TSTP Solution File: SCT081-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SCT081-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:12:29 EDT 2022
% Result : Unknown 269.02s 269.13s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT081-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 09:05:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 268.91/269.06 ----- Otter 3.3f, August 2004 -----
% 268.91/269.06 The process was started by sandbox2 on n024.cluster.edu,
% 268.91/269.06 Wed Jul 27 09:05:25 2022
% 268.91/269.06 The command was "./otter". The process ID is 13124.
% 268.91/269.06
% 268.91/269.06 set(prolog_style_variables).
% 268.91/269.06 set(auto).
% 268.91/269.06 dependent: set(auto1).
% 268.91/269.06 dependent: set(process_input).
% 268.91/269.06 dependent: clear(print_kept).
% 268.91/269.06 dependent: clear(print_new_demod).
% 268.91/269.06 dependent: clear(print_back_demod).
% 268.91/269.06 dependent: clear(print_back_sub).
% 268.91/269.06 dependent: set(control_memory).
% 268.91/269.06 dependent: assign(max_mem, 12000).
% 268.91/269.06 dependent: assign(pick_given_ratio, 4).
% 268.91/269.06 dependent: assign(stats_level, 1).
% 268.91/269.06 dependent: assign(max_seconds, 10800).
% 268.91/269.06 clear(print_given).
% 268.91/269.06
% 268.91/269.06 list(usable).
% 268.91/269.06 0 [] A=A.
% 268.91/269.06 0 [] -hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))).
% 268.91/269.06 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)))).
% 268.91/269.06 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)))|hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A)).
% 268.91/269.06 0 [] -hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))| -hBOOL(hAPP(hAPP(c_in(T_a),V_c),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A))).
% 268.91/269.06 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_B))| -hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)))).
% 268.91/269.06 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_c),V_A))| -hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)))).
% 268.91/269.06 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)))).
% 268.91/269.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_HOL_Ozero__class_Ozero(T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.06 0 [] -class_OrderedGroup_Oordered__ab__group__add(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_HOL_Ozero__class_Ozero(T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ozero__class_Ozero(T_a)=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_HOL_Ozero__class_Ozero(T_a)).
% 268.91/269.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ozero__class_Ozero(T_a)!=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)|c_HOL_Ozero__class_Ozero(T_a)=V_a.
% 268.91/269.06 0 [] -class_OrderedGroup_Oordered__ab__group__add(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)!=V_a|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.06 0 [] -class_Lattices_Olower__semilattice(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a)),V_x))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_x)).
% 268.91/269.06 0 [] -class_Lattices_Olower__semilattice(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a)),V_x))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_x)).
% 268.91/269.06 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))).
% 268.91/269.06 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)).
% 268.91/269.06 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b))).
% 268.91/269.06 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))).
% 268.91/269.06 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),V_a))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b)).
% 268.91/269.06 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),V_a)).
% 268.91/269.06 0 [] -hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))).
% 268.91/269.06 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)))).
% 268.91/269.06 0 [] -hBOOL(hAPP(hAPP(c_in(T_a),V_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))).
% 268.91/269.06 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Olower__semilattice__class_Oinf(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)).
% 268.91/269.06 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_c),c_Lattices_Olower__semilattice__class_Oinf(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)).
% 268.91/269.06 0 [] c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(V_F,V_G,tc_fun(T_a,tc_bool)),T_a)| -c_Finite__Set_Ofinite(V_F,T_a).
% 268.91/269.06 0 [] c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(V_F,V_G,tc_fun(T_a,tc_bool)),T_a)| -c_Finite__Set_Ofinite(V_G,T_a).
% 268.91/269.06 0 [] c_Set_Ovimage(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_b,tc_bool)),T_a,T_b)=c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(V_f,V_A,T_a,T_b),c_Set_Ovimage(V_f,V_B,T_a,T_b),tc_fun(T_a,tc_bool)).
% 268.91/269.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b))=V_b.
% 268.91/269.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|V_a=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)).
% 268.91/269.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|V_b=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)).
% 268.91/269.06 0 [] -class_Lattices_Oboolean__algebra(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x))=V_x.
% 268.91/269.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))=V_a.
% 268.91/269.06 0 [] hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A))=V_A.
% 268.91/269.06 0 [] hBOOL(hAPP(V_A,V_x))| -hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)).
% 268.91/269.06 0 [] hBOOL(hAPP(V_B,V_x))| -hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x)).
% 268.91/269.06 0 [] -class_Ring__and__Field_Oring(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b).
% 268.91/269.06 0 [] -class_Ring__and__Field_Oidom(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_b).
% 268.91/269.06 0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),V_b,T_a)=c_Divides_Odiv__class_Omod(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a)),V_b,T_a).
% 268.91/269.06 0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z))!=V_y|V_x=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_z).
% 268.91/269.06 0 [] c_Set_Ovimage(V_f,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_b,tc_bool)),V_A),T_a,T_b)=hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Set_Ovimage(V_f,V_A,T_a,T_b)).
% 268.91/269.06 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a)=c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a).
% 268.91/269.06 0 [] -class_Lattices_Olower__semilattice(T_a)|c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a)=c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a).
% 268.91/269.06 0 [] c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(V_B,V_A,tc_fun(T_a,tc_bool)).
% 268.91/269.06 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a)),V_c)=c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a).
% 268.91/269.06 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_Lattices_Olower__semilattice__class_Oinf(V_b,V_c,T_a))=c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a).
% 268.91/269.06 0 [] -class_OrderedGroup_Olordered__ab__group__add__meet(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a)),V_c)=c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a).
% 268.91/269.06 0 [] -class_OrderedGroup_Olordered__ab__group__add__meet(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_Lattices_Olower__semilattice__class_Oinf(V_b,V_c,T_a))=c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a).
% 268.91/269.06 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_Lattices_Olower__semilattice__class_Oinf(V_a,hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.06 0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Lattices_Olower__semilattice__class_Oinf(V_x,hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x),T_a)=c_Orderings_Obot__class_Obot(T_a).
% 268.91/269.06 0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x),V_x,T_a)=c_Orderings_Obot__class_Obot(T_a).
% 268.91/269.06 0 [] c_Lattices_Olower__semilattice__class_Oinf(V_A,hAPP(c_HOL_Ouminus__class_Ouminus(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)).
% 268.91/269.06 0 [] c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),V_A,tc_fun(T_a,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 268.91/269.06 0 [] c_Set_Ovimage(V_f,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_bool)),T_a,T_b)=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)).
% 268.91/269.06 0 [] c_Relation_OImage(V_R,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 268.91/269.06 0 [] -class_Lattices_Obounded__lattice(T_a)|c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Orderings_Obot__class_Obot(T_a),T_a)=c_Orderings_Obot__class_Obot(T_a).
% 268.91/269.06 0 [] -class_Lattices_Obounded__lattice(T_a)|c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(T_a),V_x,T_a)=c_Orderings_Obot__class_Obot(T_a).
% 268.91/269.06 0 [] c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 268.91/269.06 0 [] c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 268.91/269.06 0 [] c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a).
% 268.91/269.06 0 [] -class_Ring__and__Field_Oidom(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_a)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_b)|V_a=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)|V_a=V_b.
% 268.91/269.06 0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(V_a,V_b,T_a)!=c_Divides_Odiv__class_Omod(V_a_H,V_b,T_a)|c_Divides_Odiv__class_Omod(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),V_b,T_a)=c_Divides_Odiv__class_Omod(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a_H),V_b,T_a).
% 268.91/269.06 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a)=c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a).
% 268.91/269.06 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)=c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a).
% 268.91/269.06 0 [] -class_Lattices_Olower__semilattice(T_a)|c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)=c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a).
% 268.91/269.06 0 [] -class_Lattices_Olower__semilattice(T_a)|c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a)=c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a).
% 268.91/269.06 0 [] c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_C,tc_fun(T_a,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)).
% 268.91/269.06 0 [] c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_B,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(V_B,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_C,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool)).
% 268.91/269.06 0 [] -class_Lattices_Obounded__lattice(T_a)|c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,T_a)!=c_Orderings_Otop__class_Otop(T_a)|V_B=c_Orderings_Otop__class_Otop(T_a).
% 268.91/269.06 0 [] -class_Lattices_Obounded__lattice(T_a)|c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,T_a)!=c_Orderings_Otop__class_Otop(T_a)|V_A=c_Orderings_Otop__class_Otop(T_a).
% 268.91/269.06 0 [] -class_Lattices_Oboolean__algebra(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a))=c_Orderings_Obot__class_Obot(T_a).
% 268.91/269.06 0 [] hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)))=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 268.91/269.06 0 [] -hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)).
% 268.91/269.06 0 [] c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 268.91/269.06 0 [] -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_B))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))|c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool))!=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 268.91/269.06 0 [] -class_Lattices_Obounded__lattice(T_a)|c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Orderings_Otop__class_Otop(T_a),T_a)=V_x.
% 268.91/269.06 0 [] -class_Lattices_Obounded__lattice(T_a)|c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(T_a),V_x,T_a)=V_x.
% 268.91/269.06 0 [] c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_B,tc_fun(T_a,tc_bool))=V_B.
% 268.91/269.06 0 [] c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))=V_A.
% 268.91/269.06 0 [] hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_x)).
% 268.91/269.06 0 [] -class_Lattices_Oboolean__algebra(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)!=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_y)|V_x=V_y.
% 268.91/269.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)!=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)|V_a=V_b.
% 268.91/269.06 0 [] hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A)!=hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B)|V_A=V_B.
% 268.91/269.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b))=V_b.
% 268.91/269.06 0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_z)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z))=V_y.
% 268.91/269.06 0 [] -class_Ring__and__Field_Oring(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)).
% 268.91/269.06 0 [] -class_Ring__and__Field_Oring(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b).
% 268.91/269.06 0 [] c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),T_a)| -c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),T_a)| -c_Finite__Set_Ofinite(V_A,T_a).
% 268.91/269.06 0 [] c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_A),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).
% 268.91/269.06 0 [] c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_r,T_a).
% 268.91/269.06 0 [] -class_Ring__and__Field_Oring(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)).
% 268.91/269.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b))=V_b.
% 268.91/269.06 0 [] -class_Lattices_Oboolean__algebra(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a))=c_Orderings_Otop__class_Otop(T_a).
% 268.91/269.06 0 [] hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)))=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)).
% 268.91/269.06 0 [] -class_Lattices_Olattice(T_a)|c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a)=c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a).
% 268.91/269.06 0 [] -class_Lattices_Olower__semilattice(T_a)|c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a)=c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a).
% 268.91/269.06 0 [] c_Lattices_Olower__semilattice__class_Oinf(V_A,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),tc_fun(T_a,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)).
% 268.91/269.06 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).
% 268.91/269.06 0 [] -class_Lattices_Olower__semilattice(T_a)|c_Lattices_Olower__semilattice__class_Oinf(V_x,V_x,T_a)=V_x.
% 268.91/269.06 0 [] c_Lattices_Olower__semilattice__class_Oinf(V_A,V_A,tc_fun(T_a,tc_bool))=V_A.
% 268.91/269.06 0 [] hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),V_x))| -hBOOL(hAPP(V_B,V_x))| -hBOOL(hAPP(V_A,V_x)).
% 268.91/269.06 0 [] c_Set_Ovimage(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_a,T_b)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)).
% 268.91/269.06 0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)).
% 268.91/269.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)).
% 268.91/269.06 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),c_HOL_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)).
% 268.91/269.06 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),c_HOL_Ozero__class_Ozero(T_a))).
% 268.91/269.06 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))).
% 268.91/269.06 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))).
% 268.91/269.06 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))).
% 268.91/269.06 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))).
% 268.91/269.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)),V_b)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.06 0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_a)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a))=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_a)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b).
% 268.91/269.06 0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)!=c_HOL_Ozero__class_Ozero(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)=V_b.
% 268.91/269.06 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_Finite__Set_Osetsum(V_f,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_bool)),T_b,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.06 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(T_a),V_f,T_a,T_a,T_b),V_A,T_b,T_a)=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_Finite__Set_Osetsum(V_f,V_A,T_b,T_a)).
% 268.91/269.06 0 [] c_Relation_OImage(c_Relation_OId__on(V_A,T_a),V_B,T_a,T_a)=c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)).
% 268.91/269.06 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_b)|c_Finite__Set_Osetsum(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(T_b),c_COMBC(c_in(T_a),V_B,T_a,tc_fun(T_a,tc_bool),tc_bool),tc_bool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),V_f,T_a,T_b,tc_fun(T_b,T_b)),V_g,T_a,T_b,T_b),V_A,T_a,T_b)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_b),c_Finite__Set_Osetsum(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b)),c_Finite__Set_Osetsum(V_g,c_Lattices_Olower__semilattice__class_Oinf(V_A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B),tc_fun(T_a,tc_bool)),T_a,T_b))| -c_Finite__Set_Ofinite(V_A,T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ono__zero__divisors(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)!=c_HOL_Ozero__class_Ozero(T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)!=c_HOL_Ozero__class_Ozero(T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|V_x!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_a,V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a.
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x)=V_x.
% 268.91/269.07 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 268.91/269.07 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|V_x=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Ozero__class_Ozero(T_a)).
% 268.91/269.07 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))=V_a.
% 268.91/269.07 0 [] -class_OrderedGroup_Omonoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 268.91/269.07 0 [] -class_OrderedGroup_Omonoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))=V_a.
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))=V_a.
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y))),c_HOL_Ozero__class_Ozero(T_a))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y))))|V_x=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y))))|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a))))).
% 268.91/269.07 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b))).
% 268.91/269.07 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)).
% 268.91/269.07 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)).
% 268.91/269.07 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c))).
% 268.91/269.07 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)).
% 268.91/269.07 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)).
% 268.91/269.07 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),V_d))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_z,T_a,T_a)),c_Nat_Ocompow(c_Suc(V_n),V_R,tc_prod(T_a,T_a),tc_bool)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_y,V_z,T_a,T_a)),c_Nat_Ocompow(V_n,V_R,tc_prod(T_a,T_a),tc_bool)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_R)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_z,T_a,T_a)),c_Nat_Ocompow(c_Suc(V_n),V_R,tc_prod(T_a,T_a),tc_bool)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_y,V_z,T_a,T_a)),V_R))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Nat_Ocompow(V_n,V_R,tc_prod(T_a,T_a),tc_bool))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Osemiring__0(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Finite__Set_Osetsum(V_f,V_A,T_b,T_a)),V_r)=c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(T_a),V_f,T_a,tc_fun(T_a,T_a),T_b),V_r,T_b,T_a,T_a),V_A,T_b,T_a).
% 268.91/269.07 0 [] -hBOOL(hAPP(V_P,V_n))|hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))).
% 268.91/269.07 0 [] -hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))|hBOOL(hAPP(V_P,V_n)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_n),c_HOL_Ozero__class_Ozero(tc_nat)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_m)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n).
% 268.91/269.07 0 [] hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 268.91/269.07 0 [] -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat)))|hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))).
% 268.91/269.07 0 [] -hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))|hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 268.91/269.07 0 [] c_Suc(V_m)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] c_Suc(V_nat_H)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_k)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_n),V_k)|V_k=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=V_n.
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_m)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_n)|V_k=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=V_n.
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_m)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_n)|V_m=V_n|V_k=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_b)|c_Finite__Set_Osetsum(V_f,c_Lattices_Olower__semilattice__class_Oinf(V_A,V_B,tc_fun(T_a,tc_bool)),T_a,T_b)=c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(T_b),c_COMBC(c_in(T_a),V_B,T_a,tc_fun(T_a,tc_bool),tc_bool),tc_bool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),V_f,T_a,T_b,tc_fun(T_b,T_b)),c_HOL_Ozero__class_Ozero(T_b),T_a,T_b,T_b),V_A,T_a,T_b)| -c_Finite__Set_Ofinite(V_A,T_a).
% 268.91/269.07 0 [] c_Set_Ovimage(c_COMBC(c_COMBC(c_COMBB(c_HOL_OIf(T_b),c_COMBC(c_in(T_a),V_B,T_a,tc_fun(T_a,tc_bool),tc_bool),tc_bool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),V_c,T_a,T_b,tc_fun(T_b,T_b)),V_d,T_a,T_b,T_b),V_A,T_a,T_b)=hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(T_a,tc_bool)),V_B)| -hBOOL(hAPP(hAPP(c_in(T_b),V_d),V_A))|hBOOL(hAPP(hAPP(c_in(T_b),V_c),V_A)).
% 268.91/269.07 0 [] c_Set_Ovimage(c_COMBC(c_COMBC(c_COMBB(c_HOL_OIf(T_b),c_COMBC(c_in(T_a),V_B,T_a,tc_fun(T_a,tc_bool),tc_bool),tc_bool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),V_c,T_a,T_b,tc_fun(T_b,T_b)),V_d,T_a,T_b,T_b),V_A,T_a,T_b)=c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))| -hBOOL(hAPP(hAPP(c_in(T_b),V_d),V_A))| -hBOOL(hAPP(hAPP(c_in(T_b),V_c),V_A)).
% 268.91/269.07 0 [] c_Set_Ovimage(c_COMBC(c_COMBC(c_COMBB(c_HOL_OIf(T_b),c_COMBC(c_in(T_a),V_B,T_a,tc_fun(T_a,tc_bool),tc_bool),tc_bool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),V_c,T_a,T_b,tc_fun(T_b,T_b)),V_d,T_a,T_b,T_b),V_A,T_a,T_b)=c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool))|hBOOL(hAPP(hAPP(c_in(T_b),V_d),V_A))|hBOOL(hAPP(hAPP(c_in(T_b),V_c),V_A)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ono__zero__divisors(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_b)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Omult__zero(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Omult__zero(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oring__1__no__zero__divisors(T_a)|c_Power_Opower__class_Opower(V_a,V_n,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,V_n,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),V_A))| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Ovimage(V_f,V_A,T_a,T_b))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),V_B))| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Ovimage(V_f,V_B,T_a,T_b))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_b),V_a),c_Set_Ovimage(V_f,V_B,T_b,T_a)))| -hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_a)),V_B)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_b),V_a),c_Set_Ovimage(V_f,V_A,T_b,T_a)))| -hBOOL(hAPP(hAPP(c_in(T_a),hAPP(V_f,V_a)),V_A)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Set_Ovimage(V_f,V_B,T_a,T_b)))| -hBOOL(hAPP(hAPP(c_in(T_b),hAPP(V_f,V_a)),V_B)).
% 268.91/269.07 0 [] c_COMBC(c_in(T_a),V_R,T_a,tc_fun(T_a,tc_bool),tc_bool)!=c_COMBC(c_in(T_a),V_S,T_a,tc_fun(T_a,tc_bool),tc_bool)|V_R=V_S.
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_j),V_k))|V_k=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_i)),V_j),V_k,tc_nat)))|hBOOL(hAPP(V_P,V_j)).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Odiv(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=V_m.
% 268.91/269.07 0 [] hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_p))| -hBOOL(hAPP(V_P,V_i))| -hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(c_Suc(c_List_Osko__Divides__Xmod__induct__0__1__1(V_P,V_p)),V_p,tc_nat))).
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_n),c_Suc(c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat))))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_m))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_m).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c)),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b)),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_n)),V_m),V_n,tc_nat)=c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_n),tc_nat)=c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a)=c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)=c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_a),V_b),V_c,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(V_a,V_c,tc_nat)),c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(V_a,V_c,tc_nat)),c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat)),V_c,tc_nat)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)),V_k)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_k),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_n),V_k),tc_nat).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat))=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_n),tc_nat).
% 268.91/269.07 0 [] -class_Finite__Set_Ofinite_Ofinite(T_a)|c_Finite__Set_Ofinite(V_A,T_a).
% 268.91/269.07 0 [] c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 268.91/269.07 0 [] c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a)),V_c,T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(V_a,V_c,T_a)),V_b),V_c,T_a).
% 268.91/269.07 0 [] c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat))!=V_n|c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] -class_OrderedGroup_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)|V_b=V_c.
% 268.91/269.07 0 [] -class_OrderedGroup_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)|V_b=V_c.
% 268.91/269.07 0 [] -class_OrderedGroup_Ocancel__ab__semigroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)|V_b=V_c.
% 268.91/269.07 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)|V_y=V_z.
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n)|V_m=V_n.
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)|V_m=V_n.
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_y)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)|V_y=V_z.
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Suc(V_k)),V_m)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Suc(V_k)),V_n))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Suc(V_k)),V_m)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Suc(V_k)),V_n)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Osemiring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_c))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_i),V_u)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_j),V_u)),V_k))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j)),V_u)),V_k).
% 268.91/269.07 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(T_a),V_f,T_a,tc_fun(T_a,T_a),T_b),V_g,T_b,T_a,T_a),V_A,T_b,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Finite__Set_Osetsum(V_f,V_A,T_b,T_a)),c_Finite__Set_Osetsum(V_g,V_A,T_b,T_a)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Osemiring__0(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_r),c_Finite__Set_Osetsum(V_f,V_A,T_b,T_a))=c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_r),V_f,T_a,T_a,T_b),V_A,T_b,T_a).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)).
% 268.91/269.07 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 268.91/269.07 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] hAPP(V_f,hAPP(c_Nat_Ocompow(V_n,V_f,T_a,T_a),V_x))=hAPP(c_Nat_Ocompow(V_n,V_f,T_a,T_a),hAPP(V_f,V_x)).
% 268.91/269.07 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a)),V_c,T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(V_a,V_c,T_a)),V_b),V_c,T_a).
% 268.91/269.07 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)).
% 268.91/269.07 0 [] c_Relation_ODomain(c_Relation_OId__on(V_A,T_a),T_a,T_a)=V_A.
% 268.91/269.07 0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_u)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)=V_u.
% 268.91/269.07 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),T_a)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Power_Opower__class_Opower(V_a,V_m,T_a)),c_Power_Opower__class_Opower(V_a,V_n,T_a)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_d)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_b).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_d).
% 268.91/269.07 0 [] -class_OrderedGroup_Oab__semigroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)).
% 268.91/269.07 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)).
% 268.91/269.07 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_k)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)).
% 268.91/269.07 0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)),V_z).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(V_a,V_c,T_a)),c_Divides_Odiv__class_Omod(V_b,V_c,T_a)),V_c,T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_a).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_n),V_m).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_x).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),c_Power_Opower__class_Opower(V_x,V_q,T_a)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_Suc(V_n),T_a)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),c_Power_Opower__class_Opower(V_x,V_n,T_a)).
% 268.91/269.07 0 [] -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_Power_Opower__class_Opower(V_a,V_n,T_a)).
% 268.91/269.07 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a)),V_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_x,V_p,T_a),V_q,T_a)=c_Power_Opower__class_Opower(V_x,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_p),V_q),T_a).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat)=c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat))|c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat))=V_n.
% 268.91/269.07 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_d))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_d)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_c)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_x),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_x),V_d))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_x),V_d)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_x),V_c)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_x),V_y)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_x),V_z))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_x),V_z)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_x),V_y)).
% 268.91/269.07 0 [] c_Relation_Orefl__on(V_A,c_Relation_OId__on(V_A,T_a),T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(V_m,V_n,tc_nat),T_a)=c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),V_n,T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(V_a,V_c,T_a)),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),V_c,T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Suc(V_n),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n))=c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n)=c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a))),c_Divides_Odiv__class_Omod(V_a,V_b,T_a))),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)),V_b)),c_Divides_Odiv__class_Omod(V_a,V_b,T_a))),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_m)))).
% 268.91/269.07 0 [] V_x!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_a)|V_a=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=V_m|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_m).
% 268.91/269.07 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_nat_H).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] hBOOL(hAPP(V_P,V_n))| -hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 268.91/269.07 0 [] V_x=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)=V_n.
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat))=V_m.
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_n),V_m)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),V_m))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),V_n)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),V_m))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),V_n)).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_n),tc_nat)=c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_k)).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_n),V_m),V_n,tc_nat)=V_m| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n),V_n,tc_nat)=V_m| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),V_m))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),V_n)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),c_Suc(V_n)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_m)),V_n)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_j)).
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i)),V_i)).
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j)),V_i)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_k)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_n),V_k))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_m)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_n))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_i)),V_k))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_j),V_k))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_j)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),c_Suc(V_x))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_n))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_l)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_k),V_l))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_j)).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)=V_m| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)).
% 268.91/269.07 0 [] V_n=V_m| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_m)))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_m)).
% 268.91/269.07 0 [] V_m=V_n| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_m)))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_m)).
% 268.91/269.07 0 [] V_m=V_n|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),c_Suc(V_n))).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_l)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_k),V_l))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_j)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_j)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_m)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_j)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_k))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j)),V_k)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_z)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_y)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_m)),V_n))|c_Suc(V_m)=V_n| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_x))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),c_Suc(V_x))).
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_m))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(V_m)))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_x)),c_Suc(V_n)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_n)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_m)),c_Suc(V_n))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(V_m)),c_Suc(V_n)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)).
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))| -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))|V_x=V_y| -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_y,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))|hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))|V_x=V_y| -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)).
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_b,V_a,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))| -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))| -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)).
% 268.91/269.07 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_b)|c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(T_b),hAPP(c_fe_qual(T_a),V_a),tc_bool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),V_b,T_a,T_b,tc_fun(T_b,T_b)),c_HOL_Ozero__class_Ozero(T_b),T_a,T_b,T_b),V_S,T_a,T_b)=c_HOL_Ozero__class_Ozero(T_b)|hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_S))| -c_Finite__Set_Ofinite(V_S,T_a).
% 268.91/269.07 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_b)|c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(T_b),hAPP(c_fe_qual(T_a),V_a),tc_bool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),V_b,T_a,T_b,tc_fun(T_b,T_b)),c_HOL_Ozero__class_Ozero(T_b),T_a,T_b,T_b),V_S,T_a,T_b)=hAPP(V_b,V_a)| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_S))| -c_Finite__Set_Ofinite(V_S,T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_c))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),c_HOL_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_c))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),c_HOL_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_c))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)),c_HOL_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)),c_HOL_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),c_HOL_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_a)),c_HOL_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),c_HOL_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)).
% 268.91/269.07 0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_Power_Opower__class_Opower(V_a,V_n,T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),c_HOL_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_a))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a)),c_HOL_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a)),c_HOL_Ozero__class_Ozero(T_a))).
% 268.91/269.07 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a)),c_HOL_Ozero__class_Ozero(T_a))).
% 268.91/269.07 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a)),c_HOL_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))).
% 268.91/269.07 0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),c_HOL_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),c_HOL_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_a)),c_HOL_Ozero__class_Ozero(T_a))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_HOL_Ozero__class_Ozero(T_a))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),c_HOL_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_c))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),c_HOL_Ozero__class_Ozero(T_a)))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_c))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),c_HOL_Ozero__class_Ozero(T_a))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),c_HOL_Ozero__class_Ozero(T_a))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_c)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_c)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),c_HOL_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_c))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_c)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),c_HOL_Ozero__class_Ozero(T_a))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),c_HOL_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_c))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_c)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_c),c_HOL_Ozero__class_Ozero(T_a))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__comm__semiring__strict(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_c))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)).
% 268.91/269.07 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a))).
% 268.91/269.07 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a)=c_HOL_Ozero__class_Ozero(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a)=c_HOL_Ozero__class_Ozero(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a)!=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] V_x=V_y| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Relation_OId__on(V_A,T_a))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)).
% 268.91/269.07 0 [] hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_p))| -hBOOL(hAPP(V_P,V_i))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_List_Osko__Divides__Xmod__induct__0__1__1(V_P,V_p)),V_p)).
% 268.91/269.07 0 [] V_n=c_HOL_Ozero__class_Ozero(tc_nat)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_x))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Power_Opower__class_Opower(V_x,V_n,tc_nat))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Power_Opower__class_Opower(V_x,V_n,tc_nat)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_x)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_m)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_i)))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_x)))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a).
% 268.91/269.07 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_x).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 268.91/269.07 0 [] -class_Nat_Osemiring__char__0(T_a)|c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)!=c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)|V_m=V_n.
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(V_a,V_c,T_a)),c_Divides_Odiv__class_Omod(V_b,V_c,T_a)),V_c,T_a).
% 268.91/269.07 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a)),V_a)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_Power_Opower__class_Opower(V_a,V_n,T_a)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Power_Opower__class_Opower(V_x,V_p,T_a)),c_Power_Opower__class_Opower(V_x,V_q,T_a))=c_Power_Opower__class_Opower(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_p),V_q),T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c)),V_b,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a))|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b)),V_b,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a))|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] c_Suc(V_x)!=c_Suc(V_y)|V_x=V_y.
% 268.91/269.07 0 [] c_Suc(V_nat)!=c_Suc(V_nat_H)|V_nat=V_nat_H.
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_b,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)|c_Divides_Odiv__class_Omod(V_a,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c,T_a).
% 268.91/269.07 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 268.91/269.07 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),c_Suc(V_n))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Suc(V_m)),V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)).
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_j),V_k))|V_k=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_i)),V_j),V_k,tc_nat)))|hBOOL(hAPP(V_P,V_i)).
% 268.91/269.07 0 [] c_Relation_ORange(c_Relation_OId__on(V_A,T_a),T_a,T_a)=V_A.
% 268.91/269.07 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n),T_a)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Omod(c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_n)),V_m)),V_n,tc_nat)=c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_w),V_y)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_w),V_z)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y))|V_y=V_z|V_w=V_x.
% 268.91/269.07 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_d))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_d)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c))|V_c=V_d|V_a=V_b.
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_b),V_d))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_a),V_d)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_b),V_c))|V_c=V_d|V_a=V_b.
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_w),V_y)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_x),V_z))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_w),V_z)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_x),V_y))|V_y=V_z|V_w=V_x.
% 268.91/269.07 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_Finite__Set_Osetsum(V_f,V_A,T_b,T_a)=c_HOL_Ozero__class_Ozero(T_a)|c_Finite__Set_Ofinite(V_A,T_b).
% 268.91/269.07 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_b)|c_Finite__Set_Osetsum(V_f,V_A,T_a,T_b)=c_HOL_Ozero__class_Ozero(T_b)|c_Finite__Set_Ofinite(V_A,T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),V_b,T_a)=V_a|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_a),V_b,T_a)=V_a|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_b,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)|c_Divides_Odiv__class_Omod(V_a,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c,T_a).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_ly),V_ry)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Omod(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] c_Relation_Orefl__on(V_A,V_r,T_a)| -c_Equiv__Relations_Oe_quiv(V_A,V_r,T_a).
% 268.91/269.07 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_a),V_b),V_c,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_a),c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_a),c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat)),V_c,tc_nat)).
% 268.91/269.07 0 [] -class_OrderedGroup_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_n),V_xa))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_n),V_xb))|c_Divides_Odiv__class_Omod(V_x,V_n,tc_nat)=c_Divides_Odiv__class_Omod(V_y,V_n,tc_nat).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_b),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_m),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),c_Power_Opower__class_Opower(V_x,V_q,T_a))=c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a)),V_x)=c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Omod(V_a,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_b),V_c),tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_b),c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat))),c_Divides_Odiv__class_Omod(V_a,V_b,tc_nat)).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Odiv(V_a,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_b),V_c),tc_nat)=c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_b),c_Divides_Odiv__class_Omod(V_q,V_c,tc_nat))),V_r)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_b),V_c)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_r),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_c)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_r),V_c))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_r),V_d))|V_c=V_d|V_r=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_r),V_c))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_r),V_d))|V_c=V_d|V_r=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y))!=c_HOL_Ozero__class_Ozero(T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y))!=c_HOL_Ozero__class_Ozero(T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] c_Power_Opower__class_Opower(V_x,V_m,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_x=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] c_Suc(V_n)!=V_n.
% 268.91/269.07 0 [] V_n!=c_Suc(V_n).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat)=c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)),V_n,tc_nat).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x)),c_Arrow__Order__Mirabelle_OLin))| -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x)),c_Arrow__Order__Mirabelle_OLin))| -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),V_L),c_Arrow__Order__Mirabelle_OLin)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b)),c_Arrow__Order__Mirabelle_OLin))|V_a=V_b.
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 268.91/269.07 0 [] -class_OrderedGroup_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)=V_x.
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_d),V_x),V_d,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)),V_b))=V_a.
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a)))=c_HOL_Ozero__class_Ozero(T_a).
% 268.91/269.07 0 [] hBOOL(hAPP(V_A,hAPP(V_f,V_x)))| -hBOOL(hAPP(c_Set_Ovimage(V_f,V_A,T_a,T_b),V_x)).
% 268.91/269.07 0 [] hBOOL(hAPP(c_Set_Ovimage(V_f,V_A,T_a,T_b),V_x))| -hBOOL(hAPP(V_A,hAPP(V_f,V_x))).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Suc(V_k)),V_m)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Suc(V_k)),V_n)|V_m=V_n.
% 268.91/269.07 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)).
% 268.91/269.07 0 [] -class_OrderedGroup_Ocomm__monoid__mult(T_a)|c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),V_n,T_a)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a)),c_Power_Opower__class_Opower(V_b,V_n,T_a)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y),V_q,T_a)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a)),c_Power_Opower__class_Opower(V_y,V_q,T_a)).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(V_a,V_c,T_a)),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a)),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n),T_a)=c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a))),c_Divides_Odiv__class_Omod(V_a,V_b,T_a))=V_a.
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)),V_b)),c_Divides_Odiv__class_Omod(V_a,V_b,T_a))=V_a.
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|V_a=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)),V_b)),c_Divides_Odiv__class_Omod(V_a,V_b,T_a)).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a)),V_c).
% 268.91/269.07 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(V_a,V_b,T_a)).
% 268.91/269.07 0 [] -class_OrderedGroup_Oab__semigroup__mult(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_ly),V_rx)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ry)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)),V_k)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_n),V_k)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_z))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)),V_z).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_k)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_k)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_n),V_k)).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_m)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_n)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z)).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)).
% 268.91/269.07 0 [] hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_p))| -hBOOL(hAPP(V_P,V_i))|hBOOL(hAPP(V_P,c_List_Osko__Divides__Xmod__induct__0__1__1(V_P,V_p))).
% 268.91/269.07 0 [] hBOOL(hAPP(V_P,V_n))|hBOOL(hAPP(V_P,V_x))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 268.91/269.07 0 [] V_n=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_m))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)).
% 268.91/269.07 0 [] hBOOL(hAPP(V_P,V_n))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 268.91/269.07 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_m)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_n)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_k))|V_m=V_n.
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_k))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_k)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_n),V_k))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_k))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_m)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_n))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(V_n))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(V_x))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_m))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n))).
% 268.91/269.07 0 [] c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_k)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_n),V_k)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_k)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_m)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_n)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_k)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_i)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_j)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_k))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_j)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_i),V_k)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_j),V_k)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_k))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_i),V_j)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_m)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_n)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_k)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_m)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),V_n)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_k)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(V_i,V_m,tc_nat)),c_Power_Opower__class_Opower(V_i,V_n,tc_nat)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_i)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_m)).
% 268.91/269.07 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_b)|c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(T_b),c_COMBC(c_fe_qual(T_a),V_a,T_a,T_a,tc_bool),tc_bool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),V_b,T_a,T_b,tc_fun(T_b,T_b)),c_HOL_Ozero__class_Ozero(T_b),T_a,T_b,T_b),V_S,T_a,T_b)=hAPP(V_b,V_a)| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_S))| -c_Finite__Set_Ofinite(V_S,T_a).
% 268.91/269.07 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_b)|c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(T_b),c_COMBC(c_fe_qual(T_a),V_a,T_a,T_a,tc_bool),tc_bool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),V_b,T_a,T_b,tc_fun(T_b,T_b)),c_HOL_Ozero__class_Ozero(T_b),T_a,T_b,T_b),V_S,T_a,T_b)=c_HOL_Ozero__class_Ozero(T_b)|hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_S))| -c_Finite__Set_Ofinite(V_S,T_a).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_z)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))|V_x=V_y|V_x=V_z.
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_z)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))|V_y=V_z|V_x=V_z.
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x))).
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))|V_y=V_z| -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_z))).
% 268.91/269.07 0 [] V_x=V_y|V_y=V_x|hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x))).
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x))).
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_x))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_z)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))|V_x=V_y|V_y=V_z.
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_z)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))|V_x=V_z|V_y=V_z.
% 268.91/269.07 0 [] V_xa=V_x|V_xa=V_x|hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_xa,V_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(V_L,V_x))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),V_L))|V_x=V_z| -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_x,V_y,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(V_L,V_z))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(V_a,V_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(V_a,V_b)))|V_a=V_b.
% 268.91/269.07 0 [] c_Set_Ovimage(c_COMBC(c_COMBC(c_COMBB(c_HOL_OIf(T_b),c_COMBC(c_in(T_a),V_B,T_a,tc_fun(T_a,tc_bool),tc_bool),tc_bool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),V_c,T_a,T_b,tc_fun(T_b,T_b)),V_d,T_a,T_b,T_b),V_A,T_a,T_b)=V_B|hBOOL(hAPP(hAPP(c_in(T_b),V_d),V_A))| -hBOOL(hAPP(hAPP(c_in(T_b),V_c),V_A)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),c_Product__Type_OSigma(V_A,V_B,T_a,T_b)))| -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)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),c_Product__Type_OSigma(V_A,V_B,T_a,T_b)))| -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)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Wellfounded_Oacc(V_r,T_a)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_b,T_a,T_a)),V_r))| -hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Wellfounded_Oacc(V_r,T_a))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_y),c_Wellfounded_Oacc(V_r,T_a)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_y,V_a,T_a,T_a)),V_r))| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Wellfounded_Oacc(V_r,T_a))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_b),V_b),c_Relation_OImage(V_r,V_A,T_a,T_b)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),V_r))| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_b),c_Relation_OImage(V_r,V_A,T_b,T_a)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_b,T_a)),c_Pair(V_x,V_b,T_b,T_a)),V_r))| -hBOOL(hAPP(hAPP(c_in(T_b),V_x),V_A)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Relation_OId__on(V_A,T_a))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_x,T_a,T_a)),c_Relation_OId__on(V_A,T_a)))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))| -c_Equiv__Relations_Oe_quiv(V_A,V_r,T_a).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))| -c_Equiv__Relations_Oe_quiv(V_A,V_r,T_a).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Relation_ORange(V_r,T_b,T_a)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_b,T_a)),c_Pair(V_x,V_a,T_b,T_a)),V_r)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_b),V_b),c_Relation_ORange(V_r,T_a,T_b)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),V_r)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Relation_ODomain(V_r,T_a,T_b)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_x,T_a,T_b)),V_r)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_a),c_Relation_ODomain(V_r,T_a,T_b)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),V_r)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_b),V_b),hAPP(V_B,V_a)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),c_Product__Type_OSigma(V_A,V_B,T_a,T_b))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_b)),c_Pair(V_a,V_b,T_a,T_b)),c_Product__Type_OSigma(V_A,V_B,T_a,T_b))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_xa,V_x,T_a,T_a)),V_r))|hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_xa,T_a,T_a)),V_r))|V_x=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_Relation_Ototal__on(V_A,V_r,T_a).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_x,T_a,T_a)),V_r))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -c_Relation_Orefl__on(V_A,V_r,T_a).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_y),V_A))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))| -c_Relation_Orefl__on(V_A,V_r,T_a).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_A))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),V_r))| -c_Relation_Orefl__on(V_A,V_r,T_a).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_a,V_a,T_a,T_a)),V_r))| -hBOOL(hAPP(hAPP(c_in(T_a),V_a),V_A))| -c_Relation_Orefl__on(V_A,V_r,T_a).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_x,T_a,T_a)),c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),V_R,tc_prod(T_a,T_a),tc_bool))).
% 268.91/269.07 0 [] V_x=V_y| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),V_R,tc_prod(T_a,T_a),tc_bool))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Wellfounded_Omlex__prod(V_f,V_R,T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(V_f,V_x)),hAPP(V_f,V_y))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Wellfounded_Omeasure(V_f,T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(V_f,V_x)),hAPP(V_f,V_y))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(V_f,V_x)),hAPP(V_f,V_y)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(T_a,T_a)),c_Pair(V_x,V_y,T_a,T_a)),c_Wellfounded_Omeasure(V_f,T_a))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a))).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBC(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),V_n,tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),v_Lab____,tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lba____,tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OProf)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBC(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),V_n,tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),v_Lab____,tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lba____,tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),c_Arrow__Order__Mirabelle_OLin)).
% 268.91/269.07 0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b)).
% 268.91/269.07 0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)).
% 268.91/269.07 0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)).
% 268.91/269.07 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_a),V_b))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_b),V_a)).
% 268.91/269.07 0 [] c_Pair(V_a,V_b,T_a,T_b)!=c_Pair(V_a_H,V_b_H,T_a,T_b)|V_b=V_b_H.
% 268.91/269.07 0 [] c_Pair(V_a,V_b,T_a,T_b)!=c_Pair(V_a_H,V_b_H,T_a,T_b)|V_a=V_a_H.
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n))|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 268.91/269.07 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)).
% 268.91/269.07 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))|V_x=V_y|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)).
% 268.91/269.07 0 [] -class_Orderings_Olinorder(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))|V_x=V_y.
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_y),V_x))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_y))|V_x=V_y.
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(V_P,V_n),V_m))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_m))|V_m=V_n|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_m))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),V_n))|V_m=V_n.
% 268.91/269.07 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)).
% 268.91/269.07 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y))|V_x=V_y.
% 268.91/269.07 0 [] -class_Orderings_Opreorder(T_a)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x)).
% 268.91/269.07 0 [] -class_Orderings_Olinorder(T_a)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x)).
% 268.91/269.07 0 [] -class_Orderings_Oorder(T_a)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_x)).
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),V_n)).
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_x),V_x)).
% 268.91/269.07 0 [] -class_Orderings_Opreorder(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_z))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_z))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_x),V_y)).
% 268.91/269.07 0 [] -class_Orderings_Oorder(T_a)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_x))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_z),V_y))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(T_a),V_y),V_x)).
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat))).
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),V_n),c_HOL_Ozero__class_Ozero(tc_nat))).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_S))| -hBOOL(hAPP(V_S,V_x)).
% 268.91/269.07 0 [] hBOOL(hAPP(V_S,V_x))| -hBOOL(hAPP(hAPP(c_in(T_a),V_x),V_S)).
% 268.91/269.07 0 [] hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R)=hAPP(V_P,hAPP(V_Q,V_R)).
% 268.91/269.07 0 [] hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 268.91/269.07 0 [] v_a____!=v_b____.
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)).
% 268.91/269.07 0 [] -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_Lba____)).
% 268.91/269.07 0 [] c_Arrow__Order__Mirabelle_Ounanimity(v_F).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,c_COMBC(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),c_HOL_Ozero__class_Ozero(tc_nat),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),v_Lab____,tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lba____,tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))).
% 268.91/269.07 0 [] class_Finite__Set_Ofinite_Ofinite(tc_prod(T_2,T_1))| -class_Finite__Set_Ofinite_Ofinite(T_1)| -class_Finite__Set_Ofinite_Ofinite(T_2).
% 268.91/269.07 0 [] class_Lattices_Olower__semilattice(tc_fun(T_2,T_1))| -class_Lattices_Olattice(T_1).
% 268.91/269.07 0 [] class_Lattices_Obounded__lattice(tc_fun(T_2,T_1))| -class_Lattices_Obounded__lattice(T_1).
% 268.91/269.07 0 [] class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))| -class_Lattices_Oboolean__algebra(T_1).
% 268.91/269.07 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).
% 268.91/269.07 0 [] class_Orderings_Opreorder(tc_fun(T_2,T_1))| -class_Orderings_Opreorder(T_1).
% 268.91/269.07 0 [] class_Lattices_Olattice(tc_fun(T_2,T_1))| -class_Lattices_Olattice(T_1).
% 268.91/269.07 0 [] class_Orderings_Oorder(tc_fun(T_2,T_1))| -class_Orderings_Oorder(T_1).
% 268.91/269.07 0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 268.91/269.07 0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 268.91/269.07 0 [] class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat).
% 268.91/269.07 0 [] class_Ring__and__Field_Oordered__semiring__strict(tc_nat).
% 268.91/269.07 0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 268.91/269.07 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 268.91/269.07 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 268.91/269.07 0 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 268.91/269.07 0 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 268.91/269.07 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 268.91/269.07 0 [] class_OrderedGroup_Oab__semigroup__mult(tc_nat).
% 268.91/269.07 0 [] class_OrderedGroup_Ocomm__monoid__mult(tc_nat).
% 268.91/269.07 0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 268.91/269.07 0 [] class_Ring__and__Field_Ocomm__semiring(tc_nat).
% 268.91/269.07 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 268.91/269.07 0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 268.91/269.07 0 [] class_Lattices_Olower__semilattice(tc_nat).
% 268.91/269.07 0 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 268.91/269.07 0 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 268.91/269.07 0 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 268.91/269.07 0 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 268.91/269.07 0 [] class_Ring__and__Field_Osemiring(tc_nat).
% 268.91/269.07 0 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 268.91/269.07 0 [] class_Divides_Osemiring__div(tc_nat).
% 268.91/269.07 0 [] class_Nat_Osemiring__char__0(tc_nat).
% 268.91/269.07 0 [] class_Orderings_Opreorder(tc_nat).
% 268.91/269.07 0 [] class_Orderings_Olinorder(tc_nat).
% 268.91/269.07 0 [] class_Lattices_Olattice(tc_nat).
% 268.91/269.07 0 [] class_Orderings_Oorder(tc_nat).
% 268.91/269.07 0 [] class_Power_Opower(tc_nat).
% 268.91/269.07 0 [] class_Lattices_Olower__semilattice(tc_bool).
% 268.91/269.07 0 [] class_Lattices_Obounded__lattice(tc_bool).
% 268.91/269.07 0 [] class_Lattices_Oboolean__algebra(tc_bool).
% 268.91/269.07 0 [] class_Finite__Set_Ofinite_Ofinite(tc_bool).
% 268.91/269.07 0 [] class_Orderings_Opreorder(tc_bool).
% 268.91/269.07 0 [] class_Lattices_Olattice(tc_bool).
% 268.91/269.07 0 [] class_Orderings_Oorder(tc_bool).
% 268.91/269.07 0 [] hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 268.91/269.07 0 [] hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R)=hAPP(V_P,hAPP(V_Q,V_R)).
% 268.91/269.07 0 [] hBOOL(hAPP(hAPP(c_fe_qual(T_a),V_x),V_x)).
% 268.91/269.07 0 [] V_X=V_Y| -hBOOL(hAPP(hAPP(c_fe_qual(T_a),V_X),V_Y)).
% 268.91/269.07 end_of_list.
% 268.91/269.07
% 268.91/269.07 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 268.91/269.07
% 268.91/269.07 This ia a non-Horn set with equality. The strategy will be
% 268.91/269.07 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 268.91/269.07 deletion, with positive clauses in sos and nonpositive
% 268.91/269.07 clauses in usable.
% 268.91/269.07
% 268.91/269.07 dependent: set(knuth_bendix).
% 268.91/269.07 dependent: set(anl_eq).
% 268.91/269.07 dependent: set(para_from).
% 268.91/269.07 dependent: set(para_into).
% 268.91/269.07 dependent: clear(para_from_right).
% 268.91/269.07 dependent: clear(para_into_right).
% 268.91/269.07 dependent: set(para_from_vars).
% 268.91/269.07 dependent: set(eq_units_both_ways).
% 268.91/269.07 dependent: set(dynamic_demod_all).
% 268.91/269.07 dependent: set(dynamic_demod).
% 268.91/269.07 dependent: set(order_eq).
% 268.91/269.07 dependent: set(back_demod).
% 268.91/269.07 dependent: set(lrpo).
% 268.91/269.07 dependent: set(hyper_res).
% 268.91/269.07 dependent: set(unit_deletion).
% 268.91/269.07 dependent: set(factor).
% 268.91/269.07
% 268.91/269.07 ------------> process usable:
% 268.91/269.07 ** KEPT (pick-wt=10): 1 [] -hBOOL(hAPP(hAPP(c_in(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)))).
% 268.91/269.07 ** KEPT (pick-wt=19): 2 [] -hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(hAPP(c_in(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),C))).
% 268.91/269.07 ** KEPT (pick-wt=19): 3 [] hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(hAPP(c_in(A),B),c_Lattices_Olower__semilattice__class_Oinf(D,C,tc_fun(A,tc_bool)))).
% 268.91/269.07 ** KEPT (pick-wt=19): 4 [] hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(hAPP(c_in(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(A,tc_bool)))).
% 268.91/269.07 Following clause subsumed by 1 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)))).
% 268.91/269.07 ** KEPT (pick-wt=10): 5 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 268.91/269.07 ** KEPT (pick-wt=10): 6 [] -class_OrderedGroup_Oordered__ab__group__add(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 268.91/269.07 Following clause subsumed by 5 during input processing: 0 [flip.2] -class_OrderedGroup_Ogroup__add(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 268.91/269.07 ** KEPT (pick-wt=13): 7 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),B)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 268.91/269.07 ** KEPT (pick-wt=13): 8 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ozero__class_Ozero(A)!=hAPP(c_HOL_Ouminus__class_Ouminus(A),B)|c_HOL_Ozero__class_Ozero(A)=B.
% 268.91/269.07 ** KEPT (pick-wt=12): 9 [] -class_OrderedGroup_Oordered__ab__group__add(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),B)!=B|B=c_HOL_Ozero__class_Ozero(A).
% 268.91/269.07 ** KEPT (pick-wt=19): 10 [] -class_Lattices_Olower__semilattice(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)).
% 268.91/269.07 ** KEPT (pick-wt=19): 11 [] -class_Lattices_Olower__semilattice(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)).
% 268.91/269.07 ** KEPT (pick-wt=22): 12 [] -class_OrderedGroup_Opordered__ab__group__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))).
% 268.91/269.07 ** KEPT (pick-wt=22): 13 [] -class_OrderedGroup_Opordered__ab__group__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)).
% 268.91/269.08 ** KEPT (pick-wt=22): 14 [] -class_OrderedGroup_Opordered__ab__group__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))).
% 268.91/269.08 Following clause subsumed by 14 during input processing: 0 [] -class_OrderedGroup_Opordered__ab__group__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))).
% 268.91/269.08 ** KEPT (pick-wt=22): 15 [] -class_OrderedGroup_Opordered__ab__group__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)),B)).
% 268.91/269.08 Following clause subsumed by 15 during input processing: 0 [] -class_OrderedGroup_Opordered__ab__group__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)),B)).
% 268.91/269.08 Following clause subsumed by 1 during input processing: 0 [] -hBOOL(hAPP(hAPP(c_in(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)))).
% 268.91/269.08 Following clause subsumed by 1 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)))).
% 268.91/269.08 Following clause subsumed by 1 during input processing: 0 [] -hBOOL(hAPP(hAPP(c_in(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)))).
% 268.91/269.08 ** KEPT (pick-wt=26): 16 [] hBOOL(hAPP(hAPP(c_in(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(A,tc_bool))))| -hBOOL(hAPP(hAPP(c_in(A),B),D))| -hBOOL(hAPP(hAPP(c_in(A),B),C)).
% 268.91/269.08 Following clause subsumed by 16 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(A,tc_bool))))| -hBOOL(hAPP(hAPP(c_in(A),B),D))| -hBOOL(hAPP(hAPP(c_in(A),B),C)).
% 268.91/269.08 ** KEPT (pick-wt=11): 17 [] c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)),C)| -c_Finite__Set_Ofinite(A,C).
% 268.91/269.08 ** KEPT (pick-wt=11): 18 [] c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)),C)| -c_Finite__Set_Ofinite(B,C).
% 268.91/269.08 ** KEPT (pick-wt=11): 19 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))=B.
% 268.91/269.08 Following clause subsumed by 19 during input processing: 0 [flip.2] -class_OrderedGroup_Ogroup__add(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))=B.
% 268.91/269.08 Following clause subsumed by 19 during input processing: 0 [flip.2] -class_OrderedGroup_Ogroup__add(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))=B.
% 268.91/269.08 ** KEPT (pick-wt=11): 20 [] -class_Lattices_Oboolean__algebra(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))=B.
% 268.91/269.08 Following clause subsumed by 19 during input processing: 0 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))=B.
% 268.91/269.08 ** KEPT (pick-wt=13): 21 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_fun(D,tc_bool)),B)).
% 268.91/269.08 ** KEPT (pick-wt=13): 22 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A,tc_fun(D,tc_bool)),B)).
% 268.91/269.08 ** KEPT (pick-wt=21): 23 [] -class_Ring__and__Field_Oring(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C).
% 268.91/269.08 ** KEPT (pick-wt=21): 24 [] -class_Ring__and__Field_Oidom(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B).
% 268.91/269.08 ** KEPT (pick-wt=20): 26 [copy,25,flip.2] -class_Divides_Oring__div(A)|c_Divides_Odiv__class_Omod(hAPP(c_HOL_Ouminus__class_Ouminus(A),c_Divides_Odiv__class_Omod(B,C,A)),C,A)=c_Divides_Odiv__class_Omod(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A).
% 268.91/269.08 ** KEPT (pick-wt=21): 27 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))!=C|B=hAPP(c_HOL_Ouminus__class_Ouminus(A),D).
% 268.91/269.08 ** KEPT (pick-wt=11): 28 [] -class_Lattices_Olattice(A)|c_Lattices_Olower__semilattice__class_Oinf(B,C,A)=c_Lattices_Olower__semilattice__class_Oinf(C,B,A).
% 268.91/269.08 ** KEPT (pick-wt=11): 29 [] -class_Lattices_Olower__semilattice(A)|c_Lattices_Olower__semilattice__class_Oinf(B,C,A)=c_Lattices_Olower__semilattice__class_Oinf(C,B,A).
% 268.91/269.08 ** KEPT (pick-wt=26): 30 [] -class_OrderedGroup_Olordered__ab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D)=c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A).
% 268.91/269.08 ** KEPT (pick-wt=26): 31 [] -class_OrderedGroup_Olordered__ab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))=c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A).
% 268.91/269.08 ** KEPT (pick-wt=26): 32 [] -class_OrderedGroup_Olordered__ab__group__add__meet(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D)=c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A).
% 268.91/269.08 ** KEPT (pick-wt=26): 33 [] -class_OrderedGroup_Olordered__ab__group__add__meet(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))=c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A).
% 268.91/269.08 ** KEPT (pick-wt=16): 34 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_Lattices_Olower__semilattice__class_Oinf(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 268.91/269.08 ** KEPT (pick-wt=12): 35 [] -class_Lattices_Oboolean__algebra(A)|c_Lattices_Olower__semilattice__class_Oinf(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A)=c_Orderings_Obot__class_Obot(A).
% 268.91/269.08 ** KEPT (pick-wt=12): 36 [] -class_Lattices_Oboolean__algebra(A)|c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),B,A)=c_Orderings_Obot__class_Obot(A).
% 268.91/269.08 ** KEPT (pick-wt=10): 37 [] -class_Lattices_Obounded__lattice(A)|c_Lattices_Olower__semilattice__class_Oinf(B,c_Orderings_Obot__class_Obot(A),A)=c_Orderings_Obot__class_Obot(A).
% 268.91/269.08 ** KEPT (pick-wt=10): 38 [] -class_Lattices_Obounded__lattice(A)|c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(A),B,A)=c_Orderings_Obot__class_Obot(A).
% 268.91/269.08 ** KEPT (pick-wt=24): 39 [] -class_Ring__and__Field_Oidom(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)|B=hAPP(c_HOL_Ouminus__class_Ouminus(A),C)|B=C.
% 268.91/269.08 ** KEPT (pick-wt=26): 40 [] -class_Divides_Oring__div(A)|c_Divides_Odiv__class_Omod(B,C,A)!=c_Divides_Odiv__class_Omod(D,C,A)|c_Divides_Odiv__class_Omod(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A)=c_Divides_Odiv__class_Omod(hAPP(c_HOL_Ouminus__class_Ouminus(A),D),C,A).
% 268.91/269.08 ** KEPT (pick-wt=17): 41 [] -class_Lattices_Olattice(A)|c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A)=c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A).
% 268.91/269.08 ** KEPT (pick-wt=17): 42 [] -class_Lattices_Olattice(A)|c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A)=c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A).
% 268.91/269.08 ** KEPT (pick-wt=17): 43 [] -class_Lattices_Olower__semilattice(A)|c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A)=c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A).
% 268.91/269.08 ** KEPT (pick-wt=17): 44 [] -class_Lattices_Olower__semilattice(A)|c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A)=c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A).
% 268.91/269.08 ** KEPT (pick-wt=13): 45 [] -class_Lattices_Obounded__lattice(A)|c_Lattices_Olower__semilattice__class_Oinf(B,C,A)!=c_Orderings_Otop__class_Otop(A)|C=c_Orderings_Otop__class_Otop(A).
% 268.91/269.08 ** KEPT (pick-wt=13): 46 [] -class_Lattices_Obounded__lattice(A)|c_Lattices_Olower__semilattice__class_Oinf(B,C,A)!=c_Orderings_Otop__class_Otop(A)|B=c_Orderings_Otop__class_Otop(A).
% 268.91/269.08 ** KEPT (pick-wt=10): 47 [] -class_Lattices_Oboolean__algebra(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),c_Orderings_Otop__class_Otop(A))=c_Orderings_Obot__class_Obot(A).
% 268.91/269.08 ** KEPT (pick-wt=7): 48 [] -hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B)).
% 268.91/269.08 ** KEPT (pick-wt=9): 49 [] c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool))!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)).
% 268.91/269.08 ** KEPT (pick-wt=25): 50 [] -hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(hAPP(c_in(A),B),D))|c_Lattices_Olower__semilattice__class_Oinf(D,C,tc_fun(A,tc_bool))!=c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)).
% 268.91/269.08 ** KEPT (pick-wt=9): 51 [] -class_Lattices_Obounded__lattice(A)|c_Lattices_Olower__semilattice__class_Oinf(B,c_Orderings_Otop__class_Otop(A),A)=B.
% 268.91/269.08 ** KEPT (pick-wt=9): 52 [] -class_Lattices_Obounded__lattice(A)|c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(A),B,A)=B.
% 268.91/269.08 ** KEPT (pick-wt=14): 53 [] -class_Lattices_Oboolean__algebra(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),B)!=hAPP(c_HOL_Ouminus__class_Ouminus(A),C)|B=C.
% 268.91/269.08 ** KEPT (pick-wt=14): 54 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),B)!=hAPP(c_HOL_Ouminus__class_Ouminus(A),C)|B=C.
% 268.91/269.08 ** KEPT (pick-wt=16): 55 [] hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),B)!=hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),C)|B=C.
% 268.91/269.08 ** KEPT (pick-wt=18): 56 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))=C.
% 268.91/269.08 ** KEPT (pick-wt=18): 57 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B))=C.
% 268.91/269.08 ** KEPT (pick-wt=21): 58 [] -class_Ring__and__Field_Oring(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)).
% 268.91/269.08 ** KEPT (pick-wt=21): 60 [copy,59,flip.2] -class_Ring__and__Field_Oring(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C)=hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)).
% 268.91/269.08 ** KEPT (pick-wt=17): 61 [] c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),A)| -c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),B),A)| -c_Finite__Set_Ofinite(B,A).
% 269.02/269.08 ** KEPT (pick-wt=17): 62 [] c_Finite__Set_Ofinite(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),B),A)| -c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),A)| -c_Finite__Set_Ofinite(B,A).
% 269.02/269.08 ** KEPT (pick-wt=21): 63 [] -class_Ring__and__Field_Oring(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)).
% 269.02/269.08 ** KEPT (pick-wt=18): 64 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C))=C.
% 269.02/269.08 ** KEPT (pick-wt=10): 66 [copy,65,flip.2] -class_Lattices_Oboolean__algebra(A)|c_Orderings_Otop__class_Otop(A)=hAPP(c_HOL_Ouminus__class_Ouminus(A),c_Orderings_Obot__class_Obot(A)).
% 269.02/269.08 ** KEPT (pick-wt=14): 67 [] -class_Lattices_Olattice(A)|c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A)=c_Lattices_Olower__semilattice__class_Oinf(B,C,A).
% 269.02/269.08 ** KEPT (pick-wt=14): 68 [] -class_Lattices_Olower__semilattice(A)|c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A)=c_Lattices_Olower__semilattice__class_Oinf(B,C,A).
% 269.02/269.08 ** KEPT (pick-wt=8): 69 [] -class_Finite__Set_Ofinite_Ofinite(A)|c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),A).
% 269.02/269.08 ** KEPT (pick-wt=8): 70 [] -class_Lattices_Olower__semilattice(A)|c_Lattices_Olower__semilattice__class_Oinf(B,B,A)=B.
% 269.02/269.08 ** KEPT (pick-wt=17): 71 [] hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)),D))| -hBOOL(hAPP(B,D))| -hBOOL(hAPP(A,D)).
% 269.02/269.08 ** KEPT (pick-wt=24): 73 [copy,72,flip.2] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))=hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)).
% 269.02/269.08 ** KEPT (pick-wt=24): 74 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)).
% 269.02/269.08 ** KEPT (pick-wt=21): 75 [] -class_OrderedGroup_Opordered__ab__group__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),c_HOL_Ozero__class_Ozero(A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)).
% 269.02/269.08 ** KEPT (pick-wt=21): 76 [] -class_OrderedGroup_Opordered__ab__group__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),c_HOL_Ozero__class_Ozero(A))).
% 269.02/269.08 ** KEPT (pick-wt=21): 77 [] -class_OrderedGroup_Opordered__ab__group__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))).
% 269.02/269.08 ** KEPT (pick-wt=21): 78 [] -class_OrderedGroup_Opordered__ab__group__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))).
% 269.02/269.08 ** KEPT (pick-wt=20): 79 [] -class_Ring__and__Field_Oordered__idom(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))).
% 269.02/269.08 ** KEPT (pick-wt=20): 80 [] -class_Ring__and__Field_Oordered__idom(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))).
% 269.02/269.08 ** KEPT (pick-wt=14): 81 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),B)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=14): 82 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),B)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=14): 83 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 Following clause subsumed by 81 during input processing: 0 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),B)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=17): 84 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=c_HOL_Ozero__class_Ozero(A)|B=hAPP(c_HOL_Ouminus__class_Ouminus(A),C).
% 269.02/269.08 ** KEPT (pick-wt=17): 85 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=c_HOL_Ozero__class_Ozero(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),B)=C.
% 269.02/269.08 ** KEPT (pick-wt=13): 86 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_Finite__Set_Osetsum(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C,A)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=22): 88 [copy,87,flip.2] -class_OrderedGroup_Oab__group__add(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),c_Finite__Set_Osetsum(B,C,D,A))=c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),B,A,A,D),C,D,A).
% 269.02/269.08 ** KEPT (pick-wt=70): 89 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_Finite__Set_Osetsum(c_COMBS(c_COMBS(c_COMBB(c_HOL_OIf(A),c_COMBC(c_in(B),C,B,tc_fun(B,tc_bool),tc_bool),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),E,B,A,A),F,B,A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(D,c_Lattices_Olower__semilattice__class_Oinf(F,C,tc_fun(B,tc_bool)),B,A)),c_Finite__Set_Osetsum(E,c_Lattices_Olower__semilattice__class_Oinf(F,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(B,tc_bool)),C),tc_fun(B,tc_bool)),B,A))| -c_Finite__Set_Ofinite(F,B).
% 269.02/269.08 ** KEPT (pick-wt=19): 90 [] -class_Ring__and__Field_Ono__zero__divisors(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=19): 91 [] -class_Ring__and__Field_Oring__no__zero__divisors(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=10): 92 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=10): 93 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=15): 94 [] -class_OrderedGroup_Olordered__ab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=16): 96 [copy,95,flip.3] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=B|C=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=9): 97 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=9): 98 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 269.02/269.08 ** KEPT (pick-wt=10): 99 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=13): 100 [] -class_OrderedGroup_Olordered__ab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=11): 101 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 269.02/269.08 ** KEPT (pick-wt=11): 102 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 269.02/269.08 ** KEPT (pick-wt=13): 104 [copy,103,flip.3] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 269.02/269.08 ** KEPT (pick-wt=11): 105 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 269.02/269.08 ** KEPT (pick-wt=11): 106 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 269.02/269.08 ** KEPT (pick-wt=11): 107 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 269.02/269.08 ** KEPT (pick-wt=11): 108 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 269.02/269.08 Following clause subsumed by 101 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 269.02/269.08 ** KEPT (pick-wt=25): 109 [] -class_Ring__and__Field_Oordered__ring__strict(A)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C))),c_HOL_Ozero__class_Ozero(A))).
% 269.02/269.08 ** KEPT (pick-wt=29): 110 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C))))|B=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=29): 111 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C))))|C=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=29): 112 [] -class_Ring__and__Field_Oordered__ring__strict(A)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))))).
% 269.02/269.08 ** KEPT (pick-wt=26): 113 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))).
% 269.02/269.08 ** KEPT (pick-wt=26): 114 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)).
% 269.02/269.08 ** KEPT (pick-wt=26): 115 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)).
% 269.02/269.08 ** KEPT (pick-wt=26): 116 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))).
% 269.02/269.08 ** KEPT (pick-wt=26): 117 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)).
% 269.02/269.08 ** KEPT (pick-wt=26): 118 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)).
% 269.02/269.08 ** KEPT (pick-wt=33): 119 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)).
% 269.02/269.08 ** KEPT (pick-wt=33): 120 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))).
% 269.02/269.08 ** KEPT (pick-wt=33): 121 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))).
% 269.02/269.08 ** KEPT (pick-wt=52): 122 [] hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,C,A,A)),c_Nat_Ocompow(c_Suc(D),E,tc_prod(A,A),tc_bool)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(F,C,A,A)),c_Nat_Ocompow(D,E,tc_prod(A,A),tc_bool)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,F,A,A)),E)).
% 269.02/269.08 ** KEPT (pick-wt=52): 123 [] hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,C,A,A)),c_Nat_Ocompow(c_Suc(D),E,tc_prod(A,A),tc_bool)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(F,C,A,A)),E))| -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,F,A,A)),c_Nat_Ocompow(D,E,tc_prod(A,A),tc_bool))).
% 269.02/269.08 ** KEPT (pick-wt=31): 124 [] -class_Ring__and__Field_Osemiring__0(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Finite__Set_Osetsum(B,C,D,A)),E)=c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),D),E,D,A,A),C,D,A).
% 269.02/269.08 ** KEPT (pick-wt=12): 125 [] -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))).
% 269.02/269.08 ** KEPT (pick-wt=12): 126 [] -hBOOL(hAPP(A,c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))|hBOOL(hAPP(A,B)).
% 269.02/269.08 ** KEPT (pick-wt=13): 127 [] hBOOL(hAPP(A,c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 269.02/269.08 Following clause subsumed by 127 during input processing: 0 [] -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)))|hBOOL(hAPP(A,c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))).
% 269.02/269.08 ** KEPT (pick-wt=13): 128 [] -hBOOL(hAPP(A,c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))|hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 269.02/269.08 ** KEPT (pick-wt=5): 129 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.08 Following clause subsumed by 129 during input processing: 0 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.08 ** KEPT (pick-wt=17): 130 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.08 ** KEPT (pick-wt=13): 131 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.08 ** KEPT (pick-wt=13): 132 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.08 ** KEPT (pick-wt=20): 133 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)|B=c_HOL_Ozero__class_Ozero(tc_nat)|A=C.
% 269.02/269.08 ** KEPT (pick-wt=20): 134 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=C.
% 269.02/269.08 Following clause subsumed by 134 during input processing: 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)|B=C|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.08 ** KEPT (pick-wt=52): 135 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_Finite__Set_Osetsum(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,tc_bool)),E,A)=c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(A),c_COMBC(c_in(E),D,E,tc_fun(E,tc_bool),tc_bool),tc_bool,tc_fun(A,tc_fun(A,A)),E),B,E,A,tc_fun(A,A)),c_HOL_Ozero__class_Ozero(A),E,A,A),C,E,A)| -c_Finite__Set_Ofinite(C,E).
% 269.02/269.08 ** KEPT (pick-wt=56): 136 [] c_Set_Ovimage(c_COMBC(c_COMBC(c_COMBB(c_HOL_OIf(A),c_COMBC(c_in(B),C,B,tc_fun(B,tc_bool),tc_bool),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),E,B,A,A),F,B,A)=hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(B,tc_bool)),C)| -hBOOL(hAPP(hAPP(c_in(A),E),F))|hBOOL(hAPP(hAPP(c_in(A),D),F)).
% 269.02/269.08 ** KEPT (pick-wt=54): 137 [] c_Set_Ovimage(c_COMBC(c_COMBC(c_COMBB(c_HOL_OIf(A),c_COMBC(c_in(B),C,B,tc_fun(B,tc_bool),tc_bool),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),E,B,A,A),F,B,A)=c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool))| -hBOOL(hAPP(hAPP(c_in(A),E),F))| -hBOOL(hAPP(hAPP(c_in(A),D),F)).
% 269.02/269.08 Following clause subsumed by 90 during input processing: 0 [] -class_Ring__and__Field_Ono__zero__divisors(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=12): 138 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=12): 139 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=12): 140 [] -class_Ring__and__Field_Oring__no__zero__divisors(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=12): 141 [] -class_Ring__and__Field_Oring__no__zero__divisors(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=12): 142 [] -class_Ring__and__Field_Omult__zero(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=12): 143 [] -class_Ring__and__Field_Omult__zero(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 Following clause subsumed by 138 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=13): 144 [] -class_Ring__and__Field_Oring__1__no__zero__divisors(A)|c_Power_Opower__class_Opower(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=19): 145 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.08 ** KEPT (pick-wt=20): 146 [] hBOOL(hAPP(hAPP(c_in(A),hAPP(B,C)),D))| -hBOOL(hAPP(hAPP(c_in(E),C),c_Set_Ovimage(B,D,E,A))).
% 269.02/269.08 Following clause subsumed by 146 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(A),hAPP(B,C)),D))| -hBOOL(hAPP(hAPP(c_in(E),C),c_Set_Ovimage(B,D,E,A))).
% 269.02/269.08 ** KEPT (pick-wt=20): 147 [] hBOOL(hAPP(hAPP(c_in(A),B),c_Set_Ovimage(C,D,A,E)))| -hBOOL(hAPP(hAPP(c_in(E),hAPP(C,B)),D)).
% 269.02/269.08 Following clause subsumed by 147 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(A),B),c_Set_Ovimage(C,D,A,E)))| -hBOOL(hAPP(hAPP(c_in(E),hAPP(C,B)),D)).
% 269.02/269.08 Following clause subsumed by 147 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(A),B),c_Set_Ovimage(C,D,A,E)))| -hBOOL(hAPP(hAPP(c_in(E),hAPP(C,B)),D)).
% 269.02/269.08 ** KEPT (pick-wt=22): 148 [] c_COMBC(c_in(A),B,A,tc_fun(A,tc_bool),tc_bool)!=c_COMBC(c_in(A),C,A,tc_fun(A,tc_bool),tc_bool)|B=C.
% 269.02/269.08 ** KEPT (pick-wt=32): 149 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B))|B=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(C,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),D)),A),B,tc_nat)))|hBOOL(hAPP(C,A)).
% 269.02/269.08 ** KEPT (pick-wt=26): 150 [] hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C))| -hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Divides_Odiv__class_Omod(c_Suc(c_List_Osko__Divides__Xmod__induct__0__1__1(A,C)),C,tc_nat))).
% 269.02/269.08 ** KEPT (pick-wt=24): 151 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Suc(c_Divides_Odiv__class_Odiv(B,A,tc_nat))))).
% 269.02/269.08 ** KEPT (pick-wt=30): 152 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C).
% 269.02/269.09 ** KEPT (pick-wt=21): 153 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),C,A)=c_Divides_Odiv__class_Omod(B,C,A).
% 269.02/269.09 ** KEPT (pick-wt=21): 154 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),D,A)=c_Divides_Odiv__class_Omod(B,D,A).
% 269.02/269.09 ** KEPT (pick-wt=25): 155 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A)=c_Divides_Odiv__class_Odiv(B,D,A)|C=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.09 ** KEPT (pick-wt=25): 156 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A)=c_Divides_Odiv__class_Odiv(C,D,A)|B=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.09 ** KEPT (pick-wt=5): 157 [] -class_Finite__Set_Ofinite_Ofinite(A)|c_Finite__Set_Ofinite(B,A).
% 269.02/269.09 ** KEPT (pick-wt=35): 158 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)).
% 269.02/269.09 ** KEPT (pick-wt=19): 159 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.09 ** KEPT (pick-wt=19): 160 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.09 ** KEPT (pick-wt=24): 162 [copy,161,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A).
% 269.02/269.09 ** KEPT (pick-wt=24): 164 [copy,163,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A).
% 269.02/269.09 ** KEPT (pick-wt=15): 165 [] c_Suc(c_Divides_Odiv__class_Omod(A,B,tc_nat))!=B|c_Divides_Odiv__class_Omod(c_Suc(A),B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.09 ** KEPT (pick-wt=18): 166 [] -class_OrderedGroup_Ocancel__semigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C)|B=D.
% 269.02/269.09 ** KEPT (pick-wt=18): 167 [] -class_OrderedGroup_Ocancel__semigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)|C=D.
% 269.02/269.09 ** KEPT (pick-wt=18): 168 [] -class_OrderedGroup_Ocancel__ab__semigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)|C=D.
% 269.02/269.09 ** KEPT (pick-wt=20): 169 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)|C=D.
% 269.02/269.09 ** KEPT (pick-wt=16): 170 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 269.02/269.09 ** KEPT (pick-wt=16): 171 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B)|A=C.
% 269.02/269.09 Following clause subsumed by 170 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 269.02/269.09 ** KEPT (pick-wt=26): 172 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Suc(C)),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Suc(C)),B))).
% 269.02/269.09 ** KEPT (pick-wt=26): 173 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Suc(A)),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Suc(A)),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)).
% 269.02/269.09 ** KEPT (pick-wt=40): 175 [copy,174,flip.2] -class_Ring__and__Field_Osemiring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)),E)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),E)).
% 269.02/269.09 ** KEPT (pick-wt=35): 177 [copy,176,flip.2] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(B,C,D,A)),c_Finite__Set_Osetsum(E,C,D,A))=c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oplus__class_Oplus(A),B,A,tc_fun(A,A),D),E,D,A,A),C,D,A).
% 269.02/269.09 ** KEPT (pick-wt=26): 178 [] -class_Ring__and__Field_Osemiring__0(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Finite__Set_Osetsum(C,D,E,A))=c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,E),D,E,A).
% 269.02/269.09 ** KEPT (pick-wt=19): 179 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|A=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.09 ** KEPT (pick-wt=19): 180 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.09 ** KEPT (pick-wt=24): 182 [copy,181,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A).
% 269.02/269.09 ** KEPT (pick-wt=24): 184 [copy,183,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A).
% 269.02/269.09 ** KEPT (pick-wt=28): 185 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)=E.
% 269.02/269.09 ** KEPT (pick-wt=24): 187 [copy,186,flip.2] -class_OrderedGroup_Omonoid__mult(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A))=c_Power_Opower__class_Opower(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),A).
% 269.02/269.09 ** KEPT (pick-wt=25): 188 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 269.02/269.09 ** KEPT (pick-wt=25): 189 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)).
% 269.02/269.09 ** KEPT (pick-wt=25): 190 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C).
% 269.02/269.09 Following clause subsumed by 188 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 269.02/269.09 ** KEPT (pick-wt=25): 191 [] -class_OrderedGroup_Oab__semigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 269.02/269.09 ** KEPT (pick-wt=25): 192 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)).
% 269.02/269.09 ** KEPT (pick-wt=25): 193 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 269.02/269.09 ** KEPT (pick-wt=25): 194 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)).
% 269.02/269.09 Following clause subsumed by 188 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 269.02/269.09 ** KEPT (pick-wt=27): 196 [copy,195,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),c_Divides_Odiv__class_Omod(D,C,A)),C,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A).
% 269.02/269.09 ** KEPT (pick-wt=15): 197 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B).
% 269.02/269.09 Following clause subsumed by 197 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B).
% 269.02/269.09 ** KEPT (pick-wt=17): 198 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Power_Opower__class_Opower(B,C,A)).
% 269.02/269.09 Following clause subsumed by 198 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Power_Opower__class_Opower(B,C,A)).
% 269.02/269.09 ** KEPT (pick-wt=17): 199 [] -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Power_Opower__class_Opower(B,C,A)).
% 269.02/269.09 ** KEPT (pick-wt=17): 200 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(B,C,A)),B).
% 269.02/269.09 ** KEPT (pick-wt=19): 201 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(B,C,A),D,A)=c_Power_Opower__class_Opower(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),A).
% 269.02/269.09 ** KEPT (pick-wt=37): 202 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)).
% 269.02/269.09 Following clause subsumed by 202 during input processing: 0 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)).
% 269.02/269.09 ** KEPT (pick-wt=14): 203 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),C,A)=c_Divides_Odiv__class_Omod(B,C,A).
% 269.02/269.09 ** KEPT (pick-wt=15): 204 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(B,C,tc_nat),A)=c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(B,A),C,A).
% 269.02/269.09 Following clause subsumed by 164 during input processing: 0 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A).
% 269.02/269.09 ** KEPT (pick-wt=13): 205 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Suc(B),A)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.09 ** KEPT (pick-wt=31): 206 [] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Odiv(C,B,A))),c_Divides_Odiv__class_Omod(C,B,A))),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D).
% 269.02/269.09 ** KEPT (pick-wt=31): 207 [] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C)),c_Divides_Odiv__class_Omod(B,C,A))),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D).
% 269.02/269.09 ** KEPT (pick-wt=12): 209 [copy,208,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.09 Following clause subsumed by 209 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.09 Following clause subsumed by 129 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.09 Following clause subsumed by 129 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.09 ** KEPT (pick-wt=14): 210 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 269.02/269.09 ** KEPT (pick-wt=30): 211 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),A)).
% 269.02/269.09 ** KEPT (pick-wt=30): 212 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),A)).
% 269.02/269.09 ** KEPT (pick-wt=27): 213 [] c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat)=c_Divides_Odiv__class_Odiv(B,C,tc_nat)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)).
% 269.02/269.09 ** KEPT (pick-wt=19): 214 [] c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),A,tc_nat)=B| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)).
% 269.02/269.09 ** KEPT (pick-wt=19): 215 [] c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),B,tc_nat)=A| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)).
% 269.02/269.09 ** KEPT (pick-wt=32): 216 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),A))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),B)).
% 269.02/269.09 ** KEPT (pick-wt=15): 217 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_Suc(B)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)).
% 269.02/269.09 ** KEPT (pick-wt=15): 218 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(A)),B)).
% 269.02/269.09 ** KEPT (pick-wt=24): 219 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)).
% 269.02/269.09 ** KEPT (pick-wt=24): 220 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))).
% 269.02/269.09 ** KEPT (pick-wt=24): 221 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)).
% 269.02/269.09 ** KEPT (pick-wt=12): 222 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),B)).
% 269.02/269.09 ** KEPT (pick-wt=12): 223 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),A)).
% 269.02/269.09 ** KEPT (pick-wt=24): 224 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))).
% 269.02/269.09 ** KEPT (pick-wt=24): 225 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))).
% 269.02/269.09 ** KEPT (pick-wt=22): 226 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(A)),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)).
% 269.02/269.09 ** KEPT (pick-wt=31): 227 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),D))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)).
% 269.02/269.09 ** KEPT (pick-wt=13): 228 [] c_Divides_Odiv__class_Omod(A,B,tc_nat)=A| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)).
% 269.02/269.09 ** KEPT (pick-wt=18): 229 [] A=B| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_Suc(B)))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)).
% 269.02/269.09 ** KEPT (pick-wt=18): 230 [] A=B| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_Suc(A)))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)).
% 269.02/269.09 Following clause subsumed by 229 during input processing: 0 [] A=B|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_Suc(B))).
% 269.02/269.09 ** KEPT (pick-wt=27): 231 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),B))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),D)).
% 269.02/269.09 ** KEPT (pick-wt=19): 232 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)).
% 269.02/269.09 ** KEPT (pick-wt=19): 233 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)).
% 269.02/269.09 ** KEPT (pick-wt=19): 234 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B)).
% 269.02/269.09 Following clause subsumed by 232 during input processing: 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)).
% 269.02/269.09 Following clause subsumed by 233 during input processing: 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)).
% 269.02/269.09 ** KEPT (pick-wt=19): 235 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(A)),B))|c_Suc(A)=B| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)).
% 269.02/269.09 ** KEPT (pick-wt=15): 236 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_Suc(A))).
% 269.02/269.09 ** KEPT (pick-wt=16): 237 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(A)),c_Suc(B)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)).
% 269.02/269.09 ** KEPT (pick-wt=16): 238 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(A)),c_Suc(B))).
% 269.02/269.09 Following clause subsumed by 237 during input processing: 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Suc(A)),c_Suc(B)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)).
% 269.02/269.09 ** KEPT (pick-wt=40): 239 [] -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),C))| -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),C))|A=B| -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),C),c_Arrow__Order__Mirabelle_OLin)).
% 269.02/269.09 ** KEPT (pick-wt=40): 240 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),C))|hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),C))|B=A| -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),C),c_Arrow__Order__Mirabelle_OLin)).
% 269.02/269.09 ** KEPT (pick-wt=37): 241 [] -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),C))| -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),C))| -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),C),c_Arrow__Order__Mirabelle_OLin)).
% 269.02/269.09 ** KEPT (pick-wt=46): 242 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(A),hAPP(c_fe_qual(B),C),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),c_HOL_Ozero__class_Ozero(A),B,A,A),E,B,A)=c_HOL_Ozero__class_Ozero(A)|hBOOL(hAPP(hAPP(c_in(B),C),E))| -c_Finite__Set_Ofinite(E,B).
% 269.02/269.09 ** KEPT (pick-wt=47): 243 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(A),hAPP(c_fe_qual(B),C),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),c_HOL_Ozero__class_Ozero(A),B,A,A),E,B,A)=hAPP(D,C)| -hBOOL(hAPP(hAPP(c_in(B),C),E))| -c_Finite__Set_Ofinite(E,B).
% 269.02/269.09 ** KEPT (pick-wt=34): 244 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),D))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))).
% 269.02/269.09 ** KEPT (pick-wt=34): 245 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A)))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))).
% 269.02/269.09 ** KEPT (pick-wt=34): 246 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),D))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))).
% 269.02/269.09 ** KEPT (pick-wt=34): 247 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A)))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))).
% 269.02/269.09 ** KEPT (pick-wt=29): 248 [] -class_Ring__and__Field_Oordered__semidom(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)).
% 269.02/269.09 ** KEPT (pick-wt=31): 249 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))).
% 269.02/269.09 ** KEPT (pick-wt=31): 250 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_HOL_Ozero__class_Ozero(A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)).
% 269.02/269.09 Following clause subsumed by 249 during input processing: 0 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)).
% 269.02/269.09 ** KEPT (pick-wt=31): 251 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)).
% 269.02/269.09 ** KEPT (pick-wt=21): 252 [] -class_Ring__and__Field_Oordered__semidom(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_Power_Opower__class_Opower(B,C,A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)).
% 269.02/269.09 ** KEPT (pick-wt=31): 253 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_HOL_Ozero__class_Ozero(A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))).
% 269.02/269.09 ** KEPT (pick-wt=31): 254 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)).
% 269.02/269.09 ** KEPT (pick-wt=31): 255 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B))).
% 269.02/269.09 ** KEPT (pick-wt=31): 256 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))).
% 269.02/269.09 ** KEPT (pick-wt=23): 257 [] -class_Ring__and__Field_Oordered__idom(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B)),c_HOL_Ozero__class_Ozero(A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))).
% 269.02/269.09 ** KEPT (pick-wt=23): 258 [] -class_Ring__and__Field_Oordered__idom(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B)),c_HOL_Ozero__class_Ozero(A))).
% 269.02/269.09 ** KEPT (pick-wt=23): 259 [] -class_OrderedGroup_Olordered__ab__group__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B)),c_HOL_Ozero__class_Ozero(A))).
% 269.02/269.09 ** KEPT (pick-wt=23): 260 [] -class_OrderedGroup_Olordered__ab__group__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B)),c_HOL_Ozero__class_Ozero(A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))).
% 269.02/269.09 ** KEPT (pick-wt=31): 261 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_HOL_Ozero__class_Ozero(A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_HOL_Ozero__class_Ozero(A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))).
% 269.02/269.09 ** KEPT (pick-wt=15): 262 [] -class_Ring__and__Field_Oordered__ring__strict(A)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),c_HOL_Ozero__class_Ozero(A))).
% 269.02/269.09 ** KEPT (pick-wt=12): 263 [] -class_Ring__and__Field_Oordered__semidom(A)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_HOL_Ozero__class_Ozero(A))).
% 269.02/269.09 ** KEPT (pick-wt=35): 264 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A)))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))).
% 269.02/269.09 ** KEPT (pick-wt=35): 265 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A)))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B))).
% 269.02/269.09 ** KEPT (pick-wt=34): 266 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),D),c_HOL_Ozero__class_Ozero(A))).
% 269.02/269.09 ** KEPT (pick-wt=34): 267 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),D),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))).
% 269.02/269.09 ** KEPT (pick-wt=34): 268 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),D)).
% 269.02/269.09 ** KEPT (pick-wt=34): 269 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)).
% 269.02/269.09 Following clause subsumed by 267 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),D),C)).
% 269.02/269.09 ** KEPT (pick-wt=34): 270 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)).
% 269.02/269.09 Following clause subsumed by 269 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)).
% 269.02/269.09 Following clause subsumed by 267 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),D),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))).
% 269.02/269.09 ** KEPT (pick-wt=34): 271 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_HOL_Ozero__class_Ozero(A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),D),B)).
% 269.02/269.09 ** KEPT (pick-wt=34): 272 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)).
% 269.02/269.09 ** KEPT (pick-wt=34): 273 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)).
% 269.02/269.09 Following clause subsumed by 271 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),D),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_HOL_Ozero__class_Ozero(A))).
% 269.02/269.09 ** KEPT (pick-wt=34): 274 [] -class_Ring__and__Field_Oordered__comm__semiring__strict(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)).
% 269.02/269.09 ** KEPT (pick-wt=23): 275 [] -class_OrderedGroup_Olordered__ab__group__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))).
% 269.02/269.09 ** KEPT (pick-wt=23): 276 [] -class_OrderedGroup_Olordered__ab__group__add(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)).
% 269.02/269.09 ** KEPT (pick-wt=20): 277 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.09 ** KEPT (pick-wt=16): 278 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.09 ** KEPT (pick-wt=16): 279 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A)!=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.09 ** KEPT (pick-wt=9): 280 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.09 ** KEPT (pick-wt=18): 281 [] A=B| -hBOOL(hAPP(hAPP(c_in(tc_prod(C,C)),c_Pair(A,B,C,C)),c_Relation_OId__on(D,C))).
% 269.02/269.09 ** KEPT (pick-wt=20): 282 [] -class_Ring__and__Field_Oordered__semidom(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A))).
% 269.02/269.09 ** KEPT (pick-wt=20): 283 [] -class_Ring__and__Field_Oordered__semidom(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)).
% 269.02/269.09 ** KEPT (pick-wt=25): 284 [] hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C))| -hBOOL(hAPP(A,B))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_List_Osko__Divides__Xmod__induct__0__1__1(A,C)),C)).
% 269.02/269.09 ** KEPT (pick-wt=23): 285 [] A=c_HOL_Ozero__class_Ozero(tc_nat)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Power_Opower__class_Opower(B,A,tc_nat))).
% 269.02/269.09 ** KEPT (pick-wt=19): 286 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Power_Opower__class_Opower(A,B,tc_nat)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)).
% 269.02/269.09 ** KEPT (pick-wt=29): 287 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)).
% 269.02/269.09 ** KEPT (pick-wt=15): 288 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B).
% 269.02/269.09 ** KEPT (pick-wt=15): 289 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B).
% 269.02/269.09 Following clause subsumed by 288 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B).
% 269.02/269.09 ** KEPT (pick-wt=15): 290 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.09 ** KEPT (pick-wt=15): 291 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.09 ** KEPT (pick-wt=12): 292 [] -class_Nat_Osemiring__char__0(A)|c_Nat_Osemiring__1__class_Oof__nat(B,A)!=c_Nat_Osemiring__1__class_Oof__nat(C,A)|B=C.
% 269.02/269.09 ** KEPT (pick-wt=12): 293 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(B,C,A),C,A)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.09 ** KEPT (pick-wt=27): 295 [copy,294,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(B,C,A)),c_Divides_Odiv__class_Omod(D,C,A)),C,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A).
% 269.02/269.09 ** KEPT (pick-wt=21): 296 [] -class_OrderedGroup_Omonoid__mult(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(B,C,A)),B)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Power_Opower__class_Opower(B,C,A)).
% 269.02/269.09 ** KEPT (pick-wt=24): 297 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(B,D,A))=c_Power_Opower__class_Opower(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),A).
% 269.02/269.09 ** KEPT (pick-wt=30): 298 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),C,A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),c_Divides_Odiv__class_Odiv(B,C,A))|C=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.09 ** KEPT (pick-wt=30): 299 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),D,A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),c_Divides_Odiv__class_Odiv(B,D,A))|D=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.09 ** KEPT (pick-wt=8): 300 [] c_Suc(A)!=c_Suc(B)|A=B.
% 269.02/269.09 Following clause subsumed by 300 during input processing: 0 [] c_Suc(A)!=c_Suc(B)|A=B.
% 269.02/269.09 ** KEPT (pick-wt=39): 301 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,C,A)!=c_Divides_Odiv__class_Omod(D,C,A)|c_Divides_Odiv__class_Omod(E,C,A)!=c_Divides_Odiv__class_Omod(F,C,A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),E),B),C,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),F),D),C,A).
% 269.02/269.09 ** KEPT (pick-wt=20): 302 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.09 ** KEPT (pick-wt=18): 303 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.10 ** KEPT (pick-wt=32): 304 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B))|B=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(C,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),D)),A),B,tc_nat)))|hBOOL(hAPP(C,D)).
% 269.02/269.10 ** KEPT (pick-wt=21): 305 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),A)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)).
% 269.02/269.10 ** KEPT (pick-wt=43): 306 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))|C=E|B=D.
% 269.02/269.10 Following clause subsumed by 306 during input processing: 0 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))|C=E|B=D.
% 269.02/269.10 ** KEPT (pick-wt=39): 307 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))|B=D|A=C.
% 269.02/269.10 Following clause subsumed by 307 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))|B=D|A=C.
% 269.02/269.10 ** KEPT (pick-wt=13): 308 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_Finite__Set_Osetsum(B,C,D,A)=c_HOL_Ozero__class_Ozero(A)|c_Finite__Set_Ofinite(C,D).
% 269.02/269.10 Following clause subsumed by 308 during input processing: 0 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_Finite__Set_Osetsum(B,C,D,A)=c_HOL_Ozero__class_Ozero(A)|c_Finite__Set_Ofinite(C,D).
% 269.02/269.10 ** KEPT (pick-wt=17): 309 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A)=B|C=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.10 ** KEPT (pick-wt=17): 310 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),B,A)=C|B=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.10 ** KEPT (pick-wt=39): 311 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,C,A)!=c_Divides_Odiv__class_Omod(D,C,A)|c_Divides_Odiv__class_Omod(E,C,A)!=c_Divides_Odiv__class_Omod(F,C,A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),B),C,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),D),C,A).
% 269.02/269.10 ** KEPT (pick-wt=35): 312 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)).
% 269.02/269.10 ** KEPT (pick-wt=35): 313 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))).
% 269.02/269.10 ** KEPT (pick-wt=35): 314 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),E)).
% 269.02/269.10 ** KEPT (pick-wt=8): 315 [] c_Relation_Orefl__on(A,B,C)| -c_Equiv__Relations_Oe_quiv(A,B,C).
% 269.02/269.10 ** KEPT (pick-wt=20): 316 [] -class_OrderedGroup_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C).
% 269.02/269.10 ** KEPT (pick-wt=32): 317 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),E))|c_Divides_Odiv__class_Omod(A,B,tc_nat)=c_Divides_Odiv__class_Omod(D,B,tc_nat).
% 269.02/269.10 ** KEPT (pick-wt=21): 318 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),C),A)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.10 ** KEPT (pick-wt=17): 319 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Power_Opower__class_Opower(B,C,A))=c_Power_Opower__class_Opower(B,c_Suc(C),A).
% 269.02/269.10 ** KEPT (pick-wt=17): 320 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(B,C,A)),B)=c_Power_Opower__class_Opower(B,c_Suc(C),A).
% 269.02/269.10 ** KEPT (pick-wt=16): 321 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A)=c_Divides_Odiv__class_Omod(B,C,A).
% 269.02/269.10 ** KEPT (pick-wt=16): 322 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),B,A)=c_Divides_Odiv__class_Omod(C,B,A).
% 269.02/269.10 ** KEPT (pick-wt=40): 323 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat))),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),D),A))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)).
% 269.02/269.10 ** KEPT (pick-wt=34): 324 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E))|D=E|C=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.10 ** KEPT (pick-wt=30): 325 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),D))|C=D|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.10 ** KEPT (pick-wt=25): 326 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C))!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.10 ** KEPT (pick-wt=25): 327 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C))!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.10 ** KEPT (pick-wt=17): 328 [] c_Power_Opower__class_Opower(A,B,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.10 ** KEPT (pick-wt=4): 329 [] c_Suc(A)!=A.
% 269.02/269.10 Following clause subsumed by 329 during input processing: 0 [flip.1] c_Suc(A)!=A.
% 269.02/269.10 ** KEPT (pick-wt=24): 330 [] hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omkbot(A,B)),c_Arrow__Order__Mirabelle_OLin))| -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),A),c_Arrow__Order__Mirabelle_OLin)).
% 269.02/269.10 ** KEPT (pick-wt=24): 331 [] hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_Arrow__Order__Mirabelle_Omktop(A,B)),c_Arrow__Order__Mirabelle_OLin))| -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),A),c_Arrow__Order__Mirabelle_OLin)).
% 269.02/269.10 ** KEPT (pick-wt=10): 332 [] -class_OrderedGroup_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)=B.
% 269.02/269.10 ** KEPT (pick-wt=14): 333 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.10 ** KEPT (pick-wt=14): 334 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),B,A)=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.10 ** KEPT (pick-wt=21): 335 [] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C))=B.
% 269.02/269.10 ** KEPT (pick-wt=25): 336 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)))=c_HOL_Ozero__class_Ozero(A).
% 269.02/269.10 ** KEPT (pick-wt=14): 337 [] hBOOL(hAPP(A,hAPP(B,C)))| -hBOOL(hAPP(c_Set_Ovimage(B,A,D,E),C)).
% 269.02/269.10 ** KEPT (pick-wt=14): 338 [] hBOOL(hAPP(c_Set_Ovimage(A,B,C,D),E))| -hBOOL(hAPP(B,hAPP(A,E))).
% 269.02/269.10 ** KEPT (pick-wt=18): 339 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Suc(A)),B)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Suc(A)),C)|B=C.
% 269.02/269.10 ** KEPT (pick-wt=21): 340 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)).
% 269.02/269.10 ** KEPT (pick-wt=24): 342 [copy,341,flip.2] -class_OrderedGroup_Ocomm__monoid__mult(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(D,C,A))=c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A).
% 269.02/269.10 ** KEPT (pick-wt=24): 344 [copy,343,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(B,C,A)),c_Power_Opower__class_Opower(D,C,A))=c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A).
% 269.02/269.10 Following clause subsumed by 184 during input processing: 0 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A).
% 269.02/269.10 Following clause subsumed by 182 during input processing: 0 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A).
% 269.02/269.10 ** KEPT (pick-wt=20): 345 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.10 ** KEPT (pick-wt=18): 346 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.10 ** KEPT (pick-wt=19): 347 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),A)=c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(B,C,A),D,A).
% 269.02/269.10 ** KEPT (pick-wt=21): 348 [] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Odiv(C,B,A))),c_Divides_Odiv__class_Omod(C,B,A))=C.
% 269.02/269.10 ** KEPT (pick-wt=21): 349 [] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C)),c_Divides_Odiv__class_Omod(B,C,A))=B.
% 269.02/269.10 Following clause subsumed by 349 during input processing: 0 [flip.2] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C)),c_Divides_Odiv__class_Omod(B,C,A))=B.
% 269.02/269.10 ** KEPT (pick-wt=26): 351 [copy,350,flip.2] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(B,C,A)),D)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A).
% 269.02/269.10 ** KEPT (pick-wt=26): 353 [copy,352,flip.2] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Omod(C,D,A))=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A).
% 269.02/269.10 ** KEPT (pick-wt=25): 354 [] -class_OrderedGroup_Oab__semigroup__mult(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)).
% 269.02/269.10 ** KEPT (pick-wt=25): 355 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),C).
% 269.02/269.10 ** KEPT (pick-wt=25): 356 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)).
% 269.02/269.10 Following clause subsumed by 356 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)).
% 269.02/269.10 ** KEPT (pick-wt=25): 357 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)).
% 269.02/269.10 Following clause subsumed by 356 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)).
% 269.02/269.10 ** KEPT (pick-wt=30): 358 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)).
% 269.02/269.10 ** KEPT (pick-wt=30): 359 [] -class_Ring__and__Field_Ocomm__semiring(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)).
% 269.02/269.10 ** KEPT (pick-wt=30): 361 [copy,360,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 269.02/269.10 ** KEPT (pick-wt=22): 362 [] c_Divides_Odiv__class_Odiv(A,B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)).
% 269.02/269.10 ** KEPT (pick-wt=22): 363 [] hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C))| -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,c_List_Osko__Divides__Xmod__induct__0__1__1(A,C))).
% 269.02/269.10 ** KEPT (pick-wt=17): 365 [copy,364,factor_simp] hBOOL(hAPP(A,B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 269.02/269.10 ** KEPT (pick-wt=13): 366 [] A=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))).
% 269.02/269.10 ** KEPT (pick-wt=29): 367 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A))).
% 269.02/269.10 ** KEPT (pick-wt=18): 368 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)).
% 269.02/269.10 ** KEPT (pick-wt=18): 369 [] hBOOL(hAPP(A,B))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 269.02/269.10 ** KEPT (pick-wt=24): 370 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A))|B=C.
% 269.02/269.10 ** KEPT (pick-wt=25): 371 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A))).
% 269.02/269.10 ** KEPT (pick-wt=25): 372 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))).
% 269.02/269.10 ** KEPT (pick-wt=21): 373 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A))).
% 269.02/269.10 ** KEPT (pick-wt=21): 374 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))).
% 269.02/269.10 ** KEPT (pick-wt=14): 375 [] c_Divides_Odiv__class_Odiv(A,B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)).
% 269.02/269.10 ** KEPT (pick-wt=32): 376 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)).
% 269.02/269.10 ** KEPT (pick-wt=32): 377 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)).
% 269.02/269.10 Following clause subsumed by 377 during input processing: 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)).
% 269.02/269.10 Following clause subsumed by 376 during input processing: 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)).
% 269.02/269.10 Following clause subsumed by 225 during input processing: 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)).
% 269.02/269.10 Following clause subsumed by 377 during input processing: 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)).
% 269.02/269.10 ** KEPT (pick-wt=28): 378 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Power_Opower__class_Opower(C,A,tc_nat)),c_Power_Opower__class_Opower(C,B,tc_nat)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)).
% 269.02/269.10 Following clause subsumed by 232 during input processing: 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)).
% 269.02/269.10 Following clause subsumed by 233 during input processing: 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)).
% 269.02/269.10 ** KEPT (pick-wt=50): 379 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(A),c_COMBC(c_fe_qual(B),C,B,B,tc_bool),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),c_HOL_Ozero__class_Ozero(A),B,A,A),E,B,A)=hAPP(D,C)| -hBOOL(hAPP(hAPP(c_in(B),C),E))| -c_Finite__Set_Ofinite(E,B).
% 269.02/269.10 ** KEPT (pick-wt=49): 380 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_Finite__Set_Osetsum(c_COMBC(c_COMBS(c_COMBB(c_HOL_OIf(A),c_COMBC(c_fe_qual(B),C,B,B,tc_bool),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),c_HOL_Ozero__class_Ozero(A),B,A,A),E,B,A)=c_HOL_Ozero__class_Ozero(A)|hBOOL(hAPP(hAPP(c_in(B),C),E))| -c_Finite__Set_Ofinite(E,B).
% 269.02/269.10 ** KEPT (pick-wt=34): 381 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(C,D)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),C))|A=B|A=D.
% 269.02/269.10 ** KEPT (pick-wt=34): 382 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(C,D)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),C))|B=D|A=D.
% 269.02/269.10 ** KEPT (pick-wt=15): 383 [] -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(B,A))).
% 269.02/269.10 ** KEPT (pick-wt=15): 384 [] -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(C,A))).
% 269.02/269.10 ** KEPT (pick-wt=31): 385 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),C))|B=D| -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(C,D))).
% 269.02/269.10 ** KEPT (pick-wt=15): 386 [] -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,A,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(B,A))).
% 269.02/269.10 ** KEPT (pick-wt=15): 387 [] -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(C,B))).
% 269.02/269.10 ** KEPT (pick-wt=34): 388 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(C,D)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),C))|A=B|B=D.
% 269.02/269.10 ** KEPT (pick-wt=34): 389 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(C,D)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),C))|A=D|B=D.
% 269.02/269.10 ** KEPT (pick-wt=31): 390 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),C))|A=D| -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(C,D))).
% 269.02/269.10 ** KEPT (pick-wt=51): 391 [] c_Set_Ovimage(c_COMBC(c_COMBC(c_COMBB(c_HOL_OIf(A),c_COMBC(c_in(B),C,B,tc_fun(B,tc_bool),tc_bool),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),E,B,A,A),F,B,A)=C|hBOOL(hAPP(hAPP(c_in(A),E),F))| -hBOOL(hAPP(hAPP(c_in(A),D),F)).
% 269.02/269.10 ** KEPT (pick-wt=33): 392 [] hBOOL(hAPP(hAPP(c_in(tc_prod(A,B)),c_Pair(C,D,A,B)),c_Product__Type_OSigma(E,F,A,B)))| -hBOOL(hAPP(hAPP(c_in(B),D),hAPP(F,C)))| -hBOOL(hAPP(hAPP(c_in(A),C),E)).
% 269.02/269.10 Following clause subsumed by 392 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(A,B)),c_Pair(C,D,A,B)),c_Product__Type_OSigma(E,F,A,B)))| -hBOOL(hAPP(hAPP(c_in(B),D),hAPP(F,C)))| -hBOOL(hAPP(hAPP(c_in(A),C),E)).
% 269.02/269.10 ** KEPT (pick-wt=31): 393 [] hBOOL(hAPP(hAPP(c_in(A),B),c_Wellfounded_Oacc(C,A)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,D,A,A)),C))| -hBOOL(hAPP(hAPP(c_in(A),D),c_Wellfounded_Oacc(C,A))).
% 269.02/269.10 Following clause subsumed by 393 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(A),B),c_Wellfounded_Oacc(C,A)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,D,A,A)),C))| -hBOOL(hAPP(hAPP(c_in(A),D),c_Wellfounded_Oacc(C,A))).
% 269.02/269.10 ** KEPT (pick-wt=31): 394 [] hBOOL(hAPP(hAPP(c_in(A),B),c_Relation_OImage(C,D,E,A)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(E,A)),c_Pair(F,B,E,A)),C))| -hBOOL(hAPP(hAPP(c_in(E),F),D)).
% 269.02/269.10 Following clause subsumed by 394 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(A),B),c_Relation_OImage(C,D,E,A)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(E,A)),c_Pair(F,B,E,A)),C))| -hBOOL(hAPP(hAPP(c_in(E),F),D)).
% 269.02/269.10 ** KEPT (pick-wt=22): 395 [] hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,D,A,A)),c_Relation_OId__on(C,A))).
% 269.02/269.10 ** KEPT (pick-wt=22): 396 [] hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,B,A,A)),c_Relation_OId__on(C,A)))| -hBOOL(hAPP(hAPP(c_in(A),B),C)).
% 269.02/269.10 ** KEPT (pick-wt=24): 397 [] hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(D,B,A,A)),E))| -c_Equiv__Relations_Oe_quiv(C,E,A).
% 269.02/269.10 ** KEPT (pick-wt=24): 398 [] hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,D,A,A)),E))| -c_Equiv__Relations_Oe_quiv(C,E,A).
% 269.02/269.10 ** KEPT (pick-wt=23): 399 [] hBOOL(hAPP(hAPP(c_in(A),B),c_Relation_ORange(C,D,A)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(D,A)),c_Pair(E,B,D,A)),C)).
% 269.02/269.10 Following clause subsumed by 399 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(A),B),c_Relation_ORange(C,D,A)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(D,A)),c_Pair(E,B,D,A)),C)).
% 269.02/269.10 ** KEPT (pick-wt=23): 400 [] hBOOL(hAPP(hAPP(c_in(A),B),c_Relation_ODomain(C,A,D)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(A,D)),c_Pair(B,E,A,D)),C)).
% 269.02/269.10 Following clause subsumed by 400 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(A),B),c_Relation_ODomain(C,A,D)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(A,D)),c_Pair(B,E,A,D)),C)).
% 269.02/269.10 ** KEPT (pick-wt=26): 401 [] hBOOL(hAPP(hAPP(c_in(A),B),hAPP(C,D)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(E,A)),c_Pair(D,B,E,A)),c_Product__Type_OSigma(F,C,E,A))).
% 269.02/269.11 ** KEPT (pick-wt=24): 402 [] hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(hAPP(c_in(tc_prod(A,D)),c_Pair(B,E,A,D)),c_Product__Type_OSigma(C,F,A,D))).
% 269.02/269.11 ** KEPT (pick-wt=47): 403 [] hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,C,A,A)),D))|hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(C,B,A,A)),D))|C=B| -hBOOL(hAPP(hAPP(c_in(A),B),E))| -hBOOL(hAPP(hAPP(c_in(A),C),E))| -c_Relation_Ototal__on(E,D,A).
% 269.02/269.11 ** KEPT (pick-wt=24): 404 [] hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,B,A,A)),C))| -hBOOL(hAPP(hAPP(c_in(A),B),D))| -c_Relation_Orefl__on(D,C,A).
% 269.02/269.11 ** KEPT (pick-wt=24): 405 [] hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(D,B,A,A)),E))| -c_Relation_Orefl__on(C,E,A).
% 269.02/269.11 ** KEPT (pick-wt=24): 406 [] hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,D,A,A)),E))| -c_Relation_Orefl__on(C,E,A).
% 269.02/269.11 Following clause subsumed by 404 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,B,A,A)),C))| -hBOOL(hAPP(hAPP(c_in(A),B),D))| -c_Relation_Orefl__on(D,C,A).
% 269.02/269.11 ** KEPT (pick-wt=23): 407 [] A=B| -hBOOL(hAPP(hAPP(c_in(tc_prod(C,C)),c_Pair(A,B,C,C)),c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_prod(C,C),tc_bool))).
% 269.02/269.11 ** KEPT (pick-wt=27): 408 [] hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,C,A,A)),c_Wellfounded_Omlex__prod(D,E,A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(D,B)),hAPP(D,C))).
% 269.02/269.11 ** KEPT (pick-wt=26): 409 [] hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,C,A,A)),c_Wellfounded_Omeasure(D,A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(D,B)),hAPP(D,C))).
% 269.02/269.11 ** KEPT (pick-wt=26): 410 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(A,B)),hAPP(A,C)))| -hBOOL(hAPP(hAPP(c_in(tc_prod(D,D)),c_Pair(B,C,D,D)),c_Wellfounded_Omeasure(A,D))).
% 269.02/269.11 ** KEPT (pick-wt=20): 411 [] -class_Ring__and__Field_Oordered__semidom(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A))).
% 269.02/269.11 ** KEPT (pick-wt=20): 412 [] -class_Ring__and__Field_Oordered__semidom(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A)))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)).
% 269.02/269.11 ** KEPT (pick-wt=16): 413 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)).
% 269.02/269.11 Following clause subsumed by 413 during input processing: 0 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)).
% 269.02/269.11 ** KEPT (pick-wt=16): 414 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)).
% 269.02/269.11 ** KEPT (pick-wt=16): 415 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)).
% 269.02/269.11 ** KEPT (pick-wt=14): 416 [] c_Pair(A,B,C,D)!=c_Pair(E,F,C,D)|B=F.
% 269.02/269.11 ** KEPT (pick-wt=14): 417 [] c_Pair(A,B,C,D)!=c_Pair(E,F,C,D)|A=E.
% 269.02/269.11 ** KEPT (pick-wt=9): 418 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))).
% 269.02/269.11 ** KEPT (pick-wt=19): 419 [] -class_Orderings_Olinorder(A)|B=C|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)).
% 269.02/269.11 Following clause subsumed by 419 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))|C=B|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)).
% 269.02/269.11 Following clause subsumed by 419 during input processing: 0 [] -class_Orderings_Olinorder(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B))|C=B.
% 269.02/269.11 Following clause subsumed by 419 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)).
% 269.02/269.11 ** KEPT (pick-wt=19): 420 [] -class_Ring__and__Field_Oordered__idom(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B))|C=B.
% 269.02/269.11 ** KEPT (pick-wt=9): 421 [] -class_Orderings_Opreorder(A)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)).
% 269.02/269.11 ** KEPT (pick-wt=9): 422 [] -class_Orderings_Olinorder(A)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)).
% 269.02/269.11 ** KEPT (pick-wt=9): 423 [] -class_Orderings_Oorder(A)| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)).
% 269.02/269.11 ** KEPT (pick-wt=7): 424 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),A)).
% 269.02/269.11 Following clause subsumed by 424 during input processing: 0 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),A)).
% 269.02/269.11 ** KEPT (pick-wt=23): 425 [] -class_Orderings_Opreorder(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),D),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)).
% 269.02/269.11 ** KEPT (pick-wt=23): 426 [] -class_Orderings_Oorder(A)|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D))| -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),D),C)).
% 269.02/269.11 ** KEPT (pick-wt=8): 427 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))).
% 269.02/269.11 Following clause subsumed by 427 during input processing: 0 [] -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))).
% 269.02/269.11 ** KEPT (pick-wt=11): 428 [] hBOOL(hAPP(hAPP(c_in(A),B),C))| -hBOOL(hAPP(C,B)).
% 269.02/269.11 ** KEPT (pick-wt=11): 429 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(hAPP(c_in(C),B),A)).
% 269.02/269.11 ** KEPT (pick-wt=3): 431 [copy,430,flip.1] v_b____!=v_a____.
% 269.02/269.11 ** KEPT (pick-wt=13): 432 [] -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_Lba____)).
% 269.02/269.11 ** KEPT (pick-wt=8): 433 [] class_Finite__Set_Ofinite_Ofinite(tc_prod(A,B))| -class_Finite__Set_Ofinite_Ofinite(B)| -class_Finite__Set_Ofinite_Ofinite(A).
% 269.02/269.11 ** KEPT (pick-wt=6): 434 [] class_Lattices_Olower__semilattice(tc_fun(A,B))| -class_Lattices_Olattice(B).
% 269.02/269.11 ** KEPT (pick-wt=6): 435 [] class_Lattices_Obounded__lattice(tc_fun(A,B))| -class_Lattices_Obounded__lattice(B).
% 269.02/269.11 ** KEPT (pick-wt=6): 436 [] class_Lattices_Oboolean__algebra(tc_fun(A,B))| -class_Lattices_Oboolean__algebra(B).
% 269.02/269.11 ** KEPT (pick-wt=8): 437 [] class_Finite__Set_Ofinite_Ofinite(tc_fun(A,B))| -class_Finite__Set_Ofinite_Ofinite(B)| -class_Finite__Set_Ofinite_Ofinite(A).
% 269.02/269.11 ** KEPT (pick-wt=6): 438 [] class_Orderings_Opreorder(tc_fun(A,B))| -class_Orderings_Opreorder(B).
% 269.02/269.11 ** KEPT (pick-wt=6): 439 [] class_Lattices_Olattice(tc_fun(A,B))| -class_Lattices_Olattice(B).
% 269.02/269.11 ** KEPT (pick-wt=6): 440 [] class_Orderings_Oorder(tc_fun(A,B))| -class_Orderings_Oorder(B).
% 269.02/269.11 ** KEPT (pick-wt=10): 441 [] A=B| -hBOOL(hAPP(hAPP(c_fe_qual(C),A),B)).
% 269.02/269.11 157 back subsumes 69.
% 269.02/269.11 225 back subsumes 172.
% 269.02/269.11 241 back subsumes 239.
% 269.02/269.11 356 back subsumes 313.
% 269.02/269.11 357 back subsumes 314.
% 269.02/269.11 375 back subsumes 362.
% 269.02/269.11 384 back subsumes 383.
% 269.02/269.11 387 back subsumes 386.
% 269.02/269.11 424 back subsumes 418.
% 269.02/269.11
% 269.02/269.11 ------------> process sos:
% 269.02/269.11 ** KEPT (pick-wt=3): 505 [] A=A.
% 269.02/269.11 ** KEPT (pick-wt=10): 506 [] hBOOL(hAPP(hAPP(c_in(A),B),c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)))).
% 269.02/269.11 ** KEPT (pick-wt=19): 507 [] hBOOL(hAPP(hAPP(c_in(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),C)))|hBOOL(hAPP(hAPP(c_in(A),B),C)).
% 269.02/269.11 ** KEPT (pick-wt=25): 508 [] c_Set_Ovimage(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,tc_bool)),E,D)=c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(A,B,E,D),c_Set_Ovimage(A,C,E,D),tc_fun(E,tc_bool)).
% 269.02/269.11 ** KEPT (pick-wt=13): 509 [] hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),B))=B.
% 269.02/269.11 ---> New Demodulator: 510 [new_demod,509] hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),B))=B.
% 269.02/269.11 ** KEPT (pick-wt=21): 511 [] c_Set_Ovimage(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(B,tc_bool)),C),D,B)=hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(D,tc_bool)),c_Set_Ovimage(A,C,D,B)).
% 269.02/269.11 ** KEPT (pick-wt=13): 512 [] c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_fun(C,tc_bool)).
% 269.02/269.11 ** KEPT (pick-wt=16): 513 [] c_Lattices_Olower__semilattice__class_Oinf(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(B,tc_bool)),A),tc_fun(B,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)).
% 269.02/269.11 ** KEPT (pick-wt=16): 514 [] c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),B),B,tc_fun(A,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)).
% 269.02/269.11 ** KEPT (pick-wt=13): 515 [] c_Set_Ovimage(A,c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),C,B)=c_Orderings_Otop__class_Otop(tc_fun(C,tc_bool)).
% 269.02/269.11 ** KEPT (pick-wt=13): 516 [] c_Relation_OImage(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B,C)=c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)).
% 269.02/269.11 ** KEPT (pick-wt=14): 517 [] c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B,tc_fun(A,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)).
% 269.02/269.11 ---> New Demodulator: 518 [new_demod,517] c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B,tc_fun(A,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)).
% 269.02/269.11 ** KEPT (pick-wt=14): 519 [] c_Lattices_Olower__semilattice__class_Oinf(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),tc_fun(B,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)).
% 269.02/269.11 ---> New Demodulator: 520 [new_demod,519] c_Lattices_Olower__semilattice__class_Oinf(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),tc_fun(B,tc_bool))=c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)).
% 269.02/269.11 ** KEPT (pick-wt=6): 521 [] c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A).
% 269.02/269.11 ** KEPT (pick-wt=23): 522 [] c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)).
% 269.02/269.11 ---> New Demodulator: 523 [new_demod,522] c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)).
% 269.02/269.11 ** KEPT (pick-wt=23): 524 [] c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,tc_bool)),tc_fun(D,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_fun(D,tc_bool)),tc_fun(D,tc_bool)).
% 269.02/269.11 ** KEPT (pick-wt=14): 525 [] hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)).
% 269.02/269.11 ---> New Demodulator: 526 [new_demod,525] hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)))=c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)).
% 269.02/269.11 ** KEPT (pick-wt=11): 527 [] c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),B,tc_fun(A,tc_bool))=B.
% 269.02/269.11 ---> New Demodulator: 528 [new_demod,527] c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),B,tc_fun(A,tc_bool))=B.
% 269.02/269.11 ** KEPT (pick-wt=11): 529 [] c_Lattices_Olower__semilattice__class_Oinf(A,c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),tc_fun(B,tc_bool))=A.
% 269.02/269.11 ---> New Demodulator: 530 [new_demod,529] c_Lattices_Olower__semilattice__class_Oinf(A,c_Orderings_Otop__class_Otop(tc_fun(B,tc_bool)),tc_fun(B,tc_bool))=A.
% 269.02/269.11 ** KEPT (pick-wt=7): 531 [] hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),B)).
% 269.02/269.11 ** KEPT (pick-wt=7): 532 [] c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B,A).
% 269.02/269.11 ** KEPT (pick-wt=14): 534 [copy,533,flip.1] c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool))=hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))).
% 269.02/269.11 ---> New Demodulator: 535 [new_demod,534] c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool))=hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))).
% 269.02/269.11 ** KEPT (pick-wt=18): 536 [] c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)),tc_fun(C,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)).
% 269.02/269.11 ---> New Demodulator: 537 [new_demod,536] c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)),tc_fun(C,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)).
% 269.02/269.11 ** KEPT (pick-wt=8): 538 [] c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_fun(B,tc_bool))=A.
% 269.02/269.11 ---> New Demodulator: 539 [new_demod,538] c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_fun(B,tc_bool))=A.
% 269.02/269.11 ** KEPT (pick-wt=13): 540 [] c_Set_Ovimage(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),C,B)=c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)).
% 269.02/269.11 ** KEPT (pick-wt=14): 541 [] c_Relation_OImage(c_Relation_OId__on(A,B),C,B,B)=c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_fun(B,tc_bool)).
% 269.02/269.11 ** KEPT (pick-wt=15): 542 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.11 ** KEPT (pick-wt=15): 543 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B).
% 269.02/269.11 ** KEPT (pick-wt=10): 544 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.11 ---> New Demodulator: 545 [new_demod,544] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.11 ** KEPT (pick-wt=10): 546 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.11 ---> New Demodulator: 547 [new_demod,546] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.11 ** KEPT (pick-wt=54): 548 [] c_Set_Ovimage(c_COMBC(c_COMBC(c_COMBB(c_HOL_OIf(A),c_COMBC(c_in(B),C,B,tc_fun(B,tc_bool),tc_bool),tc_bool,tc_fun(A,tc_fun(A,A)),B),D,B,A,tc_fun(A,A)),E,B,A,A),F,B,A)=c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))|hBOOL(hAPP(hAPP(c_in(A),E),F))|hBOOL(hAPP(hAPP(c_in(A),D),F)).
% 269.02/269.11 ** KEPT (pick-wt=8): 549 [] c_Divides_Odiv__class_Odiv(A,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=A.
% 269.02/269.11 ---> New Demodulator: 550 [new_demod,549] c_Divides_Odiv__class_Odiv(A,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=A.
% 269.02/269.11 ** KEPT (pick-wt=19): 551 [] c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C),B,tc_nat)=c_Divides_Odiv__class_Omod(C,B,tc_nat).
% 269.02/269.11 ---> New Demodulator: 552 [new_demod,551] c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C),B,tc_nat)=c_Divides_Odiv__class_Omod(C,B,tc_nat).
% 269.02/269.11 ** KEPT (pick-wt=23): 553 [] c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat)=c_Divides_Odiv__class_Odiv(B,C,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.11 ** KEPT (pick-wt=41): 555 [copy,554,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),c_Divides_Odiv__class_Odiv(C,B,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),c_Divides_Odiv__class_Omod(C,B,tc_nat)),B,tc_nat))=c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 269.02/269.11 ---> New Demodulator: 556 [new_demod,555] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),c_Divides_Odiv__class_Odiv(C,B,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),c_Divides_Odiv__class_Omod(C,B,tc_nat)),B,tc_nat))=c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=24): 557 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),C)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_nat).
% 269.02/269.12 ---> New Demodulator: 558 [new_demod,557] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),C)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=24): 559 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat))=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat).
% 269.02/269.12 ---> New Demodulator: 560 [new_demod,559] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat))=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=10): 561 [] c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),A,tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.12 ---> New Demodulator: 562 [new_demod,561] c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),A,tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.12 Following clause subsumed by 505 during input processing: 0 [demod,562] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.12 ** KEPT (pick-wt=38): 564 [copy,563,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)),D)).
% 269.02/269.12 ---> New Demodulator: 565 [new_demod,564] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)),D)).
% 269.02/269.12 ** KEPT (pick-wt=15): 566 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)).
% 269.02/269.12 ** KEPT (pick-wt=19): 568 [copy,567,flip.1] hAPP(c_Nat_Ocompow(A,B,C,C),hAPP(B,D))=hAPP(B,hAPP(c_Nat_Ocompow(A,B,C,C),D)).
% 269.02/269.12 ---> New Demodulator: 569 [new_demod,568] hAPP(c_Nat_Ocompow(A,B,C,C),hAPP(B,D))=hAPP(B,hAPP(c_Nat_Ocompow(A,B,C,C),D)).
% 269.02/269.12 ** KEPT (pick-wt=13): 571 [copy,570,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.12 ---> New Demodulator: 572 [new_demod,571] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.12 ** KEPT (pick-wt=16): 573 [] hAPP(c_COMBS(A,B,C,D,E),F)=hAPP(hAPP(A,F),hAPP(B,F)).
% 269.02/269.12 ** KEPT (pick-wt=8): 574 [] c_Relation_ODomain(c_Relation_OId__on(A,B),B,B)=A.
% 269.02/269.12 ---> New Demodulator: 575 [new_demod,574] c_Relation_ODomain(c_Relation_OId__on(A,B),B,B)=A.
% 269.02/269.12 ** KEPT (pick-wt=23): 576 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)).
% 269.02/269.12 ---> New Demodulator: 577 [new_demod,576] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)).
% 269.02/269.12 ** KEPT (pick-wt=23): 578 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)).
% 269.02/269.12 ** KEPT (pick-wt=13): 579 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A).
% 269.02/269.12 ** KEPT (pick-wt=18): 581 [copy,580,flip.1] c_Suc(c_Divides_Odiv__class_Omod(A,B,tc_nat))=c_Divides_Odiv__class_Omod(c_Suc(A),B,tc_nat)|c_Suc(c_Divides_Odiv__class_Omod(A,B,tc_nat))=B.
% 269.02/269.12 ** KEPT (pick-wt=33): 582 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)).
% 269.02/269.12 Following clause subsumed by 582 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)).
% 269.02/269.12 ** KEPT (pick-wt=6): 583 [] c_Relation_Orefl__on(A,c_Relation_OId__on(A,B),B).
% 269.02/269.12 ** KEPT (pick-wt=13): 584 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.12 ---> New Demodulator: 585 [new_demod,584] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.12 ** KEPT (pick-wt=9): 586 [] c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.12 ** KEPT (pick-wt=15): 588 [copy,587,flip.1] c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)).
% 269.02/269.12 ---> New Demodulator: 589 [new_demod,588] c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)).
% 269.02/269.12 Following clause subsumed by 566 during input processing: 0 [demod,589] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)).
% 269.02/269.12 ** KEPT (pick-wt=13): 591 [copy,590,demod,589] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)))).
% 269.02/269.12 ** KEPT (pick-wt=11): 592 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.12 ---> New Demodulator: 593 [new_demod,592] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=9): 595 [copy,594,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 269.02/269.12 ---> New Demodulator: 596 [new_demod,595] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 269.02/269.12 ** KEPT (pick-wt=9): 597 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 269.02/269.12 ---> New Demodulator: 598 [new_demod,597] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 269.02/269.12 Following clause subsumed by 505 during input processing: 0 [demod,596] A=A.
% 269.02/269.12 ** KEPT (pick-wt=8): 599 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_Suc(A))).
% 269.02/269.12 Following clause subsumed by 599 during input processing: 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_Suc(A))).
% 269.02/269.12 Following clause subsumed by 599 during input processing: 0 [unit_del,424] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_Suc(A))).
% 269.02/269.12 ** KEPT (pick-wt=15): 600 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_Suc(B)))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)).
% 269.02/269.12 Following clause subsumed by 599 during input processing: 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))).
% 269.02/269.12 ** KEPT (pick-wt=13): 602 [copy,601,demod,589] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_Suc(A)))).
% 269.02/269.12 Following clause subsumed by 591 during input processing: 0 [demod,589] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)))).
% 269.02/269.12 ** KEPT (pick-wt=13): 603 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 269.02/269.12 ** KEPT (pick-wt=19): 604 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Suc(B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)).
% 269.02/269.12 ---> New Demodulator: 605 [new_demod,604] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Suc(B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)).
% 269.02/269.12 ** KEPT (pick-wt=19): 606 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Suc(A)),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)).
% 269.02/269.12 ** KEPT (pick-wt=8): 607 [] c_Relation_ORange(c_Relation_OId__on(A,B),B,B)=A.
% 269.02/269.12 ---> New Demodulator: 608 [new_demod,607] c_Relation_ORange(c_Relation_OId__on(A,B),B,B)=A.
% 269.02/269.12 Following clause subsumed by 505 during input processing: 0 [demod,589,552] c_Divides_Odiv__class_Omod(c_Suc(C),B,tc_nat)=c_Divides_Odiv__class_Omod(c_Suc(C),B,tc_nat).
% 269.02/269.12 Following clause subsumed by 505 during input processing: 0 [demod,605,545,596] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.12 ** KEPT (pick-wt=9): 609 [] c_Divides_Odiv__class_Omod(A,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.12 ---> New Demodulator: 610 [new_demod,609] c_Divides_Odiv__class_Omod(A,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.12 Following clause subsumed by 505 during input processing: 0 [demod,596] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.12 ** KEPT (pick-wt=40): 612 [copy,611,demod,560,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Odiv(B,C,tc_nat))),c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat),C,tc_nat))=c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),C,tc_nat).
% 269.02/269.12 ---> New Demodulator: 613 [new_demod,612] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Odiv(B,C,tc_nat))),c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat),C,tc_nat))=c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),C,tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=9): 615 [copy,614,demod,547,547] c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.12 ---> New Demodulator: 616 [new_demod,615] c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=35): 618 [copy,617,demod,560,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Odiv(B,A,tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat)),c_Divides_Odiv__class_Omod(B,A,tc_nat))=c_Divides_Odiv__class_Omod(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat).
% 269.02/269.12 ---> New Demodulator: 619 [new_demod,618] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Odiv(B,A,tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat)),c_Divides_Odiv__class_Omod(B,A,tc_nat))=c_Divides_Odiv__class_Omod(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=17): 620 [] c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_nat)=c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(A,B,tc_nat),C,tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=14): 622 [copy,621,flip.1] c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(A,B,tc_nat)),B,tc_nat)=c_Divides_Odiv__class_Omod(c_Suc(A),B,tc_nat).
% 269.02/269.12 ---> New Demodulator: 623 [new_demod,622] c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(A,B,tc_nat)),B,tc_nat)=c_Divides_Odiv__class_Omod(c_Suc(A),B,tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=16): 624 [] hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(A,B)),c_Arrow__Order__Mirabelle_OLin))|A=B.
% 269.02/269.12 Following clause subsumed by 505 during input processing: 0 [demod,598] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 269.02/269.12 ** KEPT (pick-wt=12): 625 [] c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=23): 626 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)).
% 269.02/269.12 ---> New Demodulator: 627 [new_demod,626] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)).
% 269.02/269.12 ** KEPT (pick-wt=28): 628 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)).
% 269.02/269.12 ** KEPT (pick-wt=28): 630 [copy,629,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)).
% 269.02/269.12 ---> New Demodulator: 631 [new_demod,630] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)).
% 269.02/269.12 ** KEPT (pick-wt=9): 632 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(A))).
% 269.02/269.12 Following clause subsumed by 632 during input processing: 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(A))).
% 269.02/269.12 ** KEPT (pick-wt=12): 633 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))).
% 269.02/269.12 ** KEPT (pick-wt=21): 634 [] A=B|B=A|hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omkbot(C,A))).
% 269.02/269.12 ** KEPT (pick-wt=18): 636 [copy,635,factor_simp] A=B|hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_Omktop(C,B))).
% 269.02/269.12 ** KEPT (pick-wt=18): 637 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1(A,B)))|A=B.
% 269.02/269.12 ** KEPT (pick-wt=20): 638 [] hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,B,A,A)),c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_prod(A,A),tc_bool))).
% 269.02/269.12 ** KEPT (pick-wt=84): 639 [] hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_COMBC(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),A,tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),v_Lab____,tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lba____,tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),c_Arrow__Order__Mirabelle_OProf)).
% 269.02/269.12 ** KEPT (pick-wt=84): 640 [] hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBC(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),A,tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),v_Lab____,tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lba____,tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)))),c_Arrow__Order__Mirabelle_OLin)).
% 269.02/269.12 ** KEPT (pick-wt=12): 641 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A))|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=17): 642 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A))|B=A.
% 269.02/269.12 Following clause subsumed by 642 during input processing: 0 [factor_simp] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C))|C=B|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),B)).
% 269.02/269.12 Following clause subsumed by 642 during input processing: 0 [] hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B))|hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A))|B=A.
% 269.02/269.12 ** KEPT (pick-wt=14): 643 [] hAPP(c_COMBB(A,B,C,D,E),F)=hAPP(A,hAPP(B,F)).
% 269.02/269.12 ---> New Demodulator: 644 [new_demod,643] hAPP(c_COMBB(A,B,C,D,E),F)=hAPP(A,hAPP(B,F)).
% 269.02/269.12 ** KEPT (pick-wt=14): 645 [] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 269.02/269.12 ** KEPT (pick-wt=11): 646 [] hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)).
% 269.02/269.12 Following clause subsumed by 646 during input processing: 0 [] hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),v_Lba____),c_Arrow__Order__Mirabelle_OLin)).
% 269.02/269.12 ** KEPT (pick-wt=2): 647 [] c_Arrow__Order__Mirabelle_Ounanimity(v_F).
% 269.02/269.12 ** KEPT (pick-wt=20): 648 [] hBOOL(hAPP(hAPP(c_in(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),hAPP(v_F,c_COMBK(v_Lba____,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_Arrow__Order__Mirabelle_Oindi))),c_Arrow__Order__Mirabelle_OLin)).
% 269.02/269.12 ** KEPT (pick-wt=87): 649 [] hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(v_a____,v_b____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,c_COMBC(c_COMBC(c_COMBB(c_HOL_OIf(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),c_COMBC(c_COMBB(c_HOL_Oord__class_Oless(tc_nat),v_h____,tc_nat,tc_fun(tc_nat,tc_bool),tc_Arrow__Order__Mirabelle_Oindi),c_HOL_Ozero__class_Ozero(tc_nat),tc_Arrow__Order__Mirabelle_Oindi,tc_nat,tc_bool),tc_bool,tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),tc_Arrow__Order__Mirabelle_Oindi),v_Lab____,tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_Lba____,tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))))).
% 269.02/269.12 ** KEPT (pick-wt=2): 650 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 651 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 652 [] class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 653 [] class_Ring__and__Field_Oordered__semiring__strict(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 654 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 655 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 656 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 657 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 658 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 659 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 660 [] class_OrderedGroup_Oab__semigroup__mult(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 661 [] class_OrderedGroup_Ocomm__monoid__mult(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 662 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 663 [] class_Ring__and__Field_Ocomm__semiring(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 664 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 665 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 666 [] class_Lattices_Olower__semilattice(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 667 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 668 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 669 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 670 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 671 [] class_Ring__and__Field_Osemiring(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 672 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 673 [] class_Divides_Osemiring__div(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 674 [] class_Nat_Osemiring__char__0(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 675 [] class_Orderings_Opreorder(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 676 [] class_Orderings_Olinorder(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 677 [] class_Lattices_Olattice(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 678 [] class_Orderings_Oorder(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 679 [] class_Power_Opower(tc_nat).
% 269.02/269.12 ** KEPT (pick-wt=2): 680 [] class_Lattices_Olower__semilattice(tc_bool).
% 269.02/269.12 ** KEPT (pick-wt=2): 681 [] class_Lattices_Obounded__lattice(tc_bool).
% 269.02/269.12 ** KEPT (pick-wt=2): 682 [] class_Lattices_Oboolean__algebra(tc_bool).
% 269.02/269.12 ** KEPT (pick-wt=2): 683 [] class_Finite__Set_Ofinite_Ofinite(tc_bool).
% 269.02/269.12 ** KEPT (pick-wt=2): 684 [] class_Orderings_Opreorder(tc_bool).
% 269.02/269.12 ** KEPT (pick-wt=2): 685 [] class_Lattices_Olattice(tc_bool).
% 269.02/269.12 ** KEPT (pick-wt=2): 686 [] class_Orderings_Oorder(tc_bool).
% 269.02/269.12 Following clause subsumed by 645 during input processing: 0 [] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 269.02/269.12 Following clause subsumed by 505 during input processing: 0 [demod,644] hAPP(A,hAPP(B,F))=hAPP(A,hAPP(B,F)).
% 269.02/269.12 ** KEPT (pick-wt=7): 687 [] hBOOL(hAPP(hAPP(c_fe_qual(A),B),B)).
% 269.02/269.12 Following clause subsumed by 505 during input processing: 0 [copy,505,flip.1] A=A.
% 269.02/269.12 505 back subsumes 502.
% 269.02/269.12 505 back subsumes 501.
% 269.02/269.12 505 back subsumes 500.
% 269.02/269.12 505 back subsumes 497.
% 269.02/269.12 505 back subsumes 459.
% 269.02/269.12 ** KEPT (pick-wt=25): 688 [copy,508,flip.1] c_Lattices_Olower__semilattice__class_Oinf(c_Set_Ovimage(A,B,C,D),c_Set_Ovimage(A,E,C,D),tc_fun(C,tc_bool))=c_Set_Ovimage(A,c_Lattices_Olower__semilattice__class_Oinf(B,E,tc_fun(D,tc_bool)),C,D).
% 269.02/269.12 >>>> Starting back demodulation with 510.
% 269.02/269.12 ** KEPT (pick-wt=21): 689 [copy,511,flip.1] hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),c_Set_Ovimage(B,C,A,D))=c_Set_Ovimage(B,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(D,tc_bool)),C),A,D).
% 269.02/269.12 Following clause subsumed by 512 during input processing: 0 [copy,512,flip.1] c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_fun(C,tc_bool)).
% 269.02/269.12 ** KEPT (pick-wt=16): 690 [copy,513,flip.1] c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(B,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),B),tc_fun(A,tc_bool)).
% 269.02/269.12 ** KEPT (pick-wt=16): 691 [copy,514,flip.1] c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),B),B,tc_fun(A,tc_bool)).
% 269.02/269.12 ** KEPT (pick-wt=23): 692 [copy,515,flip.1,demod,535,535] hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(A,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)))=c_Set_Ovimage(B,hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(C,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))),A,C).
% 269.02/269.12 ** KEPT (pick-wt=13): 693 [copy,516,flip.1] c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))=c_Relation_OImage(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C,A).
% 269.02/269.12 >>>> Starting back demodulation with 518.
% 269.02/269.12 >>>> Starting back demodulation with 520.
% 269.02/269.12 >>>> Starting back demodulation with 523.
% 269.02/269.12 Following clause subsumed by 524 during input processing: 0 [copy,524,flip.1] c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,tc_bool)),tc_fun(D,tc_bool))=c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_fun(D,tc_bool)),tc_fun(D,tc_bool)).
% 269.02/269.12 >>>> Starting back demodulation with 526.
% 269.02/269.12 >> back demodulating 444 with 526.
% 269.02/269.12 >>>> Starting back demodulation with 528.
% 269.02/269.12 >>>> Starting back demodulation with 530.
% 269.02/269.12 >>>> Starting back demodulation with 535.
% 269.02/269.12 >> back demodulating 531 with 535.
% 269.02/269.12 >> back demodulating 529 with 535.
% 269.02/269.12 >> back demodulating 527 with 535.
% 269.02/269.12 >> back demodulating 525 with 535.
% 269.02/269.12 >> back demodulating 515 with 535.
% 269.02/269.12 >> back demodulating 506 with 535.
% 269.02/269.12 >> back demodulating 454 with 535.
% 269.02/269.12 >> back demodulating 137 with 535.
% 269.02/269.12 >> back demodulating 62 with 535.
% 269.02/269.12 >> back demodulating 61 with 535.
% 269.02/269.12 >> back demodulating 49 with 535.
% 269.02/269.12 >>>> Starting back demodulation with 537.
% 269.02/269.12 >>>> Starting back demodulation with 539.
% 269.02/269.12 >> back demodulating 445 with 539.
% 269.02/269.12 >> back demodulating 443 with 539.
% 269.02/269.12 >> back demodulating 442 with 539.
% 269.02/269.12 ** KEPT (pick-wt=13): 707 [copy,540,flip.1] c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))=c_Set_Ovimage(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),A,C).
% 269.02/269.12 ** KEPT (pick-wt=14): 708 [copy,541,flip.1] c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool))=c_Relation_OImage(c_Relation_OId__on(A,C),B,C,C).
% 269.02/269.12 Following clause subsumed by 505 during input processing: 0 [copy,542,flip.1,demod,545,545] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.12 Following clause subsumed by 505 during input processing: 0 [copy,543,flip.1,demod,547,547] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 269.02/269.12 >>>> Starting back demodulation with 545.
% 269.02/269.12 >> back demodulating 542 with 545.
% 269.02/269.12 >> back demodulating 494 with 545.
% 269.02/269.12 >> back demodulating 489 with 545.
% 269.02/269.12 >> back demodulating 453 with 545.
% 269.02/269.12 >>>> Starting back demodulation with 547.
% 269.02/269.12 >> back demodulating 543 with 547.
% 269.02/269.12 >> back demodulating 493 with 547
% 269.02/269.12 Search stopped in tp_alloc by max_mem option.
% 269.02/269.12 .
% 269.02/269.12 >> back demodulating 452 with 547.
% 269.02/269.12 >>>> Starting back demodulation with 550.
% 269.02/269.12 >>>> Starting back demodulation with 552.
% 269.02/269.12 >>>> Starting back demodulation with 556.
% 269.02/269.12 >>>> Starting back demodulation with 558.
% 269.02/269.12 >>>> Starting back demodulation with 560.
% 269.02/269.12 >> back demodulating 487 with 560.
% 269.02/269.12 >> back demodulating 323 with 560.
% 269.02/269.12 >>>> Starting back demodulation with 562.
% 269.02/269.12 >>>> Starting back demodulation with 565.
% 269.02/269.12 ** KEPT (pick-wt=15): 713 [copy,566,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B).
% 269.02/269.12 >>>> Starting back demodulation with 569.
% 269.02/269.12 >>>> Starting back demodulation with 572.
% 269.02/269.12 ** KEPT (pick-wt=16): 714 [copy,573,flip.1] hAPP(hAPP(A,B),hAPP(C,B))=hAPP(c_COMBS(A,C,D,E,F),B).
% 269.02/269.12 >>>> Starting back demodulation with 575.
% 269.02/269.12 >>>> Starting back demodulation with 577.
% 269.02/269.12 >> back demodulating 555 with 577.
% 269.02/269.12 Following clause subsumed by 578 during input processing: 0 [copy,578,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)).
% 269.02/269.12 Following clause subsumed by 579 during input processing: 0 [copy,579,flip.1] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A).
% 269.02/269.12 ** KEPT (pick-wt=23): 717 [copy,582,flip.1,demod,631,631] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B)).
% 269.02/269.12 >>>> Starting back demodulation with 585.
% 269.02/269.12
% 269.02/269.12 Search stopped in tp_alloc by max_mem option.
% 269.02/269.12
% 269.02/269.12 ============ end of search ============
% 269.02/269.12
% 269.02/269.12 -------------- statistics -------------
% 269.02/269.12 clauses given 0
% 269.02/269.12 clauses generated 79
% 269.02/269.12 clauses kept 636
% 269.02/269.12 clauses forward subsumed 115
% 269.02/269.12 clauses back subsumed 14
% 269.02/269.12 Kbytes malloced 11718
% 269.02/269.12
% 269.02/269.12 ----------- times (seconds) -----------
% 269.02/269.12 user CPU time 0.10 (0 hr, 0 min, 0 sec)
% 269.02/269.12 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 269.02/269.12 wall-clock time 269 (0 hr, 4 min, 29 sec)
% 269.02/269.12
% 269.02/269.12 Process 13124 finished Wed Jul 27 09:09:54 2022
% 269.02/269.12 Otter interrupted
% 269.02/269.12 PROOF NOT FOUND
%------------------------------------------------------------------------------