TSTP Solution File: SWV658-1 by Otter---3.3

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SWV658-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Jul 27 13:21:20 EDT 2022

% Result   : Unknown 281.78s 281.85s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWV658-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Jul 27 05:53:55 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 277.97/278.05  ----- Otter 3.3f, August 2004 -----
% 277.97/278.05  The process was started by sandbox2 on n011.cluster.edu,
% 277.97/278.05  Wed Jul 27 05:53:55 2022
% 277.97/278.05  The command was "./otter".  The process ID is 23144.
% 277.97/278.05  
% 277.97/278.05  set(prolog_style_variables).
% 277.97/278.05  set(auto).
% 277.97/278.05     dependent: set(auto1).
% 277.97/278.05     dependent: set(process_input).
% 277.97/278.05     dependent: clear(print_kept).
% 277.97/278.05     dependent: clear(print_new_demod).
% 277.97/278.05     dependent: clear(print_back_demod).
% 277.97/278.05     dependent: clear(print_back_sub).
% 277.97/278.05     dependent: set(control_memory).
% 277.97/278.05     dependent: assign(max_mem, 12000).
% 277.97/278.05     dependent: assign(pick_given_ratio, 4).
% 277.97/278.05     dependent: assign(stats_level, 1).
% 277.97/278.05     dependent: assign(max_seconds, 10800).
% 277.97/278.05  clear(print_given).
% 277.97/278.05  
% 277.97/278.05  list(usable).
% 277.97/278.05  0 [] A=A.
% 277.97/278.05  0 [] hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 277.97/278.05  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).
% 277.97/278.05  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Finite__Set_Osetsum(V_g,V_A,T_b,T_a)),V_y)=c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(T_a),V_g,T_a,tc_fun(T_a,T_a),T_b),V_y,T_b,T_a,T_a),V_A,T_b,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Ofield(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(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).
% 277.97/278.05  0 [] -class_RealVector_Oreal__normed__field(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_Finite__Set_Osetsum(V_g,V_A,T_b,T_a)),V_y)=c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(T_a),V_g,T_a,tc_fun(T_a,T_a),T_b),V_y,T_b,T_a,T_a),V_A,T_b,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_lesse_quals(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)| -c_lesse_quals(V_a,V_b,T_a).
% 277.97/278.05  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.
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add(T_a)|c_lesse_quals(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),T_a)| -c_lesse_quals(V_c,V_d,T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 277.97/278.05  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.
% 277.97/278.05  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.
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)| -c_lesse_quals(V_c,V_d,T_a)| -c_lesse_quals(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a).
% 277.97/278.05  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)).
% 277.97/278.05  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)).
% 277.97/278.05  0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_e)),V_c),V_d,T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d),T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_e)),V_c),V_d,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_lesse_quals(V_c,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_a)),V_e)),V_d),T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d),T_a)| -c_lesse_quals(V_c,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_a)),V_e)),V_d),T_a).
% 277.97/278.05  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y)),V_ya)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_ya)).
% 277.97/278.05  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_a_H)),V_b)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_H),V_b)).
% 277.97/278.05  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_b_H))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(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),V_b_H)).
% 277.97/278.05  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_xa),V_y)).
% 277.97/278.05  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.
% 277.97/278.05  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).
% 277.97/278.05  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)).
% 277.97/278.05  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b)=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)).
% 277.97/278.05  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)),V_y)=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y)).
% 277.97/278.05  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b))=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b)).
% 277.97/278.05  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_xa),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x))=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_xa),V_x)).
% 277.97/278.05  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).
% 277.97/278.05  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).
% 277.97/278.05  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)).
% 277.97/278.05  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b),T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(V_a,hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b),T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y)!=c_HOL_Ozero__class_Ozero(T_a)|V_x=V_y.
% 277.97/278.05  0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=V_b.
% 277.97/278.05  0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=V_b.
% 277.97/278.05  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.
% 277.97/278.05  0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x)=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_a)=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))=V_a.
% 277.97/278.05  0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x)=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x)=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.05  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).
% 277.97/278.05  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).
% 277.97/278.05  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)).
% 277.97/278.05  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).
% 277.97/278.05  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).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(V_b,hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),T_a)| -c_lesse_quals(V_a,hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b),T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(V_a,hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b),T_a)| -c_lesse_quals(V_b,hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b),V_a,T_a)| -c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),V_b,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),V_b,T_a)| -c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b),V_a,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_a).
% 277.97/278.05  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.
% 277.97/278.05  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.
% 277.97/278.05  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)).
% 277.97/278.05  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)).
% 277.97/278.05  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.
% 277.97/278.05  0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_i),V_j)),V_k)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_i),V_k)),V_j).
% 277.97/278.05  0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_xa),V_y)!=hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x)|V_xa=V_y.
% 277.97/278.05  0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_x)!=hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)|V_x_H=V_y_H.
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),T_a).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,V_n)),c_HOL_Oone__class_Oone(tc_nat))=V_n.
% 277.97/278.05  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.
% 277.97/278.05  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.
% 277.97/278.05  0 [] -class_Orderings_Oorder(T_a)|V_x=V_y| -c_lesse_quals(V_y,V_x,T_a)| -c_lesse_quals(V_x,V_y,T_a).
% 277.97/278.05  0 [] -class_Orderings_Oorder(T_a)|V_x=V_y| -c_lesse_quals(V_y,V_x,T_a)| -c_lesse_quals(V_x,V_y,T_a).
% 277.97/278.05  0 [] -class_Orderings_Oorder(T_a)|V_x=V_y| -c_lesse_quals(V_x,V_y,T_a)| -c_lesse_quals(V_y,V_x,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y)!=hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)|c_lesse_quals(V_y,V_x,T_a)| -c_lesse_quals(V_y_H,V_x_H,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y)!=hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x_H),V_y_H)|c_lesse_quals(V_y_H,V_x_H,T_a)| -c_lesse_quals(V_y,V_x,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),hAPP(c_Suc,V_n))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),c_HOL_Oone__class_Oone(tc_nat))),V_n).
% 277.97/278.05  0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_y)).
% 277.97/278.05  0 [] -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_y)).
% 277.97/278.05  0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)).
% 277.97/278.05  0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(V_a,hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),V_a,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Ocomm__ring(T_a)| -class_OrderedGroup_Omonoid__mult(T_a)|c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(T_a),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(T_a),c_COMBB(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_z),V_h),T_a),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),tc_nat,T_a,tc_nat),T_a,tc_fun(T_a,T_a),tc_nat),c_Power_Opower__class_Opower(V_z,T_a),tc_nat,T_a,T_a),T_a,tc_fun(T_a,T_a),tc_nat),hAPP(c_Power_Opower__class_Opower(V_z,T_a),V_m),tc_nat,T_a,T_a),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat),tc_nat,T_a)=c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(T_a),c_Power_Opower__class_Opower(V_z,T_a),T_a,tc_fun(T_a,T_a),tc_nat),c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(T_a),c_COMBB(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_z),V_h),T_a),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),tc_nat,T_a,tc_nat),T_a,tc_fun(T_a,T_a),tc_nat),c_COMBB(c_Power_Opower__class_Opower(V_z,T_a),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),tc_nat,T_a,tc_nat),tc_nat,T_a,T_a),tc_nat,T_a,T_a),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat),tc_nat,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(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).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_lesse_quals(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),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(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),T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add(T_a)|c_lesse_quals(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)| -c_lesse_quals(V_a,V_b,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add(T_a)|c_lesse_quals(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),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_b)=V_a.
% 277.97/278.05  0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(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))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_c),V_d)).
% 277.97/278.05  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).
% 277.97/278.05  0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_b)=V_a.
% 277.97/278.05  0 [] -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a)),V_z)=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_z).
% 277.97/278.05  0 [] -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_z),c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a))=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_z).
% 277.97/278.05  0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a)=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_HOL_Oone__class_Oone(T_a)).
% 277.97/278.05  0 [] -class_Int_Onumber__ring(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_HOL_Oone__class_Oone(T_a))=c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_n),V_m)!=c_HOL_Ozero__class_Ozero(tc_nat)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_n)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=V_n.
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_m)=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat))=V_m.
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.05  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a))=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x).
% 277.97/278.05  0 [] c_Int_OBit1(c_Int_OMin)=c_Int_OMin.
% 277.97/278.05  0 [] c_Int_OBit1(V_k)!=c_Int_OMin|V_k=c_Int_OMin.
% 277.97/278.05  0 [] c_Int_OMin!=c_Int_OBit1(V_l)|c_Int_OMin=V_l.
% 277.97/278.05  0 [] c_Int_OMin=c_Int_OBit1(c_Int_OMin).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,V_m)),hAPP(c_Suc,V_n))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_n).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,V_m)),V_n)),hAPP(c_Suc,V_k))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_n)),V_k).
% 277.97/278.05  0 [] c_Int_OPls!=c_Int_OMin.
% 277.97/278.05  0 [] c_Int_OMin!=c_Int_OPls.
% 277.97/278.05  0 [] -class_OrderedGroup_Omonoid__mult(T_a)|hAPP(c_Power_Opower__class_Opower(V_a,T_a),c_HOL_Oone__class_Oone(tc_nat))=V_a.
% 277.97/278.05  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(c_Power_Opower__class_Opower(V_x,T_a),c_HOL_Oone__class_Oone(tc_nat))=V_x.
% 277.97/278.05  0 [] c_Int_OMin!=c_Int_OBit0(V_l).
% 277.97/278.05  0 [] c_Int_OBit0(V_k)!=c_Int_OMin.
% 277.97/278.05  0 [] -class_Ring__and__Field_Ofield(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b))=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),V_b).
% 277.97/278.05  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b))=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b)).
% 277.97/278.05  0 [] -class_Ring__and__Field_Ofield(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c)).
% 277.97/278.05  0 [] -class_RealVector_Oreal__normed__field(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y)),V_ya)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_ya)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_y),V_ya)).
% 277.97/278.05  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(T_a),V_a),V_b).
% 277.97/278.05  0 [] -class_RealVector_Oreal__normed__field(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)),V_y)=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y)).
% 277.97/278.05  0 [] -hBOOL(hAPP(V_P,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_b),V_d)),V_b)))|hBOOL(hAPP(V_P,V_d)).
% 277.97/278.05  0 [] -hBOOL(hAPP(V_P,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_b),V_x)),V_b)))|hBOOL(hAPP(V_P,V_x)).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(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))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_n).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),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))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_n).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_i),V_j)),V_k)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_i),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k)).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m)),V_n)=V_m.
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_n)=V_m.
% 277.97/278.05  0 [] c_HOL_Oone__class_Oone(tc_nat)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)|V_m=c_HOL_Oone__class_Oone(tc_nat).
% 277.97/278.05  0 [] c_HOL_Oone__class_Oone(tc_nat)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)|V_n=c_HOL_Oone__class_Oone(tc_nat).
% 277.97/278.05  0 [] c_HOL_Oone__class_Oone(tc_nat)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),V_n)=V_n.
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_n),c_HOL_Oone__class_Oone(tc_nat))=V_n.
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)!=c_HOL_Oone__class_Oone(tc_nat)|V_m=c_HOL_Oone__class_Oone(tc_nat).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)!=c_HOL_Oone__class_Oone(tc_nat)|V_n=c_HOL_Oone__class_Oone(tc_nat).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_n)),V_k)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(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)).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_k),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),V_n))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(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)).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 277.97/278.05  0 [] c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat))=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(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),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(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)),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a)| -c_lesse_quals(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),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a)| -c_lesse_quals(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),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y),V_x,T_a)| -c_lesse_quals(V_y,c_HOL_Oone__class_Oone(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_x),V_x,T_a)| -c_lesse_quals(V_y,c_HOL_Oone__class_Oone(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Ofield(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_w),V_z))=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_w),V_y))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_z))|V_z=c_HOL_Ozero__class_Ozero(T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(V_a,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_b,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),V_b,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),V_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),V_b,T_a)| -c_lesse_quals(V_b,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__idom(T_a)| -c_lesse_quals(hAPP(c_Power_Opower__class_Opower(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Oone__class_Oone(T_a)),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Oone__class_Oone(T_a)),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Oone__class_Oone(T_a)),V_b),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Oone__class_Oone(T_a)),V_b),T_a).
% 277.97/278.05  0 [] -class_RealVector_Oreal__field(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_c),V_d))),V_h)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_d)),V_h))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_c)),V_h)),V_d)).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oring__1(T_a)|hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),T_a),V_n)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_HOL_Oone__class_Oone(T_a)),T_a),V_n)),hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n)).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(hAPP(c_Power_Opower__class_Opower(V_a,T_a),hAPP(c_Suc,V_n)),hAPP(c_Power_Opower__class_Opower(V_b,T_a),hAPP(c_Suc,V_n)),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|hAPP(c_Power_Opower__class_Opower(V_a,T_a),hAPP(c_Suc,V_n))!=hAPP(c_Power_Opower__class_Opower(V_b,T_a),hAPP(c_Suc,V_n))|V_a=V_b| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a)|c_lesse_quals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(hAPP(c_Power_Opower__class_Opower(V_x,T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat)),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(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)).
% 277.97/278.05  0 [] c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 277.97/278.05  0 [] c_HOL_Oone__class_Oone(tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat).
% 277.97/278.05  0 [] hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n)),c_HOL_Oone__class_Oone(tc_nat)))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|c_lesse_quals(V_a,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),c_Int_Onumber__class_Onumber__of(V_w,T_a)),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_b,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_Int_Onumber__class_Onumber__of(V_w,T_a)),T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_Int_Onumber__class_Onumber__of(V_w,T_a)),V_b,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),c_Int_Onumber__class_Onumber__of(V_w,T_a)),V_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_Int_Onumber__class_Onumber__of(V_w,T_a)),V_b,T_a)| -c_lesse_quals(V_b,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_Int_Onumber__class_Onumber__of(V_w,T_a)),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|c_lesse_quals(c_Int_Onumber__class_Onumber__of(V_w,T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),T_a)| -c_lesse_quals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_b,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a)),V_c),T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a)),V_c),V_b,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a)),V_c),V_b,T_a)| -c_lesse_quals(V_b,hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a)),V_c),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_Int_Onumber__class_Onumber__of(V_w,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)| -c_lesse_quals(hAPP(c_Power_Opower__class_Opower(V_x,T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat)),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Ocomm__ring(T_a)| -class_OrderedGroup_Omonoid__mult(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(c_Power_Opower__class_Opower(V_x,T_a),hAPP(c_Suc,V_n))),hAPP(c_Power_Opower__class_Opower(V_y,T_a),hAPP(c_Suc,V_n)))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y)),c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(T_a),c_Power_Opower__class_Opower(V_x,T_a),T_a,tc_fun(T_a,T_a),tc_nat),c_COMBB(c_Power_Opower__class_Opower(V_y,T_a),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_n),tc_nat,T_a,tc_nat),tc_nat,T_a,T_a),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,V_n),tc_nat),tc_nat,T_a)).
% 277.97/278.05  0 [] -class_Ring__and__Field_Ocomm__ring__1(T_a)|hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))=hAPP(c_Power_Opower__class_Opower(V_a,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))=c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(V_x,V_y,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)| -c_lesse_quals(hAPP(c_Power_Opower__class_Opower(V_x,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Power_Opower__class_Opower(V_y,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(c_Power_Opower__class_Opower(V_a,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|hAPP(c_Power_Opower__class_Opower(V_x,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))!=hAPP(c_Power_Opower__class_Opower(V_y,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))|V_x=V_y| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Ocomm__ring__1(T_a)|hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n))=hAPP(c_Power_Opower__class_Opower(V_a,T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n)).
% 277.97/278.05  0 [] -class_Ring__and__Field_Ofield(T_a)|c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(V_x,T_a),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),tc_nat,T_a)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(c_Power_Opower__class_Opower(V_x,T_a),V_n)),c_HOL_Oone__class_Oone(T_a))),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),c_HOL_Oone__class_Oone(T_a)))|V_x=c_HOL_Oone__class_Oone(T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_Power_Opower__class_Opower(V_x,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(V_y,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_Power_Opower__class_Opower(V_x,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(V_y,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_Power_Opower__class_Opower(V_x,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(V_y,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(c_Power_Opower__class_Opower(V_a,T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n)),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a)| -c_lesse_quals(hAPP(c_Power_Opower__class_Opower(V_a,T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_k)),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Ocomm__ring__1(T_a)|hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_HOL_Oone__class_Oone(T_a)),T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n))=c_HOL_Oone__class_Oone(T_a).
% 277.97/278.05  0 [] hAPP(c_Suc,hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.05  0 [] hAPP(c_Suc,hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)),V_n)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)),V_n)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.05  0 [] -class_Int_Onumber__ring(T_a)|hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_y),T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_Power_Opower__class_Opower(V_x,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(V_y,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a)),V_x)),V_y)).
% 277.97/278.05  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),V_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Oordered__ab__group__add(T_a)|c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Oordered__ab__group__add(T_a)|c_lesse_quals(V_a,hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Oordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),V_a,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Oordered__ab__group__add(T_a)|c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a),V_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b))=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)).
% 277.97/278.05  0 [] -class_Orderings_Opreorder(T_a)|c_lesse_quals(V_x,V_x,T_a).
% 277.97/278.05  0 [] -class_Orderings_Oorder(T_a)|c_lesse_quals(V_x,V_x,T_a).
% 277.97/278.05  0 [] -class_Orderings_Opreorder(T_a)|c_lesse_quals(V_x,V_z,T_a)| -c_lesse_quals(V_y,V_z,T_a)| -c_lesse_quals(V_x,V_y,T_a).
% 277.97/278.05  0 [] -class_Orderings_Oorder(T_a)|c_lesse_quals(V_z,V_x,T_a)| -c_lesse_quals(V_z,V_y,T_a)| -c_lesse_quals(V_y,V_x,T_a).
% 277.97/278.05  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_y,V_x,T_a)|c_lesse_quals(V_x,V_y,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a)),V_x)=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Oone__class_Oone(T_a)),V_x)).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)=hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),c_HOL_Oone__class_Oone(tc_nat))),V_n))|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_m),c_HOL_Oone__class_Oone(tc_nat))),V_n))|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)|c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Omult__mono1(T_a)|c_lesse_quals(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_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Omult__mono(T_a)|c_lesse_quals(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_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Omult__mono(T_a)|c_lesse_quals(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_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_lesse_quals(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_lesse_quals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_b,V_a,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_lesse_quals(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_lesse_quals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_b,V_a,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)| -c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)| -c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)| -c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Opordered__cancel__semiring(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Opordered__semiring(T_a)|c_lesse_quals(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),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(V_c,V_d,T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Opordered__semiring(T_a)|c_lesse_quals(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),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(V_c,V_d,T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Opordered__cancel__semiring(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Opordered__cancel__semiring(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Opordered__cancel__semiring(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Opordered__cancel__semiring(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Opordered__cancel__semiring(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  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).
% 277.97/278.05  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).
% 277.97/278.05  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).
% 277.97/278.05  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).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),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).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)| -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_lesse_quals(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)| -c_lesse_quals(V_b,V_c,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)| -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_lesse_quals(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)| -c_lesse_quals(V_b,V_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)!=c_HOL_Ozero__class_Ozero(T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)!=c_HOL_Ozero__class_Ozero(T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  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.
% 277.97/278.05  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).
% 277.97/278.05  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)| -c_lesse_quals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_a),V_b))=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),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_a)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_y),V_b))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_x),V_a)),V_b))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_y),V_b))).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oring(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),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_a)),V_e)),V_d))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_e)),V_c)).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),V_e)),V_c)=V_d.
% 277.97/278.05  0 [] -class_Ring__and__Field_Oring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_e)),V_c)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_e)),V_d)|V_c=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_a)),V_e)),V_d).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oring(T_a)| -class_Int_Onumber(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_b),V_c))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a)),V_b)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a)),V_c)).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oring(T_a)| -class_Int_Onumber(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),V_a),V_b)),c_Int_Onumber__class_Onumber__of(V_v,T_a))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_Int_Onumber__class_Onumber__of(V_v,T_a))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),c_Int_Onumber__class_Onumber__of(V_v,T_a))).
% 277.97/278.05  0 [] -class_Int_Onumber__ring(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_x)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_HOL_Oone__class_Oone(T_a))),V_x).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a)|c_lesse_quals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(hAPP(c_Power_Opower__class_Opower(V_x,T_a),V_n),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n),hAPP(c_Power_Opower__class_Opower(V_b,T_a),V_n),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Ofield(T_a)|hAPP(c_HOL_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b))=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),hAPP(c_HOL_Ouminus__class_Ouminus(T_a),V_b))|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_c),T_a)| -c_lesse_quals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Ofield(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(T_a),V_a),V_b)|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)|c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),T_a)| -c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 277.97/278.05  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)).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(c_HOL_Oone__class_Oone(T_a),hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n),T_a)| -c_lesse_quals(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 277.97/278.05  0 [] c_HOL_Oone__class_Oone(tc_nat)=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.05  0 [] c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.05  0 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_n),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m))=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.05  0 [] V_m!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Oone__class_Oone(tc_nat).
% 277.97/278.05  0 [] hAPP(c_Suc,V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Oone__class_Oone(tc_nat)).
% 277.97/278.05  0 [] hAPP(c_Suc,V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),V_n).
% 277.97/278.05  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(c_Power_Opower__class_Opower(V_a,T_a),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n))),T_a).
% 277.97/278.05  0 [] -class_Int_Onumber__ring(T_a)|hAPP(c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n))=c_HOL_Oone__class_Oone(T_a).
% 277.97/278.06  0 [] -class_Int_Onumber__ring(T_a)|hAPP(c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),T_a),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n)))=c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__ring__1(T_a)|hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_HOL_Oone__class_Oone(T_a)),T_a),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n)))=hAPP(c_HOL_Ouminus__class_Ouminus(T_a),c_HOL_Oone__class_Oone(T_a)).
% 277.97/278.06  0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_Finite__Set_Osetsum(V_x,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_x,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(V_x,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))),hAPP(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat))).
% 277.97/278.06  0 [] -class_Power_Opower(T_a)| -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(T_a),c_Power_Opower__class_Opower(V_x,T_a),T_a,tc_fun(T_a,T_a),tc_nat),c_COMBB(c_Power_Opower__class_Opower(V_y,T_a),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_n),tc_nat,T_a,tc_nat),tc_nat,T_a,T_a),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,V_n),tc_nat),tc_nat,T_a)=c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(T_a),c_COMBB(c_Power_Opower__class_Opower(V_x,T_a),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_n),tc_nat,T_a,tc_nat),T_a,tc_fun(T_a,T_a),tc_nat),c_Power_Opower__class_Opower(V_y,T_a),tc_nat,T_a,T_a),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,V_n),tc_nat),tc_nat,T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)| -class_OrderedGroup_Omonoid__mult(T_a)|c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(T_a),c_Power_Opower__class_Opower(V_x,T_a),T_a,tc_fun(T_a,T_a),tc_nat),c_COMBB(c_Power_Opower__class_Opower(V_y,T_a),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,V_n)),tc_nat,T_a,tc_nat),tc_nat,T_a,T_a),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,V_n),tc_nat),tc_nat,T_a)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(T_a),c_Power_Opower__class_Opower(V_x,T_a),T_a,tc_fun(T_a,T_a),tc_nat),c_COMBB(c_Power_Opower__class_Opower(V_y,T_a),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),V_n),tc_nat,T_a,tc_nat),tc_nat,T_a,T_a),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,V_n),tc_nat),tc_nat,T_a)).
% 277.97/278.06  0 [] c_FFT__Mirabelle_ODFT(V_n,V_a,v_i)=c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_COMBB(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),V_a,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),tc_nat,tc_Complex_Ocomplex).
% 277.97/278.06  0 [] c_FFT__Mirabelle_OIDFT(V_n,V_a,v_i)=c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),V_a,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),tc_nat,tc_Complex_Ocomplex).
% 277.97/278.06  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.
% 277.97/278.06  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.
% 277.97/278.06  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.
% 277.97/278.06  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.
% 277.97/278.06  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.
% 277.97/278.06  0 [] c_FFT__Mirabelle_Oroot(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),c_HOL_Oone__class_Oone(T_a))=V_a.
% 277.97/278.06  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)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y))=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_z),V_y))),V_y)|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_z),V_y))),V_y)|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a)=c_HOL_Oone__class_Oone(T_a).
% 277.97/278.06  0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(c_Int_OBit1(V_w),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(V_w,T_a))),c_Int_Onumber__class_Onumber__of(V_w,T_a)).
% 277.97/278.06  0 [] c_Int_OBit1(V_k)!=c_Int_OBit0(V_l).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(V_w,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|c_Int_Onumber__class_Onumber__of(V_w,T_a)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a)),V_c)),V_c).
% 277.97/278.06  0 [] -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a))=c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a).
% 277.97/278.06  0 [] c_Int_OPls=c_Int_OBit0(c_Int_OPls).
% 277.97/278.06  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).
% 277.97/278.06  0 [] -class_Int_Onumber__ring(T_a)|hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y),T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_Power_Opower__class_Opower(V_x,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(V_y,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a)),V_x)),V_y)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(V_w,T_a)!=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a)),V_c)=V_b|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  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)).
% 277.97/278.06  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)).
% 277.97/278.06  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)).
% 277.97/278.06  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)).
% 277.97/278.06  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a_H)),V_b)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(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_H),V_b)).
% 277.97/278.06  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_ya)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_ya)).
% 277.97/278.06  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_b_H))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(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),V_b_H)).
% 277.97/278.06  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_xa),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_xa),V_y)).
% 277.97/278.06  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)).
% 277.97/278.06  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).
% 277.97/278.06  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)).
% 277.97/278.06  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)).
% 277.97/278.06  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).
% 277.97/278.06  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)).
% 277.97/278.06  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).
% 277.97/278.06  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)).
% 277.97/278.06  0 [] -class_Int_Onumber__ring(T_a)|c_HOL_Oone__class_Oone(T_a)=c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b)!=c_HOL_Oone__class_Oone(T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=V_b.
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n)=hAPP(c_Suc,hAPP(c_Suc,V_n)).
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))=hAPP(c_Suc,hAPP(c_Suc,V_n)).
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|V_n=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|V_m=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=hAPP(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).
% 277.97/278.06  0 [] -class_OrderedGroup_Omonoid__mult(T_a)|hAPP(c_Power_Opower__class_Opower(V_a,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_a).
% 277.97/278.06  0 [] -class_OrderedGroup_Ocomm__monoid__mult(T_a)|hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a),V_n)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n)),hAPP(c_Power_Opower__class_Opower(V_b,T_a),V_n)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y),T_a),V_q)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_Power_Opower__class_Opower(V_x,T_a),V_q)),hAPP(c_Power_Opower__class_Opower(V_y,T_a),V_q)).
% 277.97/278.06  0 [] -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a)),V_a)=V_a.
% 277.97/278.06  0 [] -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a))=V_a.
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,V_k)),V_m)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,V_k)),V_n)|V_m=V_n.
% 277.97/278.06  0 [] c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)=hAPP(c_Suc,hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))).
% 277.97/278.06  0 [] -class_OrderedGroup_Oab__semigroup__idem__mult(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)=V_x.
% 277.97/278.06  0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|c_Int_Onumber__class_Onumber__of(V_w,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat))=c_HOL_Oone__class_Oone(T_a).
% 277.97/278.06  0 [] hAPP(c_Suc,V_n)!=V_n.
% 277.97/278.06  0 [] V_n!=hAPP(c_Suc,V_n).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_Power_Opower__class_Opower(V_x,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(V_y,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))!=c_HOL_Ozero__class_Ozero(T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_Power_Opower__class_Opower(V_x,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(V_y,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))!=c_HOL_Ozero__class_Ozero(T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),T_a),V_n)=c_HOL_Ozero__class_Ozero(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.06  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)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),T_a),V_n)=c_HOL_Ozero__class_Ozero(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(c_Power_Opower__class_Opower(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(T_a).
% 277.97/278.06  0 [] -class_Power_Opower(T_a)|hAPP(c_Power_Opower__class_Opower(V_a,T_a),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|V_a=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_Int_Onumber__class_Onumber__of(V_w,T_a))),c_Int_Onumber__class_Onumber__of(V_w,T_a))|c_Int_Onumber__class_Onumber__of(V_w,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_Int_Onumber__class_Onumber__of(V_w,T_a))),c_Int_Onumber__class_Onumber__of(V_w,T_a))=V_a|c_Int_Onumber__class_Onumber__of(V_w,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Oring__1__no__zero__divisors(T_a)|hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  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)|hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  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).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_z),V_w))=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_y),V_w)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),T_a),V_n)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n)),hAPP(c_Power_Opower__class_Opower(V_b,T_a),V_n)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a)|V_a=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),V_c).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),V_c)=V_a.
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|V_a=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),V_c)|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c)),V_c)=V_a|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),tc_Complex_Ocomplex),V_n)=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),c_HOL_Ozero__class_Ozero(T_a))!=c_Int_Onumber__class_Onumber__of(V_w,T_a)|c_Int_Onumber__class_Onumber__of(V_w,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(V_w,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),c_HOL_Ozero__class_Ozero(T_a))=c_Int_Onumber__class_Onumber__of(V_w,T_a).
% 277.97/278.06  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)).
% 277.97/278.06  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))).
% 277.97/278.06  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)).
% 277.97/278.06  0 [] hAPP(c_Suc,hAPP(c_Suc,hAPP(c_Suc,V_n)))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)|c_HOL_Oone__class_Oone(T_a)!=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  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_Int_Onumber__class_Onumber__of(V_w,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|hAPP(c_Power_Opower__class_Opower(V_a,T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat))!=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|c_HOL_Ozero__class_Ozero(T_a)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_Int_Onumber__class_Onumber__of(V_w,T_a))),c_Int_Onumber__class_Onumber__of(V_w,T_a)).
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),hAPP(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)).
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(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)).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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.
% 277.97/278.06  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.
% 277.97/278.06  0 [] -class_OrderedGroup_Omonoid__mult(T_a)|hAPP(c_Power_Opower__class_Opower(V_a,T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n))=hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n),T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(V_w,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a)),V_c)),V_c)=c_Int_Onumber__class_Onumber__of(V_w,T_a).
% 277.97/278.06  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),c_Finite__Set_Osetsum(V_g,V_A,T_b,T_a))=c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_g,T_a,T_a,T_b),V_A,T_b,T_a).
% 277.97/278.06  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).
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,V_m)),V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(c_Suc,V_n)).
% 277.97/278.06  0 [] hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_n=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.06  0 [] hAPP(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=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)|c_HOL_Ozero__class_Ozero(T_a)!=c_HOL_Oone__class_Oone(T_a).
% 277.97/278.06  0 [] -class_OrderedGroup_Omonoid__mult(T_a)|hAPP(c_Power_Opower__class_Opower(V_a,T_a),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n)))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n),T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))).
% 277.97/278.06  0 [] hAPP(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)),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_OrderedGroup_Omonoid__mult(T_a)|hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),T_a),V_n)=c_HOL_Oone__class_Oone(T_a).
% 277.97/278.06  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))!=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.
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a))=V_a.
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a))=V_x.
% 277.97/278.06  0 [] c_Int_OBit0(V_k)!=c_Int_OBit0(V_l)|V_k=V_l.
% 277.97/278.06  0 [] c_Int_OBit0(V_k)!=c_Int_OPls|V_k=c_Int_OPls.
% 277.97/278.06  0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(T_a).
% 277.97/278.06  0 [] c_Int_OBit1(V_k)!=c_Int_OPls.
% 277.97/278.06  0 [] hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_m)),tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_i),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_j)))=hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_m),tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_i),V_j)).
% 277.97/278.06  0 [] -class_OrderedGroup_Omonoid__mult(T_a)| -class_Int_Onumber(T_a)|hAPP(c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a)),c_Int_Onumber__class_Onumber__of(V_w,T_a)).
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,V_m)),V_n)=hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)).
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(c_Suc,V_n))=hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)).
% 277.97/278.06  0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,V_m),hAPP(c_Suc,V_n),tc_nat),tc_nat,T_a)=c_Finite__Set_Osetsum(c_COMBB(V_f,c_Suc,tc_nat,T_a,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  0 [] c_Int_OPls!=c_Int_OBit1(V_l).
% 277.97/278.06  0 [] -class_OrderedGroup_Omonoid__mult(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n)),V_a)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n)).
% 277.97/278.06  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.
% 277.97/278.06  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.
% 277.97/278.06  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).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(V_w,T_a)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a)),V_c)),V_c)|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_m),V_m)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a))),V_m).
% 277.97/278.06  0 [] hAPP(c_Suc,V_nat)!=hAPP(c_Suc,V_nat_H)|V_nat=V_nat_H.
% 277.97/278.06  0 [] hAPP(c_Suc,V_x)!=hAPP(c_Suc,V_y)|V_x=V_y.
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|V_b=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),c_Int_Onumber__class_Onumber__of(V_w,T_a))),c_Int_Onumber__class_Onumber__of(V_w,T_a))|c_Int_Onumber__class_Onumber__of(V_w,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),c_Int_Onumber__class_Onumber__of(V_w,T_a))),c_Int_Onumber__class_Onumber__of(V_w,T_a))=V_b|c_Int_Onumber__class_Onumber__of(V_w,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Ozero__class_Ozero(T_a)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_c)),V_c).
% 277.97/278.06  0 [] hAPP(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).
% 277.97/278.06  0 [] hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_n=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|V_m=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat))=c_HOL_Ozero__class_Ozero(T_a)|c_Int_Onumber__class_Onumber__of(V_w,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.06  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)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat))=c_HOL_Ozero__class_Ozero(T_a)|c_Int_Onumber__class_Onumber__of(V_w,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.06  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.
% 277.97/278.06  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.
% 277.97/278.06  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.
% 277.97/278.06  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.
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(c_Power_Opower__class_Opower(V_x,T_a),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n)))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_Power_Opower__class_Opower(V_x,T_a),V_n)),hAPP(c_Power_Opower__class_Opower(V_x,T_a),V_n))).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a)),V_c)),V_c)=c_Int_Onumber__class_Onumber__of(V_w,T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_w),V_z))=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),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_w),V_y))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_z))|V_z=c_HOL_Ozero__class_Ozero(T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|V_b=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c)),V_c)|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c)),V_c)=V_b|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_y)=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_RealVector_Oreal__normed__algebra(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).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  0 [] -class_RealVector_Oreal__normed__algebra(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).
% 277.97/278.06  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),c_HOL_Ozero__class_Ozero(T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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)),V_m)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a))),V_m).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_m))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a))),V_m).
% 277.97/278.06  0 [] -class_Ring__and__Field_Osemiring(T_a)| -class_Int_Onumber(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),c_Int_Onumber__class_Onumber__of(V_v,T_a))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_Int_Onumber__class_Onumber__of(V_v,T_a))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),c_Int_Onumber__class_Onumber__of(V_v,T_a))).
% 277.97/278.06  0 [] hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|hAPP(c_Power_Opower__class_Opower(V_a,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.06  0 [] hAPP(c_Suc,V_m)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.06  0 [] hAPP(c_Suc,V_nat_H)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.06  0 [] c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_Int_Onumber__class_Onumber__of(V_w,T_a))),c_Int_Onumber__class_Onumber__of(V_w,T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] c_Int_OBit0(c_Int_OPls)=c_Int_OPls.
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(V_w,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),c_Int_Onumber__class_Onumber__of(V_w,T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(c_Power_Opower__class_Opower(V_x,T_a),V_q))=hAPP(c_Power_Opower__class_Opower(V_x,T_a),hAPP(c_Suc,V_q)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_Power_Opower__class_Opower(V_x,T_a),V_q)),V_x)=hAPP(c_Power_Opower__class_Opower(V_x,T_a),hAPP(c_Suc,V_q)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c)!=c_Int_Onumber__class_Onumber__of(V_w,T_a)|V_b=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a)),V_c)|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Osemiring__1(T_a)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)|hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b),T_a),V_n)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n)),hAPP(c_Power_Opower__class_Opower(V_b,T_a),V_n))|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.06  0 [] c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)=hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))).
% 277.97/278.06  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).
% 277.97/278.06  0 [] c_HOL_Ozero__class_Ozero(tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat).
% 277.97/278.06  0 [] -class_Int_Onumber__ring(T_a)|c_HOL_Ozero__class_Ozero(T_a)=c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Ozero__class_Ozero(T_a)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),c_HOL_Ozero__class_Ozero(T_a)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)=hAPP(c_Power_Opower__class_Opower(V_x,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y)!=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_w),V_z)|V_z=c_HOL_Ozero__class_Ozero(T_a)|V_y=c_HOL_Ozero__class_Ozero(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_w),V_y).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(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_w),V_y)|V_z=c_HOL_Ozero__class_Ozero(T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_w),V_z).
% 277.97/278.06  0 [] -class_OrderedGroup_Omonoid__mult(T_a)|hAPP(c_Power_Opower__class_Opower(V_a,T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n))=hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_m),T_a),V_n).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_c)),V_c)=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  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).
% 277.97/278.06  0 [] -class_Ring__and__Field_Osemiring__1(T_a)|hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))=c_HOL_Oone__class_Oone(T_a).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(V_w,T_a)!=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),c_HOL_Ozero__class_Ozero(T_a))|c_Int_Onumber__class_Onumber__of(V_w,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(V_w,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|c_Int_Onumber__class_Onumber__of(V_w,T_a)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),c_HOL_Ozero__class_Ozero(T_a)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)| -class_Int_Onumber(T_a)|c_Int_Onumber__class_Onumber__of(V_w,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|c_HOL_Ozero__class_Ozero(T_a)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),c_Int_Onumber__class_Onumber__of(V_w,T_a)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_Power_Opower__class_Opower(V_x,T_a),V_p)),hAPP(c_Power_Opower__class_Opower(V_x,T_a),V_q))=hAPP(c_Power_Opower__class_Opower(V_x,T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_p),V_q)).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  0 [] -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a)),V_a)=V_a.
% 277.97/278.06  0 [] -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a))=V_a.
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)!=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|V_m=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_m),V_n)!=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|V_n=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.06  0 [] c_Int_OPls!=c_Int_OBit0(V_l)|c_Int_OPls=V_l.
% 277.97/278.06  0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=hAPP(c_Suc,V_nat_H).
% 277.97/278.06  0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=hAPP(c_Suc,V_m).
% 277.97/278.06  0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),T_a),hAPP(c_Suc,V_n))=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(V_w,T_a))=c_Int_Onumber__class_Onumber__of(c_Int_OBit0(V_w),T_a).
% 277.97/278.06  0 [] -class_OrderedGroup_Omonoid__mult(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_HOL_Oone__class_Oone(T_a))=V_a.
% 277.97/278.06  0 [] -class_OrderedGroup_Omonoid__mult(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Oone__class_Oone(T_a)),V_a)=V_a.
% 277.97/278.06  0 [] -class_OrderedGroup_Ocomm__monoid__mult(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Oone__class_Oone(T_a)),V_a)=V_a.
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Oone__class_Oone(T_a)),V_x)=V_x.
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_HOL_Oone__class_Oone(T_a))=V_a.
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Oone__class_Oone(T_a)),V_a)=V_a.
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Oone__class_Oone(T_a)),hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n))=hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Oone__class_Oone(T_a)),V_a),T_a),V_n).
% 277.97/278.06  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)).
% 277.97/278.06  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)).
% 277.97/278.06  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)).
% 277.97/278.06  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)).
% 277.97/278.06  0 [] c_Int_OBit1(V_k)!=c_Int_OBit1(V_l)|V_k=V_l.
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(V_x,T_a),V_p),T_a),V_q)=hAPP(c_Power_Opower__class_Opower(V_x,T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_p),V_q)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(c_Power_Opower__class_Opower(V_x,T_a),hAPP(c_Suc,V_n))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(c_Power_Opower__class_Opower(V_x,T_a),V_n)).
% 277.97/278.06  0 [] -class_OrderedGroup_Omonoid__mult(T_a)|hAPP(c_Power_Opower__class_Opower(V_a,T_a),hAPP(c_Suc,V_n))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n)),V_a).
% 277.97/278.06  0 [] -class_Power_Opower(T_a)|hAPP(c_Power_Opower__class_Opower(V_a,T_a),hAPP(c_Suc,V_n))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(c_Power_Opower__class_Opower(V_x,T_a),hAPP(c_Suc,V_q))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(c_Power_Opower__class_Opower(V_x,T_a),V_q)).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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)).
% 277.97/278.06  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)).
% 277.97/278.06  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).
% 277.97/278.06  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))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)).
% 277.97/278.06  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)).
% 277.97/278.06  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)).
% 277.97/278.06  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)).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  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)).
% 277.97/278.06  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)).
% 277.97/278.06  0 [] -class_OrderedGroup_Omonoid__mult(T_a)|hAPP(c_Power_Opower__class_Opower(V_a,T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_m)),hAPP(c_Power_Opower__class_Opower(V_a,T_a),V_n)).
% 277.97/278.06  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)|hAPP(c_Power_Opower__class_Opower(V_a,T_a),c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R)=hAPP(V_P,hAPP(V_Q,V_R)).
% 277.97/278.06  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)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_x)=c_HOL_Oone__class_Oone(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_a)=c_HOL_Oone__class_Oone(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_a)=c_HOL_Oone__class_Oone(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] hAPP(c_Suc,hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)))=c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat).
% 277.97/278.06  0 [] -class_Ring__and__Field_Osemiring(T_a)| -class_Int_Onumber(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a)),V_b)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a)),V_c)).
% 277.97/278.06  0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(V_f,c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Ozero__class_Ozero(T_a)|c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),V_k,tc_nat),tc_nat,T_a)=c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat),tc_nat,T_a).
% 277.97/278.06  0 [] -class_OrderedGroup_Omonoid__mult(T_a)|hAPP(c_Power_Opower__class_Opower(V_a,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_a)),V_a).
% 277.97/278.06  0 [] -class_Int_Oring__char__0(T_a)| -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(V_x,T_a)!=c_Int_Onumber__class_Onumber__of(V_y,T_a)|V_x=V_y.
% 277.97/278.06  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)).
% 277.97/278.06  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).
% 277.97/278.06  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).
% 277.97/278.06  0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(c_Int_OBit0(V_w),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_Int_Onumber__class_Onumber__of(V_w,T_a))),c_Int_Onumber__class_Onumber__of(V_w,T_a)).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),c_HOL_Ozero__class_Ozero(T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_RealVector_Oreal__normed__field(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_y)=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(c_Power_Opower__class_Opower(V_x,T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_n))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(c_Power_Opower__class_Opower(V_x,T_a),V_n)),hAPP(c_Power_Opower__class_Opower(V_x,T_a),V_n)).
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|V_n=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_z),V_z).
% 277.97/278.06  0 [] -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a)),V_z)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_z),V_z).
% 277.97/278.06  0 [] -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_z),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_z),V_z).
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),V_z)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_z),V_z).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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))=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b)|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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))=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_a),V_b)|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] c_Int_OBit0(V_k)!=c_Int_OBit1(V_l).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_z)),V_y).
% 277.97/278.06  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.
% 277.97/278.06  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.
% 277.97/278.06  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.
% 277.97/278.06  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)).
% 277.97/278.06  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.
% 277.97/278.06  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.
% 277.97/278.06  0 [] V_x=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat))=V_m.
% 277.97/278.06  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)=V_n.
% 277.97/278.06  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.
% 277.97/278.06  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.
% 277.97/278.06  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)|hAPP(c_Power_Opower__class_Opower(V_a,T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat))!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 277.97/278.06  0 [] -class_Ring__and__Field_Ofield(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_b),V_c)).
% 277.97/278.06  0 [] -class_RealVector_Oreal__normed__field(T_a)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_x),V_ya)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(T_a),V_y),V_ya)).
% 277.97/278.06  0 [] c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_COMBB(v_a,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_m)),tc_Complex_Ocomplex),c_COMBB(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_i),c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_m,tc_nat),tc_nat,tc_Complex_Ocomplex)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_m))),tc_Complex_Ocomplex),v_i)),c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_COMBB(v_a,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_m,tc_nat),tc_nat,tc_Complex_Ocomplex)).
% 277.97/278.06  0 [] class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))| -class_Lattices_Oboolean__algebra(T_1).
% 277.97/278.06  0 [] class_Orderings_Opreorder(tc_fun(T_2,T_1))| -class_Orderings_Opreorder(T_1).
% 277.97/278.06  0 [] class_Orderings_Oorder(tc_fun(T_2,T_1))| -class_Orderings_Oorder(T_1).
% 277.97/278.06  0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 277.97/278.06  0 [] class_Ring__and__Field_Opordered__cancel__semiring(tc_nat).
% 277.97/278.06  0 [] class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat).
% 277.97/278.06  0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 277.97/278.06  0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 277.97/278.06  0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 277.97/278.06  0 [] class_Ring__and__Field_Opordered__semiring(tc_nat).
% 277.97/278.06  0 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 277.97/278.06  0 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 277.97/278.06  0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 277.97/278.06  0 [] class_Ring__and__Field_Ocomm__semiring__0(tc_nat).
% 277.97/278.06  0 [] class_OrderedGroup_Oab__semigroup__mult(tc_nat).
% 277.97/278.06  0 [] class_OrderedGroup_Ocomm__monoid__mult(tc_nat).
% 277.97/278.06  0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 277.97/278.06  0 [] class_Ring__and__Field_Ocomm__semiring(tc_nat).
% 277.97/278.06  0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 277.97/278.06  0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 277.97/278.06  0 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 277.97/278.06  0 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 277.97/278.06  0 [] class_Ring__and__Field_Omult__mono1(tc_nat).
% 277.97/278.06  0 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 277.97/278.06  0 [] class_Ring__and__Field_Omult__mono(tc_nat).
% 277.97/278.06  0 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 277.97/278.06  0 [] class_Ring__and__Field_Osemiring(tc_nat).
% 277.97/278.06  0 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 277.97/278.06  0 [] class_Orderings_Opreorder(tc_nat).
% 277.97/278.06  0 [] class_Orderings_Olinorder(tc_nat).
% 277.97/278.06  0 [] class_Orderings_Oorder(tc_nat).
% 277.97/278.06  0 [] class_Power_Opower(tc_nat).
% 277.97/278.06  0 [] class_Int_Onumber(tc_nat).
% 277.97/278.06  0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint).
% 277.97/278.06  0 [] class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint).
% 277.97/278.06  0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint).
% 277.97/278.06  0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint).
% 277.97/278.06  0 [] class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint).
% 277.97/278.06  0 [] class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint).
% 277.97/278.06  0 [] class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint).
% 277.97/278.06  0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Opordered__semiring(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Oordered__semidom(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint).
% 277.97/278.06  0 [] class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint).
% 277.97/278.06  0 [] class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint).
% 277.97/278.06  0 [] class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Opordered__ring(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint).
% 277.97/278.06  0 [] class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Oordered__idom(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Osemiring__1(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Osemiring__0(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Omult__mono1(tc_Int_Oint).
% 277.97/278.06  0 [] class_OrderedGroup_Oab__group__add(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Omult__zero(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Omult__mono(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Ocomm__ring(tc_Int_Oint).
% 277.97/278.06  0 [] class_OrderedGroup_Omonoid__mult(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Osemiring(tc_Int_Oint).
% 277.97/278.06  0 [] class_OrderedGroup_Omonoid__add(tc_Int_Oint).
% 277.97/278.06  0 [] class_OrderedGroup_Ogroup__add(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Oring__1(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Oring(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Oidom(tc_Int_Oint).
% 277.97/278.06  0 [] class_Orderings_Opreorder(tc_Int_Oint).
% 277.97/278.06  0 [] class_Orderings_Olinorder(tc_Int_Oint).
% 277.97/278.06  0 [] class_Orderings_Oorder(tc_Int_Oint).
% 277.97/278.06  0 [] class_Int_Oring__char__0(tc_Int_Oint).
% 277.97/278.06  0 [] class_Int_Onumber__ring(tc_Int_Oint).
% 277.97/278.06  0 [] class_Power_Opower(tc_Int_Oint).
% 277.97/278.06  0 [] class_Int_Onumber(tc_Int_Oint).
% 277.97/278.06  0 [] class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_RealVector_Oreal__field(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Ring__and__Field_Ofield(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Ring__and__Field_Oring(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Ring__and__Field_Oidom(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Int_Oring__char__0(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Int_Onumber__ring(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Power_Opower(tc_Complex_Ocomplex).
% 277.97/278.06  0 [] class_Int_Onumber(tc_Complex_Ocomplex).
% 277.97/278.06  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)).
% 277.97/278.06  0 [] hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 277.97/278.06  0 [] hAPP(c_COMBB(V_P,V_Q,T_b,T_a,T_c),V_R)=hAPP(V_P,hAPP(V_Q,V_R)).
% 277.97/278.06  0 [] c_fe_qual(V_x,V_x,T_a).
% 277.97/278.06  0 [] V_X=V_Y| -c_fe_qual(V_X,V_Y,T_a).
% 277.97/278.06  end_of_list.
% 277.97/278.06  
% 277.97/278.06  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 277.97/278.06  
% 277.97/278.06  This ia a non-Horn set with equality.  The strategy will be
% 277.97/278.06  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 277.97/278.06  deletion, with positive clauses in sos and nonpositive
% 277.97/278.06  clauses in usable.
% 277.97/278.06  
% 277.97/278.06     dependent: set(knuth_bendix).
% 277.97/278.06     dependent: set(anl_eq).
% 277.97/278.06     dependent: set(para_from).
% 277.97/278.06     dependent: set(para_into).
% 277.97/278.06     dependent: clear(para_from_right).
% 277.97/278.06     dependent: clear(para_into_right).
% 277.97/278.06     dependent: set(para_from_vars).
% 277.97/278.06     dependent: set(eq_units_both_ways).
% 277.97/278.06     dependent: set(dynamic_demod_all).
% 277.97/278.06     dependent: set(dynamic_demod).
% 277.97/278.06     dependent: set(order_eq).
% 277.97/278.06     dependent: set(back_demod).
% 277.97/278.06     dependent: set(lrpo).
% 277.97/278.06     dependent: set(hyper_res).
% 277.97/278.06     dependent: set(unit_deletion).
% 277.97/278.06     dependent: set(factor).
% 277.97/278.06  
% 277.97/278.06  ------------> process usable:
% 277.97/278.06  ** KEPT (pick-wt=31): 1 [] -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).
% 277.97/278.06  ** KEPT (pick-wt=31): 2 [] -class_RealVector_Oreal__normed__algebra(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).
% 277.97/278.06  ** KEPT (pick-wt=31): 3 [] -class_Ring__and__Field_Ofield(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_Finite__Set_Osetsum(B,C,D,A)),E)=c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),D),E,D,A,A),C,D,A).
% 277.97/278.06  ** KEPT (pick-wt=31): 4 [] -class_RealVector_Oreal__normed__field(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_Finite__Set_Osetