse_quals(hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_B),tc_fun(T_b,tc_bool))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hAPP(V_f,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(V_x,V_f,V_g,T_a,T_b))!=hAPP(V_g,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(V_x,V_f,V_g,T_a,T_b))|hAPP(c_Set_Oimage(V_f,T_a,T_b),V_x)=hAPP(c_Set_Oimage(V_g,T_a,T_b),V_x).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))|V_A=c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(V_f,T_b,T_a),hAPP(c_Set_Oinsert(V_a,T_b),V_B))=hAPP(c_Set_Oinsert(hAPP(V_f,V_a),T_a),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_B)).
% 187.43/187.53  0 [] c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(V_h,T_a,T_b),V_F),T_b)| -c_Finite__Set_Ofinite(V_F,T_a).
% 187.43/187.53  0 [] c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))!=hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A)|V_A=c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(V_f,T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))=hAPP(c_Set_Oimage(V_f,T_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool))).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),V_A),V_B),V_M,T_b,tc_fun(T_a,tc_bool))=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_M,T_b,tc_fun(T_a,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_B,V_M,T_b,tc_fun(T_a,tc_bool))).
% 187.43/187.53  0 [] c_lesse_quals(V_B,V_C,tc_fun(T_a,tc_bool))| -c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_lesse_quals(V_A,V_C,tc_fun(T_a,tc_bool))| -c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_C),V_D),tc_fun(T_a,tc_bool))| -c_lesse_quals(V_B,V_D,tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,V_C,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)!=V_B|c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)=V_A| -c_lesse_quals(V_B,V_A,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)=V_B| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))=V_A.
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),V_B)=V_B.
% 187.43/187.53  0 [] c_Finite__Set_Ofinite(V_G,T_a)| -c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_F),V_G),T_a).
% 187.43/187.53  0 [] c_Finite__Set_Ofinite(V_F,T_a)| -c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_F),V_G),T_a).
% 187.43/187.53  0 [] c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_F),V_G),T_a)| -c_Finite__Set_Ofinite(V_G,T_a)| -c_Finite__Set_Ofinite(V_F,T_a).
% 187.43/187.53  0 [] c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_F),V_G),T_a)| -c_Finite__Set_Ofinite(V_G,T_a)| -c_Finite__Set_Ofinite(V_F,T_a).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)))=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))),V_B)=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(c_Set_Oinsert(V_a,T_a),V_B))=hAPP(c_Set_Oinsert(V_a,T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(c_Set_Oinsert(V_a,T_a),V_B)),V_C)=hAPP(c_Set_Oinsert(V_a,T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)).
% 187.43/187.53  0 [] c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool))| -c_lesse_quals(V_B,V_C,tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,V_C,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_lesse_quals(V_B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_lesse_quals(V_A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_C,tc_fun(T_a,tc_bool))| -c_lesse_quals(V_B,V_C,tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,V_C,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))|V_B=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))|V_A=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_Fun_Oinj__on(V_f,V_B,T_a,T_b)| -c_Fun_Oinj__on(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b).
% 187.43/187.53  0 [] c_Fun_Oinj__on(V_f,V_A,T_a,T_b)| -c_Fun_Oinj__on(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b).
% 187.43/187.53  0 [] V_n=c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1))| -c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1).
% 187.43/187.53  0 [] c_Option_Ooption_ONone(T_a)!=c_Option_Ooption_OSome(V_a_H,T_a).
% 187.43/187.53  0 [] c_Option_Ooption_ONone(T_a)!=c_Option_Ooption_OSome(V_y,T_a).
% 187.43/187.53  0 [] hAPP(c_COMBK(V_P,T_a,T_b),V_Q)=V_P.
% 187.43/187.53  0 [] hAPP(hAPP(c_COMBC(V_P,T_b,T_c,T_a),V_Q),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 187.43/187.53  0 [] hAPP(c_Set_Oinsert(V_x,T_a),hAPP(c_Set_Oinsert(V_y,T_a),V_A))=hAPP(c_Set_Oinsert(V_y,T_a),hAPP(c_Set_Oinsert(V_x,T_a),V_A)).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),T_b,T_a),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_S))=V_S| -c_lesse_quals(V_S,V_A,tc_fun(T_a,tc_bool))| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b).
% 187.43/187.53  0 [] V_b=V_a| -hBOOL(hAPP(hAPP(c_in(T_a),V_b),hAPP(c_Set_Oinsert(V_a,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(c_COMBK(V_c,T_b,T_a),T_a,T_b),V_A)=hAPP(c_Set_Oinsert(V_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)).
% 187.43/187.53  0 [] c_Finite__Set_Ofinite(V_B,T_b)| -c_lesse_quals(V_B,hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),tc_fun(T_b,tc_bool))| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.53  0 [] c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool))| -c_lesse_quals(hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_B),tc_fun(T_b,tc_bool))| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b).
% 187.43/187.53  0 [] c_lesse_quals(hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_B),tc_fun(T_b,tc_bool))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool))| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b).
% 187.43/187.53  0 [] c_Fun_Oinj__on(V_f,V_A,T_a,T_b)| -c_Fun_Oinj__on(V_f,hAPP(c_Set_Oinsert(V_a,T_a),V_A),T_a,T_b).
% 187.43/187.53  0 [] -class_Complete__Lattice_Ocomplete__lattice(T_b)|c_lesse_quals(hAPP(V_M,V_i),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_M,T_a,T_b),T_b)| -hBOOL(hAPP(hAPP(c_in(T_a),V_i),V_A)).
% 187.43/187.53  0 [] c_lesse_quals(hAPP(V_B,V_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),tc_fun(T_b,tc_bool))| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)).
% 187.43/187.53  0 [] c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool))| -c_lesse_quals(hAPP(c_Set_Oinsert(V_x,T_a),V_A),V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_lesse_quals(V_A,hAPP(c_Set_Oinsert(V_b,T_a),V_B),tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] -class_Orderings_Obot(T_b)|hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,T_b)),v_x)=c_Orderings_Obot__class_Obot(T_b).
% 187.43/187.53  0 [] c_lesse_quals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] -class_Orderings_Obot(T_a)|c_lesse_quals(c_Orderings_Obot__class_Obot(T_a),V_x,T_a).
% 187.43/187.53  0 [] hAPP(c_Set_Oinsert(V_a,T_a),V_A)!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hAPP(c_Set_Oinsert(V_x,T_a),hAPP(c_Set_Oinsert(V_x,T_a),V_A))=hAPP(c_Set_Oinsert(V_x,T_a),V_A).
% 187.43/187.53  0 [] c_Finite__Set_Ofinite(hAPP(V_B,V_x),T_b)| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_a,tc_fun(T_b,tc_bool)),T_b)| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.53  0 [] hBOOL(hAPP(V_A,V_x))|V_y=V_x| -hBOOL(hAPP(hAPP(c_Set_Oinsert(V_y,T_a),V_A),V_x)).
% 187.43/187.53  0 [] c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool))!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))|hAPP(V_B,V_x)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))| -hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)).
% 187.43/187.53  0 [] hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),hAPP(V_f,V_x))=V_x| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -c_Fun_Oinj__on(V_f,V_A,T_a,T_b).
% 187.43/187.53  0 [] -hBOOL(hAPP(hAPP(c_in(T_aa),V_x),V_A))| -c_Fun_Oinj__on(V_f,V_A,T_aa,T_a)|hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_aa,T_a),hAPP(V_f,V_x))=V_x.
% 187.43/187.53  0 [] c_lesse_quals(hAPP(V_A,V_x),V_B,tc_fun(T_a,tc_bool))| -hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_I))| -c_lesse_quals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_b,tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_lesse_quals(V_B,hAPP(c_Set_Oinsert(V_a,T_a),V_B),tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_Finite__Set_Ofinite(V_A,T_a)| -c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(V_a,T_a),V_A),T_a).
% 187.43/187.53  0 [] c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(V_a,T_a),V_A),T_a)| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.53  0 [] c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a).
% 187.43/187.53  0 [] c_Option_Ooption_OSome(V_a_H,T_a)!=c_Option_Ooption_ONone(T_a).
% 187.43/187.53  0 [] c_Option_Ooption_OSome(V_xa,T_a)!=c_Option_Ooption_ONone(T_a).
% 187.43/187.53  0 [] c_Option_Ooption_OSome(V_a,T_a)!=c_Option_Ooption_OSome(V_a_H,T_a)|V_a=V_a_H.
% 187.43/187.53  0 [] c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_m,V_a,V_b,T_a,T_b),V_c,V_d,T_a,T_b)=c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_m,V_c,V_d,T_a,T_b),V_a,V_b,T_a,T_b)|V_a=V_c.
% 187.43/187.53  0 [] hAPP(V_f,V_x)!=hAPP(V_f,V_y)| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)|V_x=V_y.
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(V_f,T_a,T_a),V_A)=V_A| -c_Fun_Oinj__on(V_f,V_A,T_a,T_a)| -c_lesse_quals(hAPP(c_Set_Oimage(V_f,T_a,T_a),V_A),V_A,tc_fun(T_a,tc_bool))| -c_Finite__Set_Ofinite(V_A,T_a).
% 187.43/187.53  0 [] c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))!=c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool))|hAPP(V_B,V_x)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))| -hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_A,T_b,tc_fun(T_a,tc_bool))),V_B)=V_B.
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)))=V_A.
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)!=hAPP(c_Set_Oimage(V_f,T_a,T_b),V_B)| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b)|V_A=V_B.
% 187.43/187.53  0 [] c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_b,T_a),V_B,T_a,T_b)| -c_lesse_quals(V_B,hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A),tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Ohoare__derivs(V_G,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),T_a).
% 187.43/187.53  0 [] -hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(c_COMBK(V_c,T_a,T_b),T_b,T_a),V_A)=hAPP(c_Set_Oinsert(V_c,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))|V_A=c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)).
% 187.43/187.53  0 [] c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_Fun_Ofun__upd(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_x,V_z,T_a,T_b)=c_Fun_Ofun__upd(V_f,V_x,V_z,T_a,T_b).
% 187.43/187.53  0 [] hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_x)).
% 187.43/187.53  0 [] -class_Orderings_Otop(T_b)|hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,T_b)),v_x)=c_Orderings_Otop__class_Otop(T_b).
% 187.43/187.53  0 [] c_lesse_quals(V_R,V_S,tc_fun(T_a,tc_bool))| -c_lesse_quals(hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_R),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_S),tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_lesse_quals(hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_R),hAPP(c_COMBC(c_in(T_a),T_a,tc_fun(T_a,tc_bool),tc_bool),V_S),tc_fun(T_a,tc_bool))| -c_lesse_quals(V_R,V_S,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] V_A=V_B| -c_lesse_quals(V_B,V_A,tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] V_u=V_t| -c_Natural_Oevalc(V_c,V_s,V_u)| -c_Natural_Oevalc(V_c,V_s,V_t).
% 187.43/187.53  0 [] V_A=V_B| -c_lesse_quals(V_B,V_A,tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] -class_Orderings_Oorder(T_a)|V_x=V_y| -c_lesse_quals(V_y,V_x,T_a)| -c_lesse_quals(V_x,V_y,T_a).
% 187.43/187.53  0 [] -class_Orderings_Oorder(T_a)|V_x=V_y| -c_lesse_quals(V_y,V_x,T_a)| -c_lesse_quals(V_x,V_y,T_a).
% 187.43/187.53  0 [] -class_Orderings_Oorder(T_a)|V_x=V_y| -c_lesse_quals(V_x,V_y,T_a)| -c_lesse_quals(V_y,V_x,T_a).
% 187.43/187.53  0 [] hAPP(c_Set_Oinsert(V_a,T_a),hAPP(c_Set_Oinsert(V_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))!=hAPP(c_Set_Oinsert(V_c,T_a),hAPP(c_Set_Oinsert(V_d,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))|V_a=V_d|V_a=V_c.
% 187.43/187.53  0 [] hAPP(c_Set_Oinsert(V_a,T_a),hAPP(c_Set_Oinsert(V_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))!=hAPP(c_Set_Oinsert(V_c,T_a),hAPP(c_Set_Oinsert(V_d,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))|V_b=V_c|V_a=V_c.
% 187.43/187.53  0 [] hAPP(c_Set_Oinsert(V_a,T_a),hAPP(c_Set_Oinsert(V_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))!=hAPP(c_Set_Oinsert(V_c,T_a),hAPP(c_Set_Oinsert(V_d,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))|V_a=V_d|V_b=V_d.
% 187.43/187.53  0 [] hAPP(c_Set_Oinsert(V_a,T_a),hAPP(c_Set_Oinsert(V_b,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))!=hAPP(c_Set_Oinsert(V_c,T_a),hAPP(c_Set_Oinsert(V_d,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))|V_b=V_c|V_b=V_d.
% 187.43/187.53  0 [] c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(V_a,T_b),V_A),V_B,T_b,tc_fun(T_a,tc_bool))=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(V_B,V_a)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_A,V_B,T_b,tc_fun(T_a,tc_bool))).
% 187.43/187.53  0 [] c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_b,T_a)=V_f.
% 187.43/187.53  0 [] hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_x)=V_y.
% 187.43/187.53  0 [] c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_a,T_b)=V_f.
% 187.43/187.53  0 [] hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_aa),V_x)=V_y.
% 187.43/187.53  0 [] c_Fun_Ofun__upd(V_f,V_x,hAPP(V_f,V_x),T_aa,T_a)=V_f.
% 187.43/187.53  0 [] V_A=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_lesse_quals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))!=hAPP(c_Set_Oinsert(V_a,T_a),V_A).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)| -c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_G_H,T_a)| -c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a).
% 187.43/187.53  0 [] c_lesse_quals(V_A,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] -class_Orderings_Otop(T_a)|c_lesse_quals(V_x,c_Orderings_Otop__class_Otop(T_a),T_a).
% 187.43/187.53  0 [] hAPP(c_Set_Oinsert(V_a,T_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),V_B,T_b,tc_fun(T_a,tc_bool)))=hAPP(c_Set_Oinsert(V_a,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_Set_Oinsert(V_x,T_a),V_A),V_x)).
% 187.43/187.53  0 [] c_lesse_quals(hAPP(c_Set_Oinsert(V_x,T_a),V_A),V_B,tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)).
% 187.43/187.53  0 [] -class_Finite__Set_Ofinite_Ofinite(T_a)|c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a).
% 187.43/187.53  0 [] -class_Orderings_Oorder(T_a)|c_lesse_quals(V_z,V_x,T_a)| -c_lesse_quals(V_z,V_y,T_a)| -c_lesse_quals(V_y,V_x,T_a).
% 187.43/187.53  0 [] -class_Orderings_Opreorder(T_a)|c_lesse_quals(V_x,V_z,T_a)| -c_lesse_quals(V_y,V_z,T_a)| -c_lesse_quals(V_x,V_y,T_a).
% 187.43/187.53  0 [] c_lesse_quals(V_x,V_x,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_lesse_quals(V_A,V_A,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_lesse_quals(V_A,V_C,tc_fun(T_a,tc_bool))| -c_lesse_quals(V_B,V_C,tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_Fun_Oinj__on(V_f,V_A,T_a,T_b)| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool))| -c_Fun_Oinj__on(V_f,V_B,T_a,T_b).
% 187.43/187.53  0 [] hBOOL(hAPP(V_Q,V_x))| -hBOOL(hAPP(V_P,V_x))| -c_lesse_quals(V_P,V_Q,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] -class_Orderings_Oorder(T_a)|c_lesse_quals(V_x,V_x,T_a).
% 187.43/187.53  0 [] -class_Orderings_Opreorder(T_a)|c_lesse_quals(V_x,V_x,T_a).
% 187.43/187.53  0 [] c_Finite__Set_Ofinite(V_A,T_a)| -c_Finite__Set_Ofinite(V_B,T_a)| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hBOOL(hAPP(V_Q,V_x))| -c_lesse_quals(V_P,V_Q,tc_fun(T_a,tc_bool))| -hBOOL(hAPP(V_P,V_x)).
% 187.43/187.53  0 [] c_Finite__Set_Ofinite(V_A,T_a)| -c_lesse_quals(V_A,V_B,tc_fun(T_a,tc_bool))| -c_Finite__Set_Ofinite(V_B,T_a).
% 187.43/187.53  0 [] hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_f,T_a,T_b),hAPP(V_f,V_x))=V_x| -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a,T_b).
% 187.43/187.53  0 [] -c_Fun_Oinj__on(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),T_aa,T_a)|hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(T_aa,tc_bool)),V_f,T_aa,T_a),hAPP(V_f,V_x))=V_x.
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_x),hAPP(c_Set_Oinsert(V_x,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))))).
% 187.43/187.53  0 [] V_A=hAPP(c_Set_Oinsert(V_x,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))|V_A=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))| -c_lesse_quals(V_A,hAPP(c_Set_Oinsert(V_x,T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))),tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)| -c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oinsert(V_t,tc_Hoare__Mirabelle_Otriple(T_a)),V_ts),T_a).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oinsert(V_t,tc_Hoare__Mirabelle_Otriple(T_a)),V_ts),T_a)| -c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)| -c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oinsert(V_t,tc_Hoare__Mirabelle_Otriple(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a).
% 187.43/187.53  0 [] hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),V_z)=hAPP(V_f,V_z)|V_z=V_x.
% 187.43/187.53  0 [] hAPP(c_Fun_Ofun__upd(V_f,V_x,V_y,T_a,T_b),V_z)=hAPP(V_f,V_z)|V_z=V_x.
% 187.43/187.53  0 [] c_lesse_quals(hAPP(c_Set_Oinsert(V_a,T_a),V_C),hAPP(c_Set_Oinsert(V_a,T_a),V_D),tc_fun(T_a,tc_bool))| -c_lesse_quals(V_C,V_D,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] c_Finite__Set_Ofinite(V_A,T_b)| -c_Fun_Oinj__on(V_f,V_A,T_b,T_a)| -c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A),T_a).
% 187.43/187.53  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_y,V_x,T_a)|c_lesse_quals(V_x,V_y,T_a).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Otriple__valid(V_n,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),t_a)| -hBOOL(hAPP(hAPP(V_Q,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(V_P,V_Q,V_c,V_n)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(V_P,V_Q,V_c,V_n))).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Otriple__valid(V_n,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),t_a)|hBOOL(hAPP(hAPP(V_P,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(V_P,V_Q,V_c,V_n)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(V_P,V_Q,V_c,V_n))).
% 187.43/187.53  0 [] c_Com_OWT(hAPP(c_Com_Ocom_OBODY,V_pn))|hAPP(c_Com_Obody,V_pn)=c_Option_Ooption_ONone(tc_Com_Ocom).
% 187.43/187.53  0 [] hAPP(hAPP(c_COMBC(v_P,t_a,t_b,t_c),v_Q),v_R)=hAPP(hAPP(v_P,v_R),v_Q).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Otriple__valid(V_n,V_na,t_a)| -hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_na),V_ts))|hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(V_G,V_n)),V_G))| -c_Hoare__Mirabelle_Ohoare__valids(V_G,V_ts,t_a).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Ohoare__valids(V_G,V_ts,t_a)|c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(V_G,V_ts),V_x,t_a)| -hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_x),V_G)).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Otriple__valid(V_n,V_nb,t_a)| -hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_nb),V_ts))| -c_Hoare__Mirabelle_Otriple__valid(V_n,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(V_G,V_n),t_a)| -c_Hoare__Mirabelle_Ohoare__valids(V_G,V_ts,t_a).
% 187.43/187.53  0 [] hAPP(c_Option_Othe(T_a),c_Option_Ooption_OSome(V_x,T_a))=V_x.
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),V_P),V_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),V_Q,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),V_U),t_b)| -c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),V_P_H),V_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),V_Q_H,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),V_U),t_b)|c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(V_P_H,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(V_G,V_P,V_P_H,V_Q,V_Q_H,V_c0))),hAPP(V_c0,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(V_G,V_P,V_P_H,V_Q,V_Q_H,V_c0))),hAPP(V_Q_H,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(V_G,V_P,V_P_H,V_Q,V_Q_H,V_c0))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)| -c_Finite__Set_Ofinite(V_U,t_a).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),V_P),V_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),V_Q,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),V_U),t_b)| -c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),V_P_H),V_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),V_Q_H,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),V_U),t_b)| -c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(V_P,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(V_G,V_P,V_P_H,V_Q,V_Q_H,V_c0))),hAPP(V_c0,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(V_G,V_P,V_P_H,V_Q,V_Q_H,V_c0))),hAPP(V_Q,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(V_G,V_P,V_P_H,V_Q,V_Q_H,V_c0))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)| -c_Finite__Set_Ofinite(V_U,t_a).
% 187.43/187.53  0 [] hAPP(V_g,hAPP(V_h,c_List_Osko__List__Xfoldl__apply__inv__1__1(V_g,V_h,T_b,T_a)))!=c_List_Osko__List__Xfoldl__apply__inv__1__1(V_g,V_h,T_b,T_a)|c_List_Ofoldl(V_f,hAPP(V_g,V_s),V_xs,T_a,T_c)=hAPP(V_g,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(V_h,T_a,T_b,T_c),tc_fun(T_c,T_a),tc_fun(T_c,T_b),T_b),hAPP(c_COMBB(V_f,T_a,tc_fun(T_c,T_a),T_b),V_g)),V_s,V_xs,T_b,T_c)).
% 187.43/187.53  0 [] -class_Lattices_Olattice(t_b)|hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_x)=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),hAPP(c_Com_Ocom_OBODY,V_pn)),V_Q),tc_Hoare__Mirabelle_Otriple(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a)| -c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),hAPP(c_Com_Ocom_OBODY,V_pn)),V_Q),tc_Hoare__Mirabelle_Otriple(T_a)),V_G),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_Q),tc_Hoare__Mirabelle_Otriple(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),hAPP(c_Com_Ocom_OBODY,V_pn)),V_Q),tc_Hoare__Mirabelle_Otriple(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a)| -c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_Q),tc_Hoare__Mirabelle_Otriple(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a).
% 187.43/187.53  0 [] c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(V_P,V_n,V_s,V_s1),V_s1)| -c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1).
% 187.43/187.53  0 [] V_b=hAPP(V_f,c_ATP__Linkup_Osko__Set__XimageE__1__1(V_A,V_b,V_f,T_b,T_a))| -hBOOL(hAPP(hAPP(c_in(T_a),V_b),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A))).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(c_Fun_Ofun__upd(V_f,V_x,V_y,T_b,T_a),T_b,T_a),V_A)=hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A)|hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_b),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(V_A,V_f,V_z,T_b,T_a)),V_A))| -hBOOL(hAPP(hAPP(c_in(T_a),V_z),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A))).
% 187.43/187.53  0 [] hAPP(V_f,hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_b,T_a),V_y))=V_y| -hBOOL(hAPP(hAPP(c_in(T_a),V_y),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A))).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(V_f,T_a,T_b),V_x)=hAPP(c_Set_Oimage(V_g,T_a,T_b),V_x)|hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(V_x,V_f,V_g,T_a,T_b)),V_x)).
% 187.43/187.53  0 [] V_z=hAPP(V_f,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(V_A,V_f,V_z,T_b,T_a))| -hBOOL(hAPP(hAPP(c_in(T_a),V_z),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_b),c_ATP__Linkup_Osko__Set__XimageE__1__1(V_A,V_b,V_f,T_b,T_a)),V_A))| -hBOOL(hAPP(hAPP(c_in(T_a),V_b),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),V_B))| -hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))| -c_lesse_quals(hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A),V_B,tc_fun(T_a,tc_bool)).
% 187.43/187.53  0 [] hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),V_x)!=hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_a,T_b),V_y)|V_x=V_y| -hBOOL(hAPP(hAPP(c_in(T_b),V_y),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)))| -hBOOL(hAPP(hAPP(c_in(T_b),V_x),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_b),hAPP(c_Hilbert__Choice_Oinv__into(V_A,V_f,T_b,T_a),V_x)),V_A))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),hAPP(c_Set_Oimage(V_f,T_b,T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool))))).
% 187.43/187.53  0 [] hAPP(c_Set_Oinsert(hAPP(V_f,V_x),T_b),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A))=hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)).
% 187.43/187.53  0 [] hBOOL(hAPP(V_P,V_xf))| -hBOOL(hAPP(hAPP(c_in(T_a),V_xf),V_B))| -hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_P,T_a))).
% 187.43/187.53  0 [] hBOOL(hAPP(V_P,V_xg))| -hBOOL(hAPP(hAPP(c_in(T_a),V_xg),V_A))| -hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_P,T_a))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)))| -hBOOL(hAPP(V_P,V_x))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(V_A,V_B,V_P,T_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)))| -hBOOL(hAPP(V_P,V_xa))| -hBOOL(hAPP(hAPP(c_in(T_a),V_xa),V_A)).
% 187.43/187.53  0 [] hBOOL(hAPP(V_P,V_xd))| -hBOOL(hAPP(hAPP(c_in(T_a),V_xd),V_B))|hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_P,T_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))).
% 187.43/187.53  0 [] hBOOL(hAPP(V_P,V_xe))| -hBOOL(hAPP(hAPP(c_in(T_a),V_xe),V_A))|hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_P,T_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))).
% 187.43/187.53  0 [] hBOOL(hAPP(V_P,V_xc))| -hBOOL(hAPP(hAPP(c_in(T_a),V_xc),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)))| -hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(V_B,V_P,T_a)))| -hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(V_A,V_P,T_a))).
% 187.43/187.53  0 [] hBOOL(hAPP(V_P,V_x))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)))|hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(V_B,V_P,T_a)),V_B))|hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(V_A,V_P,T_a)),V_A)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(V_B,V_P,T_a)),V_B))|hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(V_A,V_P,T_a)))| -hBOOL(hAPP(V_P,V_xb))| -hBOOL(hAPP(hAPP(c_in(T_a),V_xb),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))).
% 187.43/187.53  0 [] hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(V_B,V_P,T_a)))|hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(V_A,V_P,T_a)),V_A))| -hBOOL(hAPP(V_P,V_xb))| -hBOOL(hAPP(hAPP(c_in(T_a),V_xb),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),hAPP(V_A,V_k)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_a,tc_fun(T_b,tc_bool)))=c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(V_I,V_A,T_a,tc_fun(T_b,tc_bool))| -hBOOL(hAPP(hAPP(c_in(T_a),V_k),V_I)).
% 187.43/187.53  0 [] hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(V_B,V_P,T_a)))|hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(V_A,V_P,T_a)))| -hBOOL(hAPP(V_P,V_xb))| -hBOOL(hAPP(hAPP(c_in(T_a),V_xb),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(V_B,V_P,T_a)),V_B))|hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(V_A,V_P,T_a)),V_A))| -hBOOL(hAPP(V_P,V_xb))| -hBOOL(hAPP(hAPP(c_in(T_a),V_xb),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))).
% 187.43/187.53  0 [] hBOOL(hAPP(V_P,V_xb))| -hBOOL(hAPP(hAPP(c_in(T_a),V_xb),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)))|hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(V_B,V_P,T_a)),V_B))| -hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(V_A,V_P,T_a))).
% 187.43/187.53  0 [] hBOOL(hAPP(V_P,V_xa))| -hBOOL(hAPP(hAPP(c_in(T_a),V_xa),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)))| -hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(V_B,V_P,T_a)))|hBOOL(hAPP(hAPP(c_in(T_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(V_A,V_P,T_a)),V_A)).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(hAPP(c_COMBB(V_f,T_c,T_a,T_b),V_g),T_b,T_a),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)))=hAPP(c_Set_Oimage(V_f,T_c,T_a),hAPP(c_Set_Oimage(V_g,T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)))).
% 187.43/187.53  0 [] hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v_x)=hAPP(hAPP(c_in(t_a),v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)!=hAPP(c_Set_Oimage(V_f,T_a,T_b),V_B)| -c_Fun_Oinj__on(V_f,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),T_a,T_b)|V_A=V_B.
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(V_Q,V_Z),V_s_H))| -c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)| -hBOOL(hAPP(hAPP(V_P,V_Z),V_s))| -c_Hoare__Mirabelle_Otriple__valid(V_n,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),V_P),V_c),V_Q),t_a).
% 187.43/187.53  0 [] hAPP(c_COMBK(v_P,t_a,t_b),v_Q)=v_P.
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Otriple__valid(V_n,V_x,t_a)| -hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_x),V_ts))|hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(V_n,V_ts)),V_ts)).
% 187.43/187.53  0 [] hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_R)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),V_S)),v_x)=hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),V_R),V_S)).
% 187.43/187.53  0 [] hAPP(hAPP(c_COMBB(v_P,t_a,t_b,t_c),v_Q),v_R)=hAPP(v_P,hAPP(v_Q,v_R)).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),hAPP(c_Com_Ocom_OBODY,V_pn)),V_Q),T_a).
% 187.43/187.53  0 [] hAPP(c_COMBS(v_P,v_Q,t_a,t_b,t_c),v_R)=hAPP(hAPP(v_P,v_R),hAPP(v_Q,v_R)).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Otriple__valid(V_n,V_xa,t_a)| -hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_xa),V_ts))| -c_Hoare__Mirabelle_Otriple__valid(c_Suc(V_n),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(V_n,V_ts),t_a).
% 187.43/187.53  0 [] c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn),V_s0,V_s1)| -c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_s0,V_s1).
% 187.43/187.53  0 [] c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,V_s1)| -c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_s1).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(V_P,V_pn)),hAPP(c_Com_Ocom_OBODY,V_pn)),hAPP(V_Q,V_pn)),tc_Hoare__Mirabelle_Otriple(T_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))),T_a)| -hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),V_pn),V_Procs))| -c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),V_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(T_a),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),V_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),V_Q,tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a)),V_Procs)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(T_a),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),V_P),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),V_Q,tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a)),V_Procs),T_a).
% 187.43/187.53  0 [] c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pn),V_s0,c_Suc(V_n),V_s1)| -c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_s0,V_n,V_s1).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Ohoare__derivs(V_G,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(T_a),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),V_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),V_Q,tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a)),V_Procs),T_a)| -c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool)),V_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(T_a),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),V_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),V_Q,tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a)),V_Procs)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(T_a),tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),tc_Com_Opname),V_P),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a))),V_Q,tc_Com_Opname,tc_fun(T_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(T_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(T_a)),V_Procs),T_a).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(V_f,T_b,T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_b,tc_bool)),V_A),V_B))=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A)),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_B)).
% 187.43/187.53  0 [] V_n!=c_Suc(V_n).
% 187.43/187.53  0 [] c_Suc(V_n)!=V_n.
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)))| -hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)))| -hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B)).
% 187.43/187.53  0 [] hAPP(c_Set_Oimage(V_f,T_b,T_a),hAPP(c_Set_Oimage(V_g,T_c,T_b),V_A))=hAPP(c_Set_Oimage(hAPP(c_COMBB(V_f,T_b,T_a,T_c),V_g),T_c,T_a),V_A).
% 187.43/187.53  0 [] hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1),V_com),V_fun2)!=hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H),V_com_H),V_fun2_H)|V_fun2=V_fun2_H.
% 187.43/187.53  0 [] hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1),V_com),V_fun2)!=hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H),V_com_H),V_fun2_H)|V_com=V_com_H.
% 187.43/187.53  0 [] hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1),V_com),V_fun2)!=hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_fun1_H),V_com_H),V_fun2_H)|V_fun1=V_fun1_H.
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))|hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))| -hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_x))| -hBOOL(hAPP(V_A,V_x)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_x))| -hBOOL(hAPP(V_B,V_x)).
% 187.43/187.53  0 [] hBOOL(hAPP(V_B,V_x))|hBOOL(hAPP(V_A,V_x))| -hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B),V_x)).
% 187.43/187.53  0 [] c_Suc(V_nat)!=c_Suc(V_nat_H)|V_nat=V_nat_H.
% 187.43/187.53  0 [] c_Suc(V_x)!=c_Suc(V_y)|V_x=V_y.
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Otriple__valid(V_n,V_t,T_a)| -c_Hoare__Mirabelle_Otriple__valid(c_Suc(V_n),V_t,T_a).
% 187.43/187.53  0 [] -class_Lattices_Olattice(T_b)|hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,T_b)),V_f),V_g),v_x)=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_b),hAPP(V_f,v_x)),hAPP(V_g,v_x)).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_A)=V_A.
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_x)=V_x.
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_S))| -hBOOL(hAPP(V_S,V_x)).
% 187.43/187.53  0 [] hBOOL(hAPP(V_S,V_x))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_S)).
% 187.43/187.53  0 [] hAPP(hAPP(c_COMBB(V_P,T_b,T_a,T_c),V_Q),V_R)=hAPP(V_P,hAPP(V_Q,V_R)).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Otriple__valid(c_Suc(V_n),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),hAPP(c_Com_Ocom_OBODY,V_pn)),V_Q),T_a)| -c_Hoare__Mirabelle_Otriple__valid(V_n,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_Q),T_a).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Otriple__valid(V_n,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_Q),T_a)| -c_Hoare__Mirabelle_Otriple__valid(c_Suc(V_n),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P),hAPP(c_Com_Ocom_OBODY,V_pn)),V_Q),T_a).
% 187.43/187.53  0 [] hAPP(c_COMBS(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),hAPP(V_Q,V_R)).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C))=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_C)).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)),V_C)=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_C)).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z)=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z))=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_z)).
% 187.43/187.53  0 [] -class_Lattices_Olattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z))=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_z)).
% 187.43/187.53  0 [] -class_Lattices_Olattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)),V_z)=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_z)).
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B)=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_B),V_A).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_x).
% 187.43/187.53  0 [] -class_Lattices_Olattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y)=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_y),V_x).
% 187.43/187.53  0 [] hAPP(c_Com_Ocom_OBODY,V_pname)!=hAPP(c_Com_Ocom_OBODY,V_pname_H)|V_pname=V_pname_H.
% 187.43/187.53  0 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B))=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(T_a,tc_bool)),V_A),V_B).
% 187.43/187.53  0 [] -class_Lattices_Oupper__semilattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y))=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y).
% 187.43/187.53  0 [] -class_Lattices_Olattice(T_a)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y))=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(T_a),V_x),V_y).
% 187.43/187.53  0 [] -hBOOL(hAPP(hAPP(c_in(T_aa),V_x),V_A))|hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),hAPP(c_Set_Oimage(V_f,T_aa,T_a),V_A))).
% 187.43/187.53  0 [] -hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A))|hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A))).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_x)),hAPP(c_Set_Oimage(V_f,T_b,T_a),V_A)))| -hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_x)),hAPP(c_Set_Oimage(V_f,T_a,T_b),V_A)))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)).
% 187.43/187.53  0 [] hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v_Procs)).
% 187.43/187.53  0 [] -c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(v_Q,v_x)),t_a).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Otriple__valid(v_na,V_x,t_a)| -hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),V_x),v_G)).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,V_x)),hAPP(c_Com_Ocom_OBODY,V_x)),hAPP(v_Q,V_x)),t_a)| -hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),V_x),v_Procs)).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Otriple__valid(V_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,V_nb)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_nb))),hAPP(v_Q,V_nb)),t_a)| -hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),V_nb),v_Procs))|hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(V_na)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs)))).
% 187.43/187.53  0 [] c_Hoare__Mirabelle_Otriple__valid(V_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,V_nc)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_nc))),hAPP(v_Q,V_nc)),t_a)| -hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),V_nc),v_Procs))| -c_Hoare__Mirabelle_Otriple__valid(V_na,v_n(V_na),t_a).
% 187.43/187.53  0 [] class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1))| -class_Complete__Lattice_Ocomplete__lattice(T_1).
% 187.43/187.53  0 [] class_Lattices_Oupper__semilattice(tc_fun(T_2,T_1))| -class_Lattices_Olattice(T_1).
% 187.43/187.53  0 [] class_Lattices_Obounded__lattice(tc_fun(T_2,T_1))| -class_Lattices_Obounded__lattice(T_1).
% 187.43/187.53  0 [] class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))| -class_Lattices_Oboolean__algebra(T_1).
% 187.43/187.53  0 [] class_Finite__Set_Ofinite_Ofinite(tc_fun(T_2,T_1))| -class_Finite__Set_Ofinite_Ofinite(T_1)| -class_Finite__Set_Ofinite_Ofinite(T_2).
% 187.43/187.53  0 [] class_Orderings_Opreorder(tc_fun(T_2,T_1))| -class_Orderings_Opreorder(T_1).
% 187.43/187.53  0 [] class_Lattices_Olattice(tc_fun(T_2,T_1))| -class_Lattices_Olattice(T_1).
% 187.43/187.53  0 [] class_Orderings_Oorder(tc_fun(T_2,T_1))| -class_Orderings_Oorder(T_1).
% 187.43/187.53  0 [] class_Orderings_Otop(tc_fun(T_2,T_1))| -class_Orderings_Otop(T_1).
% 187.43/187.53  0 [] class_Orderings_Obot(tc_fun(T_2,T_1))| -class_Orderings_Obot(T_1).
% 187.43/187.53  0 [] class_HOL_Ouminus(tc_fun(T_2,T_1))| -class_HOL_Ouminus(T_1).
% 187.43/187.53  0 [] class_HOL_Ominus(tc_fun(T_2,T_1))| -class_HOL_Ominus(T_1).
% 187.43/187.53  0 [] class_HOL_Oord(tc_fun(T_2,T_1))| -class_HOL_Oord(T_1).
% 187.43/187.53  0 [] class_Lattices_Oupper__semilattice(tc_nat).
% 187.43/187.53  0 [] class_Orderings_Opreorder(tc_nat).
% 187.43/187.53  0 [] class_Orderings_Olinorder(tc_nat).
% 187.43/187.53  0 [] class_Lattices_Olattice(tc_nat).
% 187.43/187.53  0 [] class_Orderings_Oorder(tc_nat).
% 187.43/187.53  0 [] class_Orderings_Obot(tc_nat).
% 187.43/187.53  0 [] class_HOL_Ominus(tc_nat).
% 187.43/187.53  0 [] class_HOL_Oord(tc_nat).
% 187.43/187.53  0 [] class_Complete__Lattice_Ocomplete__lattice(tc_bool).
% 187.43/187.53  0 [] class_Lattices_Oupper__semilattice(tc_bool).
% 187.43/187.53  0 [] class_Lattices_Obounded__lattice(tc_bool).
% 187.43/187.53  0 [] class_Lattices_Oboolean__algebra(tc_bool).
% 187.43/187.53  0 [] class_Finite__Set_Ofinite_Ofinite(tc_bool).
% 187.43/187.53  0 [] class_Orderings_Opreorder(tc_bool).
% 187.43/187.53  0 [] class_Lattices_Olattice(tc_bool).
% 187.43/187.53  0 [] class_Orderings_Oorder(tc_bool).
% 187.43/187.53  0 [] class_Orderings_Otop(tc_bool).
% 187.43/187.53  0 [] class_Orderings_Obot(tc_bool).
% 187.43/187.53  0 [] class_HOL_Ouminus(tc_bool).
% 187.43/187.53  0 [] class_HOL_Ominus(tc_bool).
% 187.43/187.53  0 [] class_HOL_Oord(tc_bool).
% 187.43/187.53  0 [] class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(T_1))| -class_Finite__Set_Ofinite_Ofinite(T_1).
% 187.43/187.53  0 [] hAPP(c_COMBS(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),hAPP(V_Q,V_R)).
% 187.43/187.53  0 [] hAPP(hAPP(c_COMBC(V_P,T_b,T_c,T_a),V_Q),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 187.43/187.53  0 [] hAPP(hAPP(c_COMBB(V_P,T_b,T_a,T_c),V_Q),V_R)=hAPP(V_P,hAPP(V_Q,V_R)).
% 187.43/187.53  0 [] c_fe_qual(V_x,V_x,T_a).
% 187.43/187.53  0 [] V_X=V_Y| -c_fe_qual(V_X,V_Y,T_a).
% 187.43/187.53  end_of_list.
% 187.43/187.53  
% 187.43/187.53  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 187.43/187.53  
% 187.43/187.53  This ia a non-Horn set with equality.  The strategy will be
% 187.43/187.53  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 187.43/187.53  deletion, with positive clauses in sos and nonpositive
% 187.43/187.53  clauses in usable.
% 187.43/187.53  
% 187.43/187.53     dependent: set(knuth_bendix).
% 187.43/187.53     dependent: set(anl_eq).
% 187.43/187.53     dependent: set(para_from).
% 187.43/187.53     dependent: set(para_into).
% 187.43/187.53     dependent: clear(para_from_right).
% 187.43/187.53     dependent: clear(para_into_right).
% 187.43/187.53     dependent: set(para_from_vars).
% 187.43/187.53     dependent: set(eq_units_both_ways).
% 187.43/187.53     dependent: set(dynamic_demod_all).
% 187.43/187.53     dependent: set(dynamic_demod).
% 187.43/187.53     dependent: set(order_eq).
% 187.43/187.53     dependent: set(back_demod).
% 187.43/187.53     dependent: set(lrpo).
% 187.43/187.53     dependent: set(hyper_res).
% 187.43/187.53     dependent: set(unit_deletion).
% 187.43/187.53     dependent: set(factor).
% 187.43/187.53  
% 187.43/187.53  ------------> process usable:
% 187.43/187.53  ** KEPT (pick-wt=9): 1 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 187.43/187.53  ** KEPT (pick-wt=9): 2 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 187.43/187.53  ** KEPT (pick-wt=9): 3 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 187.43/187.53    Following clause subsumed by 2 during input processing: 0 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 187.43/187.53  ** KEPT (pick-wt=11): 4 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 187.43/187.53  ** KEPT (pick-wt=12): 5 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ouminus__class_Ouminus(B,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 187.43/187.53  ** KEPT (pick-wt=28): 6 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),c_HOL_Ominus__class_Ominus(D,E,tc_fun(C,tc_bool)),tc_fun(C,tc_bool))| -c_lesse_quals(E,B,tc_fun(C,tc_bool))| -c_lesse_quals(A,D,tc_fun(C,tc_bool)).
% 187.43/187.53  ** KEPT (pick-wt=12): 7 [] -class_Lattices_Oboolean__algebra(A)|c_HOL_Ouminus__class_Ouminus(B,A)!=c_HOL_Ouminus__class_Ouminus(C,A)|B=C.
% 187.43/187.53  ** KEPT (pick-wt=12): 8 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ouminus__class_Ouminus(B,A)!=c_HOL_Ouminus__class_Ouminus(C,A)|B=C.
% 187.43/187.53  ** KEPT (pick-wt=14): 9 [] c_HOL_Ouminus__class_Ouminus(A,tc_fun(B,tc_bool))!=c_HOL_Ouminus__class_Ouminus(C,tc_fun(B,tc_bool))|A=C.
% 187.43/187.53  ** KEPT (pick-wt=6): 10 [] c_Com_OWT(A)| -c_Com_OWT(c_Com_Ocom_OSemi(B,A)).
% 187.43/187.53  ** KEPT (pick-wt=6): 11 [] c_Com_OWT(A)| -c_Com_OWT(c_Com_Ocom_OSemi(A,B)).
% 187.43/187.53  ** KEPT (pick-wt=9): 13 [copy,12,flip.2] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 187.43/187.53  ** KEPT (pick-wt=5): 14 [] c_Com_Ocom_OSemi(A,B)!=c_Com_Ocom_OSKIP.
% 187.43/187.53  ** KEPT (pick-wt=15): 15 [] -class_HOL_Ouminus(A)|hAPP(c_HOL_Ouminus__class_Ouminus(B,tc_fun(t_a,A)),v_x)=c_HOL_Ouminus__class_Ouminus(hAPP(B,v_x),A).
% 187.43/187.53  ** KEPT (pick-wt=9): 16 [] -class_OrderedGroup_Oordered__ab__group__add(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 187.43/187.53    Following clause subsumed by 13 during input processing: 0 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 187.43/187.53  ** KEPT (pick-wt=8): 17 [] c_Com_OWT(c_Com_Ocom_OSemi(A,B))| -c_Com_OWT(B)| -c_Com_OWT(A).
% 187.43/187.53  ** KEPT (pick-wt=24): 18 [] c_Fun_Ocomp(A,B,C,D,E)!=c_Fun_Ocomp(F,G,H,D,E)|hAPP(A,hAPP(B,I))=hAPP(F,hAPP(G,I)).
% 187.43/187.53  ** KEPT (pick-wt=28): 19 [] hAPP(A,hAPP(B,C))!=hAPP(D,hAPP(E,F))|hAPP(c_Fun_Ocomp(A,B,G,H,I),C)=hAPP(c_Fun_Ocomp(D,E,J,H,K),F).
% 187.43/187.53  ** KEPT (pick-wt=15): 20 [] hBOOL(hAPP(A,hAPP(B,C)))| -hBOOL(hAPP(hAPP(c_Set_Ovimage(B,D,E),A),C)).
% 187.43/187.53  ** KEPT (pick-wt=15): 21 [] hBOOL(hAPP(hAPP(c_Set_Ovimage(A,B,C),D),E))| -hBOOL(hAPP(D,hAPP(A,E))).
% 187.43/187.53  ** KEPT (pick-wt=25): 22 [] c_HOL_Ominus__class_Ominus(A,c_HOL_Ominus__class_Ominus(B,C,tc_fun(D,tc_bool)),tc_fun(D,tc_bool))=C| -c_lesse_quals(A,B,tc_fun(D,tc_bool))| -c_lesse_quals(C,A,tc_fun(D,tc_bool)).
% 187.43/187.53  ** KEPT (pick-wt=19): 23 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,E,A)|c_lesse_quals(E,D,A)| -c_lesse_quals(C,B,A).
% 187.43/187.53  ** KEPT (pick-wt=19): 24 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,E,A)|c_lesse_quals(C,B,A)| -c_lesse_quals(E,D,A).
% 187.43/187.53    Following clause subsumed by 14 during input processing: 0 [flip.1] c_Com_Ocom_OSemi(A,B)!=c_Com_Ocom_OSKIP.
% 187.43/187.53  ** KEPT (pick-wt=66): 26 [copy,25,flip.1] hAPP(c_Fun_Ocomp(c_Fun_Othe__inv__into(A,B,C,D),c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(B,C,D),A),E,D,F),D,C,F),G)=hAPP(c_Fun_Othe__inv__into(A,c_Fun_Ocomp(E,B,D,F,C),C,F),G)| -hBOOL(hAPP(hAPP(c_in(F),G),hAPP(c_Set_Oimage(E,D,F),hAPP(c_Set_Oimage(B,C,D),A))))| -c_Fun_Oinj__on(B,A,C,D)| -c_Fun_Oinj__on(E,hAPP(c_Set_Oimage(B,C,D),A),D,F).
% 187.43/187.54  ** KEPT (pick-wt=14): 27 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 187.43/187.54  ** KEPT (pick-wt=14): 28 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ouminus__class_Ouminus(B,A),A).
% 187.43/187.54  ** KEPT (pick-wt=13): 29 [] -class_OrderedGroup_Oordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ouminus__class_Ouminus(B,A),B,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 187.43/187.54  ** KEPT (pick-wt=13): 30 [] -class_OrderedGroup_Oordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(c_HOL_Ouminus__class_Ouminus(B,A),B,A).
% 187.43/187.54  ** KEPT (pick-wt=13): 31 [] -class_OrderedGroup_Oordered__ab__group__add(A)|c_lesse_quals(B,c_HOL_Ouminus__class_Ouminus(B,A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 187.43/187.54  ** KEPT (pick-wt=13): 32 [] -class_OrderedGroup_Oordered__ab__group__add(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ouminus__class_Ouminus(B,A),A).
% 187.43/187.54  ** KEPT (pick-wt=13): 33 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ouminus__class_Ouminus(B,A),B,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 187.43/187.54  ** KEPT (pick-wt=13): 34 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(c_HOL_Ouminus__class_Ouminus(B,A),B,A).
% 187.43/187.54  ** KEPT (pick-wt=13): 35 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(B,c_HOL_Ouminus__class_Ouminus(B,A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 187.43/187.54  ** KEPT (pick-wt=13): 36 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ouminus__class_Ouminus(B,A),A).
% 187.43/187.54  ** KEPT (pick-wt=14): 37 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A).
% 187.43/187.54  ** KEPT (pick-wt=14): 38 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,C,A).
% 187.43/187.54  ** KEPT (pick-wt=14): 39 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 187.43/187.54  ** KEPT (pick-wt=14): 40 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ozero__class_Ozero(A),A).
% 187.43/187.54  ** KEPT (pick-wt=24): 41 [] c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(A,B),C),D,tc_fun(B,tc_bool))=c_HOL_Ominus__class_Ominus(C,D,tc_fun(B,tc_bool))| -hBOOL(hAPP(hAPP(c_in(B),A),D)).
% 187.43/187.54  ** KEPT (pick-wt=17): 42 [] -class_OrderedGroup_Olordered__ab__group__add(A)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),c_HOL_Ouminus__class_Ouminus(B,A))!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 187.43/187.54  ** KEPT (pick-wt=29): 43 [] c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(A,hAPP(c_Set_Oinsert(B,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))),tc_fun(C,tc_bool)),C)=c_Finite__Set_Ocard(A,C)|hBOOL(hAPP(hAPP(c_in(C),B),A))| -c_Finite__Set_Ofinite(A,C).
% 187.43/187.54  ** KEPT (pick-wt=27): 45 [copy,44,flip.1] c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(A,hAPP(c_Set_Oinsert(B,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))),tc_fun(C,tc_bool)),C))=c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(B,C),A),C)| -c_Finite__Set_Ofinite(A,C).
% 187.43/187.54  ** KEPT (pick-wt=20): 46 [] c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),C)| -c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(A,hAPP(c_Set_Oinsert(D,C),B),tc_fun(C,tc_bool)),C).
% 187.43/187.54  ** KEPT (pick-wt=20): 47 [] c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(A,hAPP(c_Set_Oinsert(B,C),D),tc_fun(C,tc_bool)),C)| -c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(A,D,tc_fun(C,tc_bool)),C).
% 187.43/187.54  ** KEPT (pick-wt=14): 48 [] -class_Orderings_Olinorder(A)|c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(B,A),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),A)=B.
% 187.43/187.54  ** KEPT (pick-wt=14): 49 [] -class_Orderings_Olinorder(A)|c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(B,A),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),A)=B.
% 187.43/187.54  ** KEPT (pick-wt=16): 50 [] A=c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))| -c_lesse_quals(A,c_HOL_Ouminus__class_Ouminus(A,tc_fun(B,tc_bool)),tc_fun(B,tc_bool)).
% 187.43/187.54  ** KEPT (pick-wt=23): 51 [] hAPP(c_Fun_Othe__inv__into(A,B,C,D),hAPP(B,E))=E| -hBOOL(hAPP(hAPP(c_in(C),E),A))| -c_Fun_Oinj__on(B,A,C,D).
% 187.43/187.54    Following clause subsumed by 51 during input processing: 0 [] -c_Fun_Oinj__on(A,B,C,D)|hAPP(c_Fun_Othe__inv__into(B,A,C,D),hAPP(A,E))=E| -hBOOL(hAPP(hAPP(c_in(C),E),B)).
% 187.43/187.54  ** KEPT (pick-wt=9): 52 [] -class_Lattices_Oboolean__algebra(A)|c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(A),A)=c_Orderings_Obot__class_Obot(A).
% 187.43/187.54  ** KEPT (pick-wt=9): 54 [copy,53,flip.2] -class_Lattices_Oboolean__algebra(A)|c_Orderings_Otop__class_Otop(A)=c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(A),A).
% 187.43/187.54  ** KEPT (pick-wt=22): 55 [] c_Finite__Set_Ocard(A,B)!=c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),B)| -c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),B)|A=c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)).
% 187.43/187.54  ** KEPT (pick-wt=16): 56 [] c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),A)| -c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(B,tc_fun(A,tc_bool)),A)| -c_Finite__Set_Ofinite(B,A).
% 187.43/187.54  ** KEPT (pick-wt=16): 57 [] c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(A,tc_fun(B,tc_bool)),B)| -c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),B)| -c_Finite__Set_Ofinite(A,B).
% 187.43/187.54  ** KEPT (pick-wt=24): 58 [] c_lesse_quals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,tc_bool)),C),D),tc_fun(B,tc_bool))| -c_lesse_quals(c_HOL_Ominus__class_Ominus(A,C,tc_fun(B,tc_bool)),D,tc_fun(B,tc_bool)).
% 187.43/187.54  ** KEPT (pick-wt=24): 59 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool))| -c_lesse_quals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,tc_bool)),B),D),tc_fun(C,tc_bool)).
% 187.43/187.54  ** KEPT (pick-wt=21): 60 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),c_HOL_Ominus__class_Ominus(C,B,tc_fun(A,tc_bool)))=C| -c_lesse_quals(B,C,tc_fun(A,tc_bool)).
% 187.43/187.54  ** KEPT (pick-wt=13): 61 [] -class_Lattices_Oboolean__algebra(A)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),c_HOL_Ouminus__class_Ouminus(B,A))=c_Orderings_Otop__class_Otop(A).
% 187.43/187.54  ** KEPT (pick-wt=13): 62 [] -class_Lattices_Oboolean__algebra(A)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),c_HOL_Ouminus__class_Ouminus(B,A)),B)=c_Orderings_Otop__class_Otop(A).
% 187.43/187.54  ** KEPT (pick-wt=25): 63 [] c_Fun_Oinj__on(c_Fun_Ocomp(A,B,C,D,E),F,E,D)| -c_Fun_Oinj__on(A,hAPP(c_Set_Oimage(B,E,C),F),C,D)| -c_Fun_Oinj__on(B,F,E,C).
% 187.43/187.54  ** KEPT (pick-wt=20): 64 [] c_Fun_Oinj__on(A,hAPP(c_Set_Oimage(B,C,D),E),D,F)| -c_Fun_Oinj__on(c_Fun_Ocomp(A,B,D,F,C),E,C,F).
% 187.43/187.54  ** KEPT (pick-wt=19): 65 [] c_Fun_Oinj__on(c_Fun_Othe__inv__into(A,B,C,D),hAPP(c_Set_Oimage(B,C,D),A),D,C)| -c_Fun_Oinj__on(B,A,C,D).
% 187.43/187.54  ** KEPT (pick-wt=22): 66 [] hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(A,B,C,D),D,C),hAPP(c_Set_Oimage(B,C,D),A))=A| -c_Fun_Oinj__on(B,A,C,D).
% 187.43/187.54  ** KEPT (pick-wt=17): 67 [] c_Finite__Set_Ocard(hAPP(c_Set_Oimage(A,B,C),D),C)=c_Finite__Set_Ocard(D,B)| -c_Fun_Oinj__on(A,D,B,C).
% 187.43/187.54  ** KEPT (pick-wt=22): 68 [] hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),B,A,C),hAPP(B,D))=D| -c_Fun_Oinj__on(B,c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),A,C).
% 187.43/187.54  ** KEPT (pick-wt=30): 69 [] c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(A,hAPP(c_Set_Oinsert(B,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))),tc_fun(C,tc_bool)),C))=c_Finite__Set_Ocard(A,C)| -hBOOL(hAPP(hAPP(c_in(C),B),A))| -c_Finite__Set_Ofinite(A,C).
% 187.43/187.54  ** KEPT (pick-wt=14): 70 [] c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),C)| -c_Finite__Set_Ofinite(A,C)| -c_Finite__Set_Ofinite(B,C).
% 187.43/187.54  ** KEPT (pick-wt=14): 71 [] c_Finite__Set_Ofinite(A,B)| -c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(A,C,tc_fun(B,tc_bool)),B)| -c_Finite__Set_Ofinite(C,B).
% 187.43/187.54  ** KEPT (pick-wt=10): 72 [] c_Com_Ocom_OSemi(A,B)!=c_Com_Ocom_OSemi(C,D)|A=C.
% 187.43/187.54  ** KEPT (pick-wt=10): 73 [] c_Com_Ocom_OSemi(A,B)!=c_Com_Ocom_OSemi(C,D)|B=D.
% 187.43/187.54  ** KEPT (pick-wt=20): 74 [] c_lesse_quals(c_HOL_Ouminus__class_Ouminus(A,tc_fun(B,tc_bool)),c_HOL_Ouminus__class_Ouminus(C,tc_fun(B,tc_bool)),tc_fun(B,tc_bool))| -c_lesse_quals(C,A,tc_fun(B,tc_bool)).
% 187.43/187.54  ** KEPT (pick-wt=20): 75 [] c_lesse_quals(A,B,tc_fun(C,tc_bool))| -c_lesse_quals(c_HOL_Ouminus__class_Ouminus(B,tc_fun(C,tc_bool)),c_HOL_Ouminus__class_Ouminus(A,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)).
% 187.43/187.54    Following clause subsumed by 74 during input processing: 0 [] c_lesse_quals(c_HOL_Ouminus__class_Ouminus(A,tc_fun(B,tc_bool)),c_HOL_Ouminus__class_Ouminus(C,tc_fun(B,tc_bool)),tc_fun(B,tc_bool))| -c_lesse_quals(C,A,tc_fun(B,tc_bool)).
% 187.43/187.54  ** KEPT (pick-wt=14): 76 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A)| -c_lesse_quals(C,B,A).
% 187.43/187.54  ** KEPT (pick-wt=14): 77 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_HOL_Ouminus__class_Ouminus(C,A),c_HOL_Ouminus__class_Ouminus(B,A),A).
% 187.43/187.54  ** KEPT (pick-wt=15): 78 [] c_Fun_Oinj__on(A,c_HOL_Ominus__class_Ominus(B,C,tc_fun(D,tc_bool)),D,E)| -c_Fun_Oinj__on(A,B,D,E).
% 187.43/187.54  ** KEPT (pick-wt=11): 79 [] c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),C)| -c_Finite__Set_Ofinite(A,C).
% 187.43/187.54  ** KEPT (pick-wt=12): 80 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Ouminus__class_Ouminus(B,A)|c_HOL_Ozero__class_Ozero(A)=B.
% 187.43/187.54  ** KEPT (pick-wt=14): 81 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,D,A)|B=C.
% 187.43/187.54  ** KEPT (pick-wt=14): 82 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)!=c_HOL_Ominus__class_Ominus(C,D,A)|C=D.
% 187.43/187.54  ** KEPT (pick-wt=17): 83 [] c_Natural_Oevaln(c_Com_Ocom_OSemi(A,B),C,D,E)| -c_Natural_Oevaln(B,F,D,E)| -c_Natural_Oevaln(A,C,D,F).
% 187.43/187.54  ** KEPT (pick-wt=14): 84 [] c_Natural_Oevalc(c_Com_Ocom_OSemi(A,B),C,D)| -c_Natural_Oevalc(B,E,D)| -c_Natural_Oevalc(A,C,E).
% 187.43/187.54  ** KEPT (pick-wt=14): 85 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 187.43/187.54  ** KEPT (pick-wt=12): 86 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 187.43/187.54  ** KEPT (pick-wt=12): 87 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 187.43/187.54  ** KEPT (pick-wt=22): 88 [] c_lesse_quals(hAPP(c_Set_Ovimage(A,B,C),D),hAPP(c_Set_Ovimage(A,B,C),E),tc_fun(B,tc_bool))| -c_lesse_quals(D,E,tc_fun(C,tc_bool)).
% 187.43/187.54  ** KEPT (pick-wt=19): 89 [] -class_HOL_Ominus(A)|hAPP(c_HOL_Ominus__class_Ominus(B,C,tc_fun(t_a,A)),v_x)=c_HOL_Ominus__class_Ominus(hAPP(B,v_x),hAPP(C,v_x),A).
% 187.43/187.54  ** KEPT (pick-wt=11): 90 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ouminus__class_Ouminus(B,A).
% 187.43/187.54  ** KEPT (pick-wt=8): 91 [] A=B| -c_Natural_Oevaln(c_Com_Ocom_OSKIP,B,C,A).
% 187.43/187.54  ** KEPT (pick-wt=11): 92 [] -class_OrderedGroup_Oordered__ab__group__add(A)|c_HOL_Ouminus__class_Ouminus(B,A)!=B|B=c_HOL_Ozero__class_Ozero(A).
% 187.43/187.54  ** KEPT (pick-wt=9): 93 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A)=B.
% 187.43/187.54  ** KEPT (pick-wt=9): 94 [] -class_Lattices_Oboolean__algebra(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A)=B.
% 187.43/187.54    Following clause subsumed by 93 during input processing: 0 [flip.2] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A)=B.
% 187.43/187.54    Following clause subsumed by 93 during input processing: 0 [flip.2] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A)=B.
% 187.43/187.54    Following clause subsumed by 93 during input processing: 0 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A)=B.
% 187.43/187.54  ** KEPT (pick-wt=13): 95 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(B,C,A),A)=c_HOL_Ominus__class_Ominus(C,B,A).
% 187.43/187.54  ** KEPT (pick-wt=7): 96 [] A=B| -c_Natural_Oevalc(c_Com_Ocom_OSKIP,B,A).
% 187.43/187.54  ** KEPT (pick-wt=14): 97 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(B,c_HOL_Ouminus__class_Ouminus(C,A),A)| -c_lesse_quals(C,c_HOL_Ouminus__class_Ouminus(B,A),A).
% 187.43/187.54    Following clause subsumed by 97 during input processing: 0 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(B,c_HOL_Ouminus__class_Ouminus(C,A),A)| -c_lesse_quals(C,c_HOL_Ouminus__class_Ouminus(B,A),A).
% 187.43/187.54  ** KEPT (pick-wt=14): 98 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ouminus__class_Ouminus(B,A),C,A)| -c_lesse_quals(c_HOL_Ouminus__class_Ouminus(C,A),B,A).
% 187.43/187.54    Following clause subsumed by 98 during input processing: 0 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ouminus__class_Ouminus(B,A),C,A)| -c_lesse_quals(c_HOL_Ouminus__class_Ouminus(C,A),B,A).
% 187.43/187.54  ** KEPT (pick-wt=19): 99 [] -hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(hAPP(c_in(A),B),c_HOL_Ominus__class_Ominus(D,C,tc_fun(A,tc_bool)))).
% 187.43/187.54  ** KEPT (pick-wt=19): 100 [] hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(hAPP(c_in(A),B),c_HOL_Ominus__class_Ominus(C,D,tc_fun(A,tc_bool)))).
% 187.43/187.54  ** KEPT (pick-wt=18): 101 [] -hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(hAPP(c_in(A),B),c_HOL_Ouminus__class_Ouminus(C,tc_fun(A,tc_bool)))).
% 187.43/187.54  ** KEPT (pick-wt=26): 102 [] hBOOL(hAPP(hAPP(c_in(A),B),c_HOL_Ominus__class_Ominus(C,D,tc_fun(A,tc_bool))))|hBOOL(hAPP(hAPP(c_in(A),B),D))| -hBOOL(hAPP(hAPP(c_in(A),B),C)).
% 187.43/187.54    Following clause subsumed by 102 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(A),B),c_HOL_Ominus__class_Ominus(C,D,tc_fun(A,tc_bool))))|hBOOL(hAPP(hAPP(c_in(A),B),D))| -hBOOL(hAPP(hAPP(c_in(A),B),C)).
% 187.43/187.54  ** KEPT (pick-wt=21): 103 [] hBOOL(hAPP(hAPP(c_in(A),B),hAPP(c_Set_Ovimage(C,A,D),E)))| -hBOOL(hAPP(hAPP(c_in(D),hAPP(C,B)),E)).
% 187.43/187.54    Following clause subsumed by 103 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(A),B),hAPP(c_Set_Ovimage(C,A,D),E)))| -hBOOL(hAPP(hAPP(c_in(D),hAPP(C,B)),E)).
% 187.43/187.54    Following clause subsumed by 103 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(A),B),hAPP(c_Set_Ovimage(C,A,D),E)))| -hBOOL(hAPP(hAPP(c_in(D),hAPP(C,B)),E)).
% 187.43/187.54  ** KEPT (pick-wt=21): 104 [] hBOOL(hAPP(hAPP(c_in(A),hAPP(B,C)),D))| -hBOOL(hAPP(hAPP(c_in(E),C),hAPP(c_Set_Ovimage(B,E,A),D))).
% 187.43/187.54    Following clause subsumed by 104 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(A),hAPP(B,C)),D))| -hBOOL(hAPP(hAPP(c_in(E),C),hAPP(c_Set_Ovimage(B,E,A),D))).
% 187.43/187.54  ** KEPT (pick-wt=5): 105 [] hAPP(c_Com_Ocom_OBODY,A)!=c_Com_Ocom_OSKIP.
% 187.43/187.54  ** KEPT (pick-wt=7): 106 [] hAPP(c_Com_Ocom_OBODY,A)!=c_Com_Ocom_OSemi(B,C).
% 187.43/187.54  ** KEPT (pick-wt=7): 107 [] c_Com_Ocom_OSemi(A,B)!=hAPP(c_Com_Ocom_OBODY,C).
% 187.43/187.54    Following clause subsumed by 105 during input processing: 0 [flip.1] hAPP(c_Com_Ocom_OBODY,A)!=c_Com_Ocom_OSKIP.
% 187.43/187.54  ** KEPT (pick-wt=18): 108 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,c_Finite__Set_Olinorder__class_OMax(C,A),A)| -hBOOL(hAPP(hAPP(c_in(A),B),C))| -c_Finite__Set_Ofinite(C,A).
% 187.43/187.54  ** KEPT (pick-wt=18): 109 [] -class_Orderings_Olinorder(A)|c_lesse_quals(c_Finite__Set_Olinorder__class_OMin(B,A),C,A)| -hBOOL(hAPP(hAPP(c_in(A),C),B))| -c_Finite__Set_Ofinite(B,A).
% 187.43/187.54  ** KEPT (pick-wt=20): 110 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(hAPP(c_in(A),c_Finite__Set_Olinorder__class_OMin(B,A)),B))|B=c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))| -c_Finite__Set_Ofinite(B,A).
% 187.43/187.54  ** KEPT (pick-wt=20): 111 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(hAPP(c_in(A),c_Finite__Set_Olinorder__class_OMax(B,A)),B))|B=c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))| -c_Finite__Set_Ofinite(B,A).
% 187.43/187.54  ** KEPT (pick-wt=21): 112 [] c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(A,B),C),B)=c_Finite__Set_Ocard(C,B)| -hBOOL(hAPP(hAPP(c_in(B),A),C))| -c_Finite__Set_Ofinite(C,B).
% 187.43/187.54  ** KEPT (pick-wt=26): 113 [] hAPP(c_Set_Oinsert(A,B),c_HOL_Ominus__class_Ominus(C,hAPP(c_Set_Oinsert(A,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))),tc_fun(B,tc_bool)))=C| -hBOOL(hAPP(hAPP(c_in(B),A),C)).
% 187.43/187.54  ** KEPT (pick-wt=24): 114 [] hAPP(A,B)=C| -hBOOL(hAPP(hAPP(c_in(D),B),hAPP(c_Set_Ovimage(A,D,E),hAPP(c_Set_Oinsert(C,E),c_Orderings_Obot__class_Obot(tc_fun(E,tc_bool)))))).
% 187.43/187.54  ** KEPT (pick-wt=15): 115 [] c_Finite__Set_Ocard(A,B)!=c_HOL_Ozero__class_Ozero(tc_nat)| -c_Finite__Set_Ofinite(A,B)|A=c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)).
% 187.43/187.54  ** KEPT (pick-wt=38): 116 [] c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(A,hAPP(c_COMBB(c_Set_Oinsert(B,C),tc_fun(C,tc_bool),tc_fun(C,tc_bool),D),E),D,tc_fun(C,tc_bool))=hAPP(c_Set_Oinsert(B,C),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(A,E,D,tc_fun(C,tc_bool)))| -hBOOL(hAPP(hAPP(c_in(D),F),A)).
% 187.43/187.54  ** KEPT (pick-wt=29): 118 [copy,117,flip.2] -class_Lattices_Oupper__semilattice(A)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),C,D,A,A))=c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),C,hAPP(c_Set_Oinsert(B,A),D),A,A)| -c_Finite__Set_Ofinite(D,A).
% 187.43/187.54  ** KEPT (pick-wt=34): 119 [] c_lesse_quals(A,hAPP(c_Set_Oinsert(B,C),D),tc_fun(C,tc_bool))| -c_lesse_quals(A,D,tc_fun(C,tc_bool))| -c_lesse_quals(c_HOL_Ominus__class_Ominus(A,hAPP(c_Set_Oinsert(B,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))),tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool)).
% 187.43/187.54  ** KEPT (pick-wt=28): 120 [] hAPP(A,hAPP(c_Fun_Othe__inv__into(B,A,C,D),E))=E| -hBOOL(hAPP(hAPP(c_in(D),E),hAPP(c_Set_Oimage(A,C,D),B)))| -c_Fun_Oinj__on(A,B,C,D).
% 187.43/187.54  ** KEPT (pick-wt=21): 121 [] hAPP(c_Set_Ovimage(c_COMBK(A,B,C),C,B),D)=c_Orderings_Otop__class_Otop(tc_fun(C,tc_bool))| -hBOOL(hAPP(hAPP(c_in(B),A),D)).
% 187.43/187.54    Following clause subsumed by 67 during input processing: 0 [] c_Finite__Set_Ocard(hAPP(c_Set_Oimage(A,B,C),D),C)=c_Finite__Set_Ocard(D,B)| -c_Fun_Oinj__on(A,D,B,C)| -c_Finite__Set_Ofinite(D,B).
% 187.43/187.54  ** KEPT (pick-wt=20): 122 [] c_Finite__Set_Ocard(hAPP(c_Set_Oimage(A,B,C),D),C)!=c_Finite__Set_Ocard(D,B)| -c_Finite__Set_Ofinite(D,B)|c_Fun_Oinj__on(A,D,B,C).
% 187.43/187.54  ** KEPT (pick-wt=19): 123 [] c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(A,B,C),D),B)| -c_Fun_Oinj__on(A,c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),B,C)| -c_Finite__Set_Ofinite(D,C).
% 187.43/187.54  ** KEPT (pick-wt=45): 124 [] hAPP(c_Set_Oimage(A,B,C),c_HOL_Ominus__class_Ominus(D,E,tc_fun(B,tc_bool)))=c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(A,B,C),D),hAPP(c_Set_Oimage(A,B,C),E),tc_fun(C,tc_bool))| -c_lesse_quals(E,F,tc_fun(B,tc_bool))| -c_lesse_quals(D,F,tc_fun(B,tc_bool))| -c_Fun_Oinj__on(A,F,B,C).
% 187.43/187.54  ** KEPT (pick-wt=21): 125 [] hAPP(c_Set_Ovimage(A,B,C),hAPP(c_Set_Oimage(A,B,C),D))=D| -c_Fun_Oinj__on(A,c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),B,C).
% 187.43/187.54  ** KEPT (pick-wt=36): 126 [] hAPP(c_Set_Oimage(A,B,C),c_HOL_Ominus__class_Ominus(D,E,tc_fun(B,tc_bool)))=c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(A,B,C),D),hAPP(c_Set_Oimage(A,B,C),E),tc_fun(C,tc_bool))| -c_Fun_Oinj__on(A,c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),B,C).
% 187.43/187.54  ** KEPT (pick-wt=28): 127 [] c_Fun_Ocomp(c_Fun_Ocomp(A,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),C,B,D),B,E,D),C,D,E,B)=A| -c_Fun_Oinj__on(C,c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),B,D).
% 187.43/187.54  ** KEPT (pick-wt=29): 128 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(C,tc_bool)),D,C,E),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(A,D,C,E))))| -c_Fun_Oinj__on(D,c_Orderings_Otop__class_Otop(tc_fun(C,tc_bool)),C,E).
% 187.43/187.54  ** KEPT (pick-wt=27): 129 [] -class_Lattices_Oupper__semilattice(A)|c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),C,D,A,A),A)| -hBOOL(hAPP(hAPP(c_in(A),B),D))| -c_Finite__Set_Ofinite(D,A).
% 187.43/187.54  ** KEPT (pick-wt=19): 130 [] c_Fun_Oinj__on(A,B,C,C)| -c_lesse_quals(B,hAPP(c_Set_Oimage(A,C,C),B),tc_fun(C,tc_bool))| -c_Finite__Set_Ofinite(B,C).
% 187.43/187.54  ** KEPT (pick-wt=13): 131 [] c_Fun_Ofun__upd(A,B,C,D,E)!=A|hAPP(A,B)=C.
% 187.43/187.54  ** KEPT (pick-wt=5): 132 [] -class_Finite__Set_Ofinite_Ofinite(A)|c_Finite__Set_Ofinite(B,A).
% 187.43/187.54  ** KEPT (pick-wt=28): 133 [] hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),B,A,C),C,A),hAPP(c_Set_Oimage(B,A,C),D))=D| -c_Fun_Oinj__on(B,c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),A,C).
% 187.43/187.54    Following clause subsumed by 133 during input processing: 0 [] hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),B,A,C),C,A),hAPP(c_Set_Oimage(B,A,C),D))=D| -c_Fun_Oinj__on(B,c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),A,C).
% 187.43/187.54  ** KEPT (pick-wt=23): 134 [] c_lesse_quals(A,B,tc_fun(C,tc_bool))| -c_lesse_quals(A,hAPP(c_Set_Oinsert(D,C),B),tc_fun(C,tc_bool))|hBOOL(hAPP(hAPP(c_in(C),D),A)).
% 187.43/187.54  ** KEPT (pick-wt=23): 135 [] c_lesse_quals(A,hAPP(c_Set_Oinsert(B,C),D),tc_fun(C,tc_bool))| -c_lesse_quals(A,D,tc_fun(C,tc_bool))|hBOOL(hAPP(hAPP(c_in(C),B),A)).
% 187.43/187.54    Following clause subsumed by 134 during input processing: 0 [] c_lesse_quals(A,B,tc_fun(C,tc_bool))|hBOOL(hAPP(hAPP(c_in(C),D),A))| -c_lesse_quals(A,hAPP(c_Set_Oinsert(D,C),B),tc_fun(C,tc_bool)).
% 187.43/187.54    Following clause subsumed by 135 during input processing: 0 [] c_lesse_quals(A,hAPP(c_Set_Oinsert(B,C),D),tc_fun(C,tc_bool))| -c_lesse_quals(A,D,tc_fun(C,tc_bool))|hBOOL(hAPP(hAPP(c_in(C),B),A)).
% 187.43/187.54  ** KEPT (pick-wt=12): 136 [] hBOOL(hAPP(hAPP(c_Set_Oinsert(A,B),C),D))| -hBOOL(hAPP(C,D)).
% 187.43/187.54  ** KEPT (pick-wt=18): 137 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(B,c_COMBK(C,A,D),D,A)=C|B=c_Orderings_Obot__class_Obot(tc_fun(D,tc_bool)).
% 187.43/187.54  ** KEPT (pick-wt=17): 138 [] hBOOL(hAPP(hAPP(c_in(A),B),C))| -c_lesse_quals(hAPP(c_Set_Oinsert(B,A),D),C,tc_fun(A,tc_bool)).
% 187.43/187.54  ** KEPT (pick-wt=22): 139 [] c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oinsert(B,tc_Hoare__Mirabelle_Otriple(C)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(C),tc_bool))),C)| -c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oinsert(B,tc_Hoare__Mirabelle_Otriple(C)),D),C).
% 187.43/187.54  ** KEPT (pick-wt=17): 140 [] hAPP(c_Set_Oinsert(A,B),C)!=c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))|hBOOL(hAPP(hAPP(c_in(B),A),C)).
% 187.43/187.54  ** KEPT (pick-wt=20): 141 [] hAPP(c_Set_Oinsert(A,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))!=hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))|A=C.
% 187.43/187.54  ** KEPT (pick-wt=30): 142 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(B,C),D,C,A)=c_List_Ofoldl(c_COMBC(hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(A),A,tc_fun(A,A),C),D),C,A,A),c_Orderings_Obot__class_Obot(A),B,A,C).
% 187.43/187.54  ** KEPT (pick-wt=41): 143 [] hAPP(c_Set_Oimage(c_Fun_Ofun__upd(A,B,C,D,E),D,E),F)=hAPP(c_Set_Oinsert(C,E),hAPP(c_Set_Oimage(A,D,E),c_HOL_Ominus__class_Ominus(F,hAPP(c_Set_Oinsert(B,D),c_Orderings_Obot__class_Obot(tc_fun(D,tc_bool))),tc_fun(D,tc_bool))))| -hBOOL(hAPP(hAPP(c_in(D),B),F)).
% 187.43/187.54  ** KEPT (pick-wt=35): 144 [] -hBOOL(hAPP(hAPP(c_in(A),hAPP(B,C)),hAPP(c_Set_Oimage(B,D,A),c_HOL_Ominus__class_Ominus(E,hAPP(c_Set_Oinsert(C,D),c_Orderings_Obot__class_Obot(tc_fun(D,tc_bool))),tc_fun(D,tc_bool)))))| -c_Fun_Oinj__on(B,hAPP(c_Set_Oinsert(C,D),E),D,A).
% 187.43/187.54  ** KEPT (pick-wt=40): 145 [] c_Fun_Oinj__on(A,hAPP(c_Set_Oinsert(B,C),D),C,E)|hBOOL(hAPP(hAPP(c_in(E),hAPP(A,B)),hAPP(c_Set_Oimage(A,C,E),c_HOL_Ominus__class_Ominus(D,hAPP(c_Set_Oinsert(B,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))),tc_fun(C,tc_bool)))))| -c_Fun_Oinj__on(A,D,C,E).
% 187.43/187.54  ** KEPT (pick-wt=27): 146 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(B,C,D,A)=c_Finite__Set_Ofold(hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(A),A,tc_fun(A,A),D),C),c_Orderings_Obot__class_Obot(A),B,D,A)| -c_Finite__Set_Ofinite(B,D).
% 187.43/187.54  ** KEPT (pick-wt=12): 147 [] c_Hoare__Mirabelle_Ohoare__valids(A,B,t_a)| -c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(A,B),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(A,B),t_a).
% 187.43/187.54  ** KEPT (pick-wt=62): 148 [] c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(B),C),c_Com_Ocom_OSemi(D,E)),F),tc_Hoare__Mirabelle_Otriple(B)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(B),tc_bool))),B)| -c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(B),G),E),F),tc_Hoare__Mirabelle_Otriple(B)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(B),tc_bool))),B)| -c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(B),C),D),G),tc_Hoare__Mirabelle_Otriple(B)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(B),tc_bool))),B).
% 187.43/187.54  ** KEPT (pick-wt=66): 150 [copy,149,flip.1] hAPP(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(A,B,C,D),c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(B,C,D),A),E,D,F),D,C,F),G)=hAPP(c_Hilbert__Choice_Oinv__into(A,c_Fun_Ocomp(E,B,D,F,C),C,F),G)| -hBOOL(hAPP(hAPP(c_in(F),G),hAPP(c_Set_Oimage(E,D,F),hAPP(c_Set_Oimage(B,C,D),A))))| -c_Fun_Oinj__on(B,A,C,D)| -c_Fun_Oinj__on(E,hAPP(c_Set_Oimage(B,C,D),A),D,F).
% 187.43/187.55  ** KEPT (pick-wt=30): 151 [] c_lesse_quals(hAPP(c_Set_Ovimage(A,B,C),D),E,tc_fun(B,tc_bool))| -c_lesse_quals(D,hAPP(c_Set_Oimage(A,B,C),E),tc_fun(C,tc_bool))| -c_Fun_Oinj__on(A,c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),B,C).
% 187.43/187.55  ** KEPT (pick-wt=32): 152 [] c_lesse_quals(hAPP(c_Set_Oimage(A,B,C),c_HOL_Ouminus__class_Ouminus(D,tc_fun(B,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(A,B,C),D),tc_fun(C,tc_bool)),tc_fun(C,tc_bool))| -c_Fun_Oinj__on(A,c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),B,C).
% 187.43/187.55  ** KEPT (pick-wt=45): 153 [] c_Finite__Set_Ocard(A,B)=c_Finite__Set_Ocard(C,D)| -c_Finite__Set_Ofinite(C,D)| -c_Finite__Set_Ofinite(A,B)| -c_lesse_quals(hAPP(c_Set_Oimage(E,D,B),C),A,tc_fun(B,tc_bool))| -c_Fun_Oinj__on(E,C,D,B)| -c_lesse_quals(hAPP(c_Set_Oimage(F,B,D),A),C,tc_fun(D,tc_bool))| -c_Fun_Oinj__on(F,A,B,D).
% 187.43/187.55  ** KEPT (pick-wt=39): 155 [copy,154,flip.3] -c_Fun_Oinj__on(A,c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),B,C)|hBOOL(hAPP(hAPP(c_in(C),hAPP(A,D)),hAPP(c_Set_Oimage(A,B,C),c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)))))|hAPP(A,c_ATP__Linkup_Osko__Fun__Xrange__ex1__e_q__1__2(hAPP(A,D),A,D,C,B))=hAPP(A,D).
% 187.43/187.55  ** KEPT (pick-wt=31): 156 [] hBOOL(hAPP(A,B))|hBOOL(hAPP(hAPP(c_in(C),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(A,D,E,C)),hAPP(c_Set_Oimage(D,E,C),c_Orderings_Otop__class_Otop(tc_fun(E,tc_bool)))))| -c_Fun_Oinj__on(D,c_Orderings_Otop__class_Otop(tc_fun(E,tc_bool)),E,C).
% 187.43/187.55  ** KEPT (pick-wt=35): 157 [] c_ATP__Linkup_Osko__Fun__Xrange__ex1__e_q__1__2(hAPP(A,B),A,B,C,D)!=B| -c_Fun_Oinj__on(A,c_Orderings_Otop__class_Otop(tc_fun(D,tc_bool)),D,C)|hBOOL(hAPP(hAPP(c_in(C),hAPP(A,B)),hAPP(c_Set_Oimage(A,D,C),c_Orderings_Otop__class_Otop(tc_fun(D,tc_bool))))).
% 187.43/187.55  ** KEPT (pick-wt=32): 159 [copy,158,flip.1] hAPP(A,c_ATP__Linkup_Osko__Fun__Xrange__ex1__e_q__1__1(B,A,C,D))=B| -hBOOL(hAPP(hAPP(c_in(C),B),hAPP(c_Set_Oimage(A,D,C),c_Orderings_Otop__class_Otop(tc_fun(D,tc_bool)))))| -c_Fun_Oinj__on(A,c_Orderings_Otop__class_Otop(tc_fun(D,tc_bool)),D,C).
% 187.43/187.55  ** KEPT (pick-wt=34): 161 [copy,160,flip.3] -hBOOL(hAPP(hAPP(c_in(A),hAPP(B,C)),hAPP(c_Set_Oimage(B,D,A),c_Orderings_Otop__class_Otop(tc_fun(D,tc_bool)))))| -c_Fun_Oinj__on(B,c_Orderings_Otop__class_Otop(tc_fun(D,tc_bool)),D,A)|c_ATP__Linkup_Osko__Fun__Xrange__ex1__e_q__1__1(hAPP(B,C),B,A,D)=C.
% 187.43/187.55  ** KEPT (pick-wt=36): 162 [] hBOOL(hAPP(hAPP(c_in(A),hAPP(c_Fun_Othe__inv__into(B,C,A,D),E)),F))| -c_lesse_quals(B,F,tc_fun(A,tc_bool))| -hBOOL(hAPP(hAPP(c_in(D),E),hAPP(c_Set_Oimage(C,A,D),B)))| -c_Fun_Oinj__on(C,B,A,D).
% 187.43/187.55  ** KEPT (pick-wt=31): 163 [] -class_Complete__Lattice_Ocomplete__lattice(A)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(C,D,E,A))=c_Finite__Set_Ofold(hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(A),A,tc_fun(A,A),E),D),B,C,E,A)| -c_Finite__Set_Ofinite(C,E).
% 187.43/187.55  ** KEPT (pick-wt=35): 164 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(A,hAPP(c_Set_Oinsert(B,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))),tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool))| -hBOOL(hAPP(hAPP(c_in(C),B),A))| -c_lesse_quals(A,hAPP(c_Set_Oinsert(B,C),D),tc_fun(C,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=35): 165 [] c_lesse_quals(A,hAPP(c_Set_Oinsert(B,C),D),tc_fun(C,tc_bool))| -hBOOL(hAPP(hAPP(c_in(C),B),A))| -c_lesse_quals(c_HOL_Ominus__class_Ominus(A,hAPP(c_Set_Oinsert(B,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))),tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool)).
% 187.43/187.55    Following clause subsumed by 165 during input processing: 0 [] c_lesse_quals(A,hAPP(c_Set_Oinsert(B,C),D),tc_fun(C,tc_bool))| -hBOOL(hAPP(hAPP(c_in(C),B),A))| -c_lesse_quals(c_HOL_Ominus__class_Ominus(A,hAPP(c_Set_Oinsert(B,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))),tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=22): 166 [] c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(A,B),C),B)=c_Suc(c_Finite__Set_Ocard(C,B))|hBOOL(hAPP(hAPP(c_in(B),A),C))| -c_Finite__Set_Ofinite(C,B).
% 187.43/187.55  ** KEPT (pick-wt=25): 167 [] -class_Orderings_Olinorder(A)|c_lesse_quals(c_Finite__Set_Olinorder__class_OMax(B,A),c_Finite__Set_Olinorder__class_OMax(C,A),A)| -c_Finite__Set_Ofinite(C,A)|B=c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))| -c_lesse_quals(B,C,tc_fun(A,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=25): 168 [] -class_Orderings_Olinorder(A)|c_lesse_quals(c_Finite__Set_Olinorder__class_OMin(B,A),c_Finite__Set_Olinorder__class_OMin(C,A),A)| -c_Finite__Set_Ofinite(B,A)|C=c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))| -c_lesse_quals(C,B,tc_fun(A,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=9): 169 [] c_Natural_Oevalc(A,B,C)| -c_Natural_Oevaln(A,B,D,C).
% 187.43/187.55    Following clause subsumed by 169 during input processing: 0 [] c_Natural_Oevalc(A,B,C)| -c_Natural_Oevaln(A,B,D,C).
% 187.43/187.55  ** KEPT (pick-wt=16): 170 [] -class_HOL_Oord(A)|c_lesse_quals(hAPP(B,C),hAPP(D,C),A)| -c_lesse_quals(B,D,tc_fun(E,A)).
% 187.43/187.55  ** KEPT (pick-wt=18): 171 [] hBOOL(hAPP(hAPP(c_in(A),B),hAPP(c_Set_Oinsert(C,A),D)))| -hBOOL(hAPP(hAPP(c_in(A),B),D)).
% 187.43/187.55    Following clause subsumed by 171 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(A),B),hAPP(c_Set_Oinsert(C,A),D)))| -hBOOL(hAPP(hAPP(c_in(A),B),D)).
% 187.43/187.55  ** KEPT (pick-wt=20): 172 [] hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(hAPP(c_in(A),B),D))| -c_lesse_quals(D,C,tc_fun(A,tc_bool)).
% 187.43/187.55    Following clause subsumed by 172 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(A),B),C))| -c_lesse_quals(D,C,tc_fun(A,tc_bool))| -hBOOL(hAPP(hAPP(c_in(A),B),D)).
% 187.43/187.55    Following clause subsumed by 172 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(hAPP(c_in(A),B),D))| -c_lesse_quals(D,C,tc_fun(A,tc_bool)).
% 187.43/187.55    Following clause subsumed by 172 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(hAPP(c_in(A),B),D))| -c_lesse_quals(D,C,tc_fun(A,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=10): 173 [] -hBOOL(hAPP(hAPP(c_in(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)))).
% 187.43/187.55    Following clause subsumed by 173 during input processing: 0 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(hAPP(c_in(C),B),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)))).
% 187.43/187.55    Following clause subsumed by 173 during input processing: 0 [] -hBOOL(hAPP(hAPP(c_in(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)))).
% 187.43/187.55    Following clause subsumed by 173 during input processing: 0 [] -hBOOL(hAPP(hAPP(c_in(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)))).
% 187.43/187.55  ** KEPT (pick-wt=21): 174 [] hBOOL(hAPP(hAPP(c_in(A),B),C))|B=D| -hBOOL(hAPP(hAPP(c_in(A),B),hAPP(c_Set_Oinsert(D,A),C))).
% 187.43/187.55  ** KEPT (pick-wt=29): 175 [] hAPP(A,B)!=hAPP(A,C)| -hBOOL(hAPP(hAPP(c_in(D),C),E))| -hBOOL(hAPP(hAPP(c_in(D),B),E))|B=C| -c_Fun_Oinj__on(A,E,D,F).
% 187.43/187.55    Following clause subsumed by 175 during input processing: 0 [] hAPP(A,B)!=hAPP(A,C)| -hBOOL(hAPP(hAPP(c_in(D),C),E))| -hBOOL(hAPP(hAPP(c_in(D),B),E))| -c_Fun_Oinj__on(A,E,D,F)|B=C.
% 187.43/187.55    Following clause subsumed by 175 during input processing: 0 [] hAPP(A,B)!=hAPP(A,C)| -hBOOL(hAPP(hAPP(c_in(D),C),E))| -hBOOL(hAPP(hAPP(c_in(D),B),E))| -c_Fun_Oinj__on(A,E,D,F)|B=C.
% 187.43/187.55    Following clause subsumed by 175 during input processing: 0 [] hAPP(A,B)!=hAPP(A,C)| -c_Fun_Oinj__on(A,D,E,F)|B=C| -hBOOL(hAPP(hAPP(c_in(E),C),D))| -hBOOL(hAPP(hAPP(c_in(E),B),D)).
% 187.43/187.55    Following clause subsumed by 173 during input processing: 0 [] -hBOOL(hAPP(A,B))| -hBOOL(hAPP(hAPP(c_in(C),B),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)))).
% 187.43/187.55  ** KEPT (pick-wt=24): 176 [] hAPP(c_COMBC(c_in(A),A,tc_fun(A,tc_bool),tc_bool),B)!=hAPP(c_COMBC(c_in(A),A,tc_fun(A,tc_bool),tc_bool),C)|B=C.
% 187.43/187.55  ** KEPT (pick-wt=28): 177 [] hAPP(c_Set_Oinsert(A,B),C)!=hAPP(c_Set_Oinsert(A,B),D)|hBOOL(hAPP(hAPP(c_in(B),A),D))|hBOOL(hAPP(hAPP(c_in(B),A),C))|C=D.
% 187.43/187.55  ** KEPT (pick-wt=29): 178 [] hBOOL(hAPP(hAPP(c_in(A),B),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(C,D,E,tc_fun(A,tc_bool))))| -hBOOL(hAPP(hAPP(c_in(A),B),hAPP(D,F)))| -hBOOL(hAPP(hAPP(c_in(E),F),C)).
% 187.43/187.55    Following clause subsumed by 178 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(A),B),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(C,D,E,tc_fun(A,tc_bool))))| -hBOOL(hAPP(hAPP(c_in(A),B),hAPP(D,F)))| -hBOOL(hAPP(hAPP(c_in(E),F),C)).
% 187.43/187.55  ** KEPT (pick-wt=19): 179 [] hBOOL(hAPP(A,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(B,C,A,D)))| -hBOOL(hAPP(A,E))| -hBOOL(hAPP(hAPP(c_in(D),E),C)).
% 187.43/187.55  ** KEPT (pick-wt=19): 180 [] hBOOL(hAPP(A,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(B,C,A,D)))| -hBOOL(hAPP(A,E))| -hBOOL(hAPP(hAPP(c_in(D),E),B)).
% 187.43/187.55  ** KEPT (pick-wt=14): 181 [] hAPP(c_Set_Oinsert(A,B),C)=C| -hBOOL(hAPP(hAPP(c_in(B),A),C)).
% 187.43/187.55  ** KEPT (pick-wt=23): 182 [] hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(A,B,C,tc_fun(D,tc_bool)),E))| -hBOOL(hAPP(hAPP(B,F),E))| -hBOOL(hAPP(hAPP(c_in(C),F),A)).
% 187.43/187.55    Following clause subsumed by 182 during input processing: 0 [] hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(A,B,C,tc_fun(D,tc_bool)),E))| -hBOOL(hAPP(hAPP(B,F),E))| -hBOOL(hAPP(hAPP(c_in(C),F),A)).
% 187.43/187.55  ** KEPT (pick-wt=27): 183 [] c_Fun_Oinj__on(c_Fun_Ofun__upd(A,B,C,D,E),F,D,E)|hBOOL(hAPP(hAPP(c_in(E),C),hAPP(c_Set_Oimage(A,D,E),F)))| -c_Fun_Oinj__on(A,F,D,E).
% 187.43/187.55  ** KEPT (pick-wt=29): 184 [] hBOOL(hAPP(hAPP(c_in(A),hAPP(B,C)),hAPP(c_Set_Oimage(B,D,A),E)))| -hBOOL(hAPP(hAPP(c_in(D),C),E))| -c_Fun_Oinj__on(B,c_Orderings_Otop__class_Otop(tc_fun(D,tc_bool)),D,A).
% 187.43/187.55  ** KEPT (pick-wt=29): 185 [] hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(hAPP(c_in(D),hAPP(E,B)),hAPP(c_Set_Oimage(E,A,D),C)))| -c_Fun_Oinj__on(E,c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),A,D).
% 187.43/187.55  ** KEPT (pick-wt=28): 186 [] c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(hAPP(c_COMBB(A,B,C,D),E),D,C),c_Orderings_Otop__class_Otop(tc_fun(D,tc_bool))),C)| -c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(E,D,B),c_Orderings_Otop__class_Otop(tc_fun(D,tc_bool))),B).
% 187.43/187.55  ** KEPT (pick-wt=5): 187 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 187.43/187.55    Following clause subsumed by 187 during input processing: 0 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 187.43/187.55  ** KEPT (pick-wt=11): 188 [] c_Natural_Oevaln(A,B,c_Suc(C),D)| -c_Natural_Oevaln(A,B,C,D).
% 187.43/187.55    Following clause subsumed by 187 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 187.43/187.55    Following clause subsumed by 187 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 187.43/187.55  ** KEPT (pick-wt=15): 189 [] -class_Lattices_Oupper__semilattice(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D),C,A).
% 187.43/187.55  ** KEPT (pick-wt=15): 190 [] -class_Lattices_Oupper__semilattice(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B),C,A).
% 187.43/187.55  ** KEPT (pick-wt=15): 191 [] -class_Lattices_Oupper__semilattice(A)|c_lesse_quals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D),A)| -c_lesse_quals(B,C,A).
% 187.43/187.55  ** KEPT (pick-wt=15): 192 [] -class_Lattices_Oupper__semilattice(A)|c_lesse_quals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D),A)| -c_lesse_quals(B,D,A).
% 187.43/187.55    Following clause subsumed by 189 during input processing: 0 [] -class_Lattices_Oupper__semilattice(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D),C,A).
% 187.43/187.55    Following clause subsumed by 190 during input processing: 0 [] -class_Lattices_Oupper__semilattice(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B),C,A).
% 187.43/187.55  ** KEPT (pick-wt=14): 193 [] -class_Lattices_Oupper__semilattice(A)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)=C| -c_lesse_quals(B,C,A).
% 187.43/187.55  ** KEPT (pick-wt=14): 194 [] -class_Lattices_Oupper__semilattice(A)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)!=C|c_lesse_quals(B,C,A).
% 187.43/187.55  ** KEPT (pick-wt=14): 195 [] -class_Lattices_Oupper__semilattice(A)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)=B| -c_lesse_quals(C,B,A).
% 187.43/187.55  ** KEPT (pick-wt=11): 196 [] -class_Lattices_Obounded__lattice(A)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),c_Orderings_Obot__class_Obot(A)),B)=B.
% 187.43/187.55  ** KEPT (pick-wt=11): 197 [] -class_Lattices_Obounded__lattice(A)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),c_Orderings_Obot__class_Obot(A))=B.
% 187.43/187.55  ** KEPT (pick-wt=12): 198 [] -class_Lattices_Obounded__lattice(A)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),c_Orderings_Otop__class_Otop(A)),B)=c_Orderings_Otop__class_Otop(A).
% 187.43/187.55  ** KEPT (pick-wt=12): 199 [] -class_Lattices_Obounded__lattice(A)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),c_Orderings_Otop__class_Otop(A))=c_Orderings_Otop__class_Otop(A).
% 187.43/187.55  ** KEPT (pick-wt=19): 200 [] -class_Lattices_Oupper__semilattice(A)|c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A)| -c_lesse_quals(C,D,A)| -c_lesse_quals(B,D,A).
% 187.43/187.55  ** KEPT (pick-wt=11): 201 [] -class_Lattices_Oupper__semilattice(A)|c_lesse_quals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),A).
% 187.43/187.55  ** KEPT (pick-wt=11): 202 [] -class_Lattices_Oupper__semilattice(A)|c_lesse_quals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B),A).
% 187.43/187.55    Following clause subsumed by 200 during input processing: 0 [] -class_Lattices_Oupper__semilattice(A)|c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A)| -c_lesse_quals(C,D,A)| -c_lesse_quals(B,D,A).
% 187.43/187.55    Following clause subsumed by 200 during input processing: 0 [] -class_Lattices_Oupper__semilattice(A)|c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A)| -c_lesse_quals(C,D,A)| -c_lesse_quals(B,D,A).
% 187.43/187.55  ** KEPT (pick-wt=11): 203 [] -class_Lattices_Olattice(A)|c_lesse_quals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B),A).
% 187.43/187.55  ** KEPT (pick-wt=11): 204 [] -class_Lattices_Olattice(A)|c_lesse_quals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),A).
% 187.43/187.55  ** KEPT (pick-wt=15): 205 [] -class_Lattices_Obounded__lattice(A)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)!=c_Orderings_Obot__class_Obot(A)|B=c_Orderings_Obot__class_Obot(A).
% 187.43/187.55  ** KEPT (pick-wt=15): 206 [] -class_Lattices_Obounded__lattice(A)|hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)!=c_Orderings_Obot__class_Obot(A)|C=c_Orderings_Obot__class_Obot(A).
% 187.43/187.55  ** KEPT (pick-wt=22): 207 [] -c_lesse_quals(A,B,tc_fun(C,tc_bool))|c_lesse_quals(hAPP(c_Set_Oimage(D,C,E),A),hAPP(c_Set_Oimage(D,C,E),B),tc_fun(E,tc_bool)).
% 187.43/187.55    Following clause subsumed by 207 during input processing: 0 [] c_lesse_quals(hAPP(c_Set_Oimage(A,B,C),D),hAPP(c_Set_Oimage(A,B,C),E),tc_fun(C,tc_bool))| -c_lesse_quals(D,E,tc_fun(B,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=30): 208 [] hAPP(A,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(B,A,C,D,E))!=hAPP(C,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(B,A,C,D,E))|hAPP(c_Set_Oimage(A,D,E),B)=hAPP(c_Set_Oimage(C,D,E),B).
% 187.43/187.55  ** KEPT (pick-wt=17): 209 [] hAPP(c_Set_Oimage(A,B,C),D)!=c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))|D=c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=11): 210 [] c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(A,B,C),D),C)| -c_Finite__Set_Ofinite(D,B).
% 187.43/187.55  ** KEPT (pick-wt=17): 211 [] c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))!=hAPP(c_Set_Oimage(B,C,A),D)|D=c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=19): 212 [] c_lesse_quals(A,B,tc_fun(C,tc_bool))| -c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,tc_bool)),D),A),B,tc_fun(C,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=19): 213 [] c_lesse_quals(A,B,tc_fun(C,tc_bool))| -c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,tc_bool)),A),D),B,tc_fun(C,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=32): 214 [] c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),D),E),tc_fun(A,tc_bool))| -c_lesse_quals(C,E,tc_fun(A,tc_bool))| -c_lesse_quals(B,D,tc_fun(A,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=16): 215 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C)!=C|c_lesse_quals(B,C,tc_fun(A,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=16): 216 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C)=B| -c_lesse_quals(C,B,tc_fun(A,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=16): 217 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C)=C| -c_lesse_quals(B,C,tc_fun(A,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=13): 218 [] c_Finite__Set_Ofinite(A,B)| -c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,tc_bool)),C),A),B).
% 187.43/187.55  ** KEPT (pick-wt=13): 219 [] c_Finite__Set_Ofinite(A,B)| -c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,tc_bool)),A),C),B).
% 187.43/187.55  ** KEPT (pick-wt=16): 220 [] c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C),A)| -c_Finite__Set_Ofinite(C,A)| -c_Finite__Set_Ofinite(B,A).
% 187.43/187.55    Following clause subsumed by 220 during input processing: 0 [] c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C),A)| -c_Finite__Set_Ofinite(C,A)| -c_Finite__Set_Ofinite(B,A).
% 187.43/187.55  ** KEPT (pick-wt=25): 221 [] c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C),D,tc_fun(A,tc_bool))| -c_lesse_quals(C,D,tc_fun(A,tc_bool))| -c_lesse_quals(B,D,tc_fun(A,tc_bool)).
% 187.43/187.55    Following clause subsumed by 221 during input processing: 0 [] c_lesse_quals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C),D,tc_fun(A,tc_bool))| -c_lesse_quals(C,D,tc_fun(A,tc_bool))| -c_lesse_quals(B,D,tc_fun(A,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=19): 222 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))|C=c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=19): 223 [] hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),B),C)!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))|B=c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=17): 224 [] c_Fun_Oinj__on(A,B,C,D)| -c_Fun_Oinj__on(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,tc_bool)),E),B),C,D).
% 187.43/187.55  ** KEPT (pick-wt=17): 225 [] c_Fun_Oinj__on(A,B,C,D)| -c_Fun_Oinj__on(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,tc_bool)),B),E),C,D).
% 187.43/187.55  ** KEPT (pick-wt=15): 227 [copy,226,flip.1] c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(A,B,C,D))=B| -c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,A),C,B,D).
% 187.43/187.55  ** KEPT (pick-wt=6): 228 [] c_Option_Ooption_ONone(A)!=c_Option_Ooption_OSome(B,A).
% 187.43/187.55    Following clause subsumed by 228 during input processing: 0 [] c_Option_Ooption_ONone(A)!=c_Option_Ooption_OSome(B,A).
% 187.43/187.55  ** KEPT (pick-wt=28): 229 [] hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(A,B,C,D),D,C),hAPP(c_Set_Oimage(B,C,D),E))=E| -c_lesse_quals(E,A,tc_fun(C,tc_bool))| -c_Fun_Oinj__on(B,A,C,D).
% 187.43/187.55  ** KEPT (pick-wt=17): 230 [] A=B| -hBOOL(hAPP(hAPP(c_in(C),A),hAPP(c_Set_Oinsert(B,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))))).
% 187.43/187.55  ** KEPT (pick-wt=25): 231 [] hAPP(c_Set_Oimage(c_COMBK(A,B,C),C,B),D)=hAPP(c_Set_Oinsert(A,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)))| -hBOOL(hAPP(hAPP(c_in(C),E),D)).
% 187.43/187.55  ** KEPT (pick-wt=17): 232 [] c_Finite__Set_Ofinite(A,B)| -c_lesse_quals(A,hAPP(c_Set_Oimage(C,D,B),E),tc_fun(B,tc_bool))| -c_Finite__Set_Ofinite(E,D).
% 187.43/187.55  ** KEPT (pick-wt=30): 233 [] c_lesse_quals(A,B,tc_fun(C,tc_bool))| -c_lesse_quals(hAPP(c_Set_Oimage(D,C,E),A),hAPP(c_Set_Oimage(D,C,E),B),tc_fun(E,tc_bool))| -c_Fun_Oinj__on(D,c_Orderings_Otop__class_Otop(tc_fun(C,tc_bool)),C,E).
% 187.43/187.55    Following clause subsumed by 207 during input processing: 0 [] c_lesse_quals(hAPP(c_Set_Oimage(A,B,C),D),hAPP(c_Set_Oimage(A,B,C),E),tc_fun(C,tc_bool))| -c_lesse_quals(D,E,tc_fun(B,tc_bool))| -c_Fun_Oinj__on(A,c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),B,C).
% 187.43/187.55  ** KEPT (pick-wt=14): 234 [] c_Fun_Oinj__on(A,B,C,D)| -c_Fun_Oinj__on(A,hAPP(c_Set_Oinsert(E,C),B),C,D).
% 187.43/187.55  ** KEPT (pick-wt=19): 235 [] -class_Complete__Lattice_Ocomplete__lattice(A)|c_lesse_quals(hAPP(B,C),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(D,B,E,A),A)| -hBOOL(hAPP(hAPP(c_in(E),C),D)).
% 187.43/187.55  ** KEPT (pick-wt=21): 236 [] c_lesse_quals(hAPP(A,B),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(C,A,D,tc_fun(E,tc_bool)),tc_fun(E,tc_bool))| -hBOOL(hAPP(hAPP(c_in(D),B),C)).
% 187.43/187.55  ** KEPT (pick-wt=16): 237 [] c_lesse_quals(A,B,tc_fun(C,tc_bool))| -c_lesse_quals(hAPP(c_Set_Oinsert(D,C),A),B,tc_fun(C,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=16): 238 [] c_lesse_quals(A,hAPP(c_Set_Oinsert(B,C),D),tc_fun(C,tc_bool))| -c_lesse_quals(A,D,tc_fun(C,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=11): 239 [] -class_Orderings_Obot(A)|hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,A)),v_x)=c_Orderings_Obot__class_Obot(A).
% 187.43/187.55  ** KEPT (pick-wt=7): 240 [] -class_Orderings_Obot(A)|c_lesse_quals(c_Orderings_Obot__class_Obot(A),B,A).
% 187.43/187.55  ** KEPT (pick-wt=10): 241 [] hAPP(c_Set_Oinsert(A,B),C)!=c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=24): 242 [] c_Finite__Set_Ofinite(hAPP(A,B),C)| -hBOOL(hAPP(hAPP(c_in(D),B),E))| -c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(E,A,D,tc_fun(C,tc_bool)),C)| -c_Finite__Set_Ofinite(E,D).
% 187.43/187.55  ** KEPT (pick-wt=15): 243 [] hBOOL(hAPP(A,B))|C=B| -hBOOL(hAPP(hAPP(c_Set_Oinsert(C,D),A),B)).
% 187.43/187.55  ** KEPT (pick-wt=27): 244 [] c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(A,B,C,tc_fun(D,tc_bool))!=c_Orderings_Obot__class_Obot(tc_fun(D,tc_bool))|hAPP(B,E)=c_Orderings_Obot__class_Obot(tc_fun(D,tc_bool))| -hBOOL(hAPP(hAPP(c_in(C),E),A)).
% 187.43/187.55  ** KEPT (pick-wt=23): 245 [] hAPP(c_Hilbert__Choice_Oinv__into(A,B,C,D),hAPP(B,E))=E| -hBOOL(hAPP(hAPP(c_in(C),E),A))| -c_Fun_Oinj__on(B,A,C,D).
% 187.43/187.55    Following clause subsumed by 245 during input processing: 0 [] -hBOOL(hAPP(hAPP(c_in(A),B),C))| -c_Fun_Oinj__on(D,C,A,E)|hAPP(c_Hilbert__Choice_Oinv__into(C,D,A,E),hAPP(D,B))=B.
% 187.43/187.55  ** KEPT (pick-wt=27): 246 [] c_lesse_quals(hAPP(A,B),C,tc_fun(D,tc_bool))| -hBOOL(hAPP(hAPP(c_in(E),B),F))| -c_lesse_quals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(F,A,E,tc_fun(D,tc_bool)),C,tc_fun(D,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=10): 247 [] c_Finite__Set_Ofinite(A,B)| -c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(C,B),A),B).
% 187.43/187.55  ** KEPT (pick-wt=10): 248 [] c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(A,B),C),B)| -c_Finite__Set_Ofinite(C,B).
% 187.43/187.55  ** KEPT (pick-wt=6): 249 [] c_Option_Ooption_OSome(A,B)!=c_Option_Ooption_ONone(B).
% 187.43/187.55    Following clause subsumed by 249 during input processing: 0 [] c_Option_Ooption_OSome(A,B)!=c_Option_Ooption_ONone(B).
% 187.43/187.55  ** KEPT (pick-wt=10): 250 [] c_Option_Ooption_OSome(A,B)!=c_Option_Ooption_OSome(C,B)|A=C.
% 187.43/187.55  ** KEPT (pick-wt=18): 251 [] hAPP(A,B)!=hAPP(A,C)| -c_Fun_Oinj__on(A,c_Orderings_Otop__class_Otop(tc_fun(D,tc_bool)),D,E)|B=C.
% 187.43/187.55  ** KEPT (pick-wt=27): 252 [] hAPP(c_Set_Oimage(A,B,B),C)=C| -c_Fun_Oinj__on(A,C,B,B)| -c_lesse_quals(hAPP(c_Set_Oimage(A,B,B),C),C,tc_fun(B,tc_bool))| -c_Finite__Set_Ofinite(C,B).
% 187.43/187.55  ** KEPT (pick-wt=27): 253 [] c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))!=c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(B,C,D,tc_fun(A,tc_bool))|hAPP(C,E)=c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))| -hBOOL(hAPP(hAPP(c_in(D),E),B)).
% 187.43/187.55  ** KEPT (pick-wt=24): 254 [] hAPP(c_Set_Oimage(A,B,C),D)!=hAPP(c_Set_Oimage(A,B,C),E)| -c_Fun_Oinj__on(A,c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),B,C)|D=E.
% 187.43/187.55  ** KEPT (pick-wt=20): 255 [] c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(A,B,C,D),E,D,C)| -c_lesse_quals(E,hAPP(c_Set_Oimage(B,C,D),A),tc_fun(D,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=7): 256 [] -hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B)).
% 187.43/187.55  ** KEPT (pick-wt=9): 257 [] c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool))!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=11): 258 [] -class_Orderings_Otop(A)|hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,A)),v_x)=c_Orderings_Otop__class_Otop(A).
% 187.43/187.55  ** KEPT (pick-wt=30): 259 [] c_lesse_quals(A,B,tc_fun(C,tc_bool))| -c_lesse_quals(hAPP(c_COMBC(c_in(C),C,tc_fun(C,tc_bool),tc_bool),A),hAPP(c_COMBC(c_in(C),C,tc_fun(C,tc_bool),tc_bool),B),tc_fun(C,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=30): 260 [] c_lesse_quals(hAPP(c_COMBC(c_in(A),A,tc_fun(A,tc_bool),tc_bool),B),hAPP(c_COMBC(c_in(A),A,tc_fun(A,tc_bool),tc_bool),C),tc_fun(A,tc_bool))| -c_lesse_quals(B,C,tc_fun(A,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=15): 261 [] A=B| -c_lesse_quals(B,A,tc_fun(C,tc_bool))| -c_lesse_quals(A,B,tc_fun(C,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=11): 262 [] A=B| -c_Natural_Oevalc(C,D,A)| -c_Natural_Oevalc(C,D,B).
% 187.43/187.55    Following clause subsumed by 261 during input processing: 0 [] A=B| -c_lesse_quals(B,A,tc_fun(C,tc_bool))| -c_lesse_quals(A,B,tc_fun(C,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=13): 263 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(C,B,A)| -c_lesse_quals(B,C,A).
% 187.43/187.55    Following clause subsumed by 263 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(C,B,A)| -c_lesse_quals(B,C,A).
% 187.43/187.55    Following clause subsumed by 263 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(B,C,A)| -c_lesse_quals(C,B,A).
% 187.43/187.55  ** KEPT (pick-wt=31): 264 [] hAPP(c_Set_Oinsert(A,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))))!=hAPP(c_Set_Oinsert(D,B),hAPP(c_Set_Oinsert(E,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))))|A=E|A=D.
% 187.43/187.55  ** KEPT (pick-wt=31): 265 [] hAPP(c_Set_Oinsert(A,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))))!=hAPP(c_Set_Oinsert(D,B),hAPP(c_Set_Oinsert(E,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))))|C=D|A=D.
% 187.43/187.55  ** KEPT (pick-wt=31): 266 [] hAPP(c_Set_Oinsert(A,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))))!=hAPP(c_Set_Oinsert(D,B),hAPP(c_Set_Oinsert(E,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))))|A=E|C=E.
% 187.43/187.55  ** KEPT (pick-wt=31): 267 [] hAPP(c_Set_Oinsert(A,B),hAPP(c_Set_Oinsert(C,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))))!=hAPP(c_Set_Oinsert(D,B),hAPP(c_Set_Oinsert(E,B),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))))|C=D|C=E.
% 187.43/187.55  ** KEPT (pick-wt=15): 268 [] A=c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))| -c_lesse_quals(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),tc_fun(B,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=10): 269 [] c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))!=hAPP(c_Set_Oinsert(B,A),C).
% 187.43/187.55  ** KEPT (pick-wt=12): 270 [] c_Hoare__Mirabelle_Ohoare__derivs(A,B,C)| -c_Hoare__Mirabelle_Ohoare__derivs(A,D,C)| -c_Hoare__Mirabelle_Ohoare__derivs(D,B,C).
% 187.43/187.55  ** KEPT (pick-wt=7): 271 [] -class_Orderings_Otop(A)|c_lesse_quals(B,c_Orderings_Otop__class_Otop(A),A).
% 187.43/187.55  ** KEPT (pick-wt=23): 272 [] c_lesse_quals(hAPP(c_Set_Oinsert(A,B),C),D,tc_fun(B,tc_bool))| -c_lesse_quals(C,D,tc_fun(B,tc_bool))| -hBOOL(hAPP(hAPP(c_in(B),A),D)).
% 187.43/187.55    Following clause subsumed by 132 during input processing: 0 [] -class_Finite__Set_Ofinite_Ofinite(A)|c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),A).
% 187.43/187.55  ** KEPT (pick-wt=14): 273 [] -class_Orderings_Oorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(B,D,A)| -c_lesse_quals(D,C,A).
% 187.43/187.55  ** KEPT (pick-wt=14): 274 [] -class_Orderings_Opreorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(D,C,A)| -c_lesse_quals(B,D,A).
% 187.43/187.55  ** KEPT (pick-wt=18): 275 [] c_lesse_quals(A,B,tc_fun(C,tc_bool))| -c_lesse_quals(D,B,tc_fun(C,tc_bool))| -c_lesse_quals(A,D,tc_fun(C,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=16): 276 [] c_Fun_Oinj__on(A,B,C,D)| -c_lesse_quals(B,E,tc_fun(C,tc_bool))| -c_Fun_Oinj__on(A,E,C,D).
% 187.43/187.55  ** KEPT (pick-wt=14): 277 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(C,B))| -c_lesse_quals(C,A,tc_fun(D,tc_bool)).
% 187.43/187.55  ** KEPT (pick-wt=6): 278 [] -class_Orderings_Oorder(A)|c_lesse_quals(B,B,A).
% 187.43/187.55  ** KEPT (pick-wt=6): 279 [] -class_Orderings_Opreorder(A)|c_lesse_quals(B,B,A).
% 187.43/187.55  ** KEPT (pick-wt=12): 280 [] c_Finite__Set_Ofinite(A,B)| -c_Finite__Set_Ofinite(C,B)| -c_lesse_quals(A,C,tc_fun(B,tc_bool)).
% 187.43/187.55    Following clause subsumed by 277 during input processing: 0 [] hBOOL(hAPP(A,B))| -c_lesse_quals(C,A,tc_fun(D,tc_bool))| -hBOOL(hAPP(C,B)).
% 187.43/187.56    Following clause subsumed by 280 during input processing: 0 [] c_Finite__Set_Ofinite(A,B)| -c_lesse_quals(A,C,tc_fun(B,tc_bool))| -c_Finite__Set_Ofinite(C,B).
% 187.43/187.56  ** KEPT (pick-wt=22): 281 [] hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),B,A,C),hAPP(B,D))=D| -c_Fun_Oinj__on(B,c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),A,C).
% 187.43/187.56    Following clause subsumed by 281 during input processing: 0 [] -c_Fun_Oinj__on(A,c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),B,C)|hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),A,B,C),hAPP(A,D))=D.
% 187.43/187.56  ** KEPT (pick-wt=29): 282 [] A=hAPP(c_Set_Oinsert(B,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)))|A=c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))| -c_lesse_quals(A,hAPP(c_Set_Oinsert(B,C),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))),tc_fun(C,tc_bool)).
% 187.43/187.56  ** KEPT (pick-wt=13): 283 [] c_Hoare__Mirabelle_Ohoare__derivs(A,B,C)| -c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oinsert(D,tc_Hoare__Mirabelle_Otriple(C)),B),C).
% 187.43/187.56  ** KEPT (pick-wt=26): 284 [] c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oinsert(B,tc_Hoare__Mirabelle_Otriple(C)),D),C)| -c_Hoare__Mirabelle_Ohoare__derivs(A,D,C)| -c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oinsert(B,tc_Hoare__Mirabelle_Otriple(C)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(C),tc_bool))),C).
% 187.43/187.56  ** KEPT (pick-wt=20): 285 [] c_lesse_quals(hAPP(c_Set_Oinsert(A,B),C),hAPP(c_Set_Oinsert(A,B),D),tc_fun(B,tc_bool))| -c_lesse_quals(C,D,tc_fun(B,tc_bool)).
% 187.43/187.56  ** KEPT (pick-wt=16): 286 [] c_Finite__Set_Ofinite(A,B)| -c_Fun_Oinj__on(C,A,B,D)| -c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(C,B,D),A),D).
% 187.43/187.56  ** KEPT (pick-wt=10): 287 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)|c_lesse_quals(C,B,A).
% 187.43/187.56  ** KEPT (pick-wt=25): 288 [] c_Hoare__Mirabelle_Otriple__valid(A,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),B),C),D),t_a)| -hBOOL(hAPP(hAPP(D,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(B,D,C,A)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(B,D,C,A))).
% 187.43/187.56  ** KEPT (pick-wt=26): 289 [] c_Hoare__Mirabelle_Otriple__valid(A,B,t_a)| -hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),B),C))|hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(D,A)),D))| -c_Hoare__Mirabelle_Ohoare__valids(D,C,t_a).
% 187.43/187.56  ** KEPT (pick-wt=18): 290 [] c_Hoare__Mirabelle_Ohoare__valids(A,B,t_a)|c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(A,B),C,t_a)| -hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),C),A)).
% 187.43/187.56  ** KEPT (pick-wt=22): 291 [] c_Hoare__Mirabelle_Otriple__valid(A,B,t_a)| -hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),B),C))| -c_Hoare__Mirabelle_Otriple__valid(A,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(D,A),t_a)| -c_Hoare__Mirabelle_Ohoare__valids(D,C,t_a).
% 187.43/187.56  ** KEPT (pick-wt=151): 292 [] c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),B),C,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),D,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),E),t_b)| -c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),F),C,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),G,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),E),t_b)|c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(F,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(A,B,F,D,G,C))),hAPP(C,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(A,B,F,D,G,C))),hAPP(G,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(A,B,F,D,G,C))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)| -c_Finite__Set_Ofinite(E,t_a).
% 187.43/187.56  ** KEPT (pick-wt=151): 293 [] c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),B),C,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),D,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),E),t_b)| -c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),F),C,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),G,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),E),t_b)| -c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(B,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(A,B,F,D,G,C))),hAPP(C,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(A,B,F,D,G,C))),hAPP(D,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(A,B,F,D,G,C))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)| -c_Finite__Set_Ofinite(E,t_a).
% 187.43/187.56  ** KEPT (pick-wt=54): 295 [copy,294,flip.2] hAPP(A,hAPP(B,c_List_Osko__List__Xfoldl__apply__inv__1__1(A,B,C,D)))!=c_List_Osko__List__Xfoldl__apply__inv__1__1(A,B,C,D)|hAPP(A,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(B,D,C,E),tc_fun(E,D),tc_fun(E,C),C),hAPP(c_COMBB(F,D,tc_fun(E,D),C),A)),G,H,C,E))=c_List_Ofoldl(F,hAPP(A,G),H,D,E).
% 187.43/187.56  ** KEPT (pick-wt=23): 296 [] -class_Lattices_Olattice(t_b)|hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_x)=hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)).
% 187.43/187.56  ** KEPT (pick-wt=61): 297 [] c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(B),C),hAPP(c_Com_Ocom_OBODY,D)),E),tc_Hoare__Mirabelle_Otriple(B)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(B),tc_bool))),B)| -c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(B),C),hAPP(c_Com_Ocom_OBODY,D)),E),tc_Hoare__Mirabelle_Otriple(B)),A),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(B),C),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,D))),E),tc_Hoare__Mirabelle_Otriple(B)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(B),tc_bool))),B).
% 187.43/187.56  ** KEPT (pick-wt=47): 298 [] c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(B),C),hAPP(c_Com_Ocom_OBODY,D)),E),tc_Hoare__Mirabelle_Otriple(B)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(B),tc_bool))),B)| -c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(B),C),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,D))),E),tc_Hoare__Mirabelle_Otriple(B)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(B),tc_bool))),B).
% 187.43/187.56  ** KEPT (pick-wt=21): 299 [] c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,A)),B,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(A,C,B,D),D)| -c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,A),B,C,D).
% 187.43/187.56  ** KEPT (pick-wt=22): 301 [copy,300,flip.1] hAPP(A,c_ATP__Linkup_Osko__Set__XimageE__1__1(B,C,A,D,E))=C| -hBOOL(hAPP(hAPP(c_in(E),C),hAPP(c_Set_
% 187.43/187.56  Search stopped in tp_alloc by max_mem option.
% 187.43/187.56  Oimage(A,D,E),B))).
% 187.43/187.56  ** KEPT (pick-wt=24): 302 [] hBOOL(hAPP(hAPP(c_in(A),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(B,C,D,A,E)),B))| -hBOOL(hAPP(hAPP(c_in(E),D),hAPP(c_Set_Oimage(C,A,E),B))).
% 187.43/187.56  ** KEPT (pick-wt=23): 303 [] hAPP(A,hAPP(c_Hilbert__Choice_Oinv__into(B,A,C,D),E))=E| -hBOOL(hAPP(hAPP(c_in(D),E),hAPP(c_Set_Oimage(A,C,D),B))).
% 187.43/187.56  ** KEPT (pick-wt=22): 305 [copy,304,flip.1] hAPP(A,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(B,A,C,D,E))=C| -hBOOL(hAPP(hAPP(c_in(E),C),hAPP(c_Set_Oimage(A,D,E),B))).
% 187.43/187.56  ** KEPT (pick-wt=24): 306 [] hBOOL(hAPP(hAPP(c_in(A),c_ATP__Linkup_Osko__Set__XimageE__1__1(B,C,D,A,E)),B))| -hBOOL(hAPP(hAPP(c_in(E),C),hAPP(c_Set_Oimage(D,A,E),B))).
% 187.43/187.56  ** KEPT (pick-wt=27): 307 [] hBOOL(hAPP(hAPP(c_in(A),hAPP(B,C)),D))| -hBOOL(hAPP(hAPP(c_in(E),C),F))| -c_lesse_quals(hAPP(c_Set_Oimage(B,E,A),F),D,tc_fun(A,tc_bool)).
% 187.43/187.56  ** KEPT (pick-wt=42): 308 [] hAPP(c_Hilbert__Choice_Oinv__into(A,B,C,D),E)!=hAPP(c_Hilbert__Choice_Oinv__into(A,B,C,D),F)|E=F| -hBOOL(hAPP(hAPP(c_in(D),F),hAPP(c_Set_Oimage(B,C,D),A)))| -hBOOL(hAPP(hAPP(c_in(D),E),hAPP(c_Set_Oimage(B,C,D),A))).
% 187.43/187.56  ** KEPT (pick-wt=25): 309 [] hBOOL(hAPP(hAPP(c_in(A),hAPP(c_Hilbert__Choice_Oinv__into(B,C,A,D),E)),B))| -hBOOL(hAPP(hAPP(c_in(D),E),hAPP(c_Set_Oimage(C,A,D),B))).
% 187.43/187.56  ** KEPT (pick-wt=26): 310 [] hAPP(c_Set_Oinsert(hAPP(A,B),C),hAPP(c_Set_Oimage(A,D,C),E))=hAPP(c_Set_Oimage(A,D,C),E)| -hBOOL(hAPP(hAPP(c_in(D),B),E)).
% 187.43/187.56  
% 187.43/187.56  Search stopped in tp_alloc by max_mem option.
% 187.43/187.56  
% 187.43/187.56  ============ end of search ============
% 187.43/187.56  
% 187.43/187.56  -------------- statistics -------------
% 187.43/187.56  clauses given                  0
% 187.43/187.56  clauses generated              0
% 187.43/187.56  clauses kept                 297
% 187.43/187.56  clauses forward subsumed      55
% 187.43/187.56  clauses back subsumed          0
% 187.43/187.56  Kbytes malloced            11718
% 187.43/187.56  
% 187.43/187.56  ----------- times (seconds) -----------
% 187.43/187.56  user CPU time          0.08          (0 hr, 0 min, 0 sec)
% 187.43/187.56  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 187.43/187.56  wall-clock time      187             (0 hr, 3 min, 7 sec)
% 187.43/187.56  
% 187.43/187.56  Process 6989 finished Wed Jul 27 06:02:02 2022
% 187.43/187.56  Otter interrupted
% 187.43/187.56  PROOF NOT FOUND
%------------------------------------------------------------------------------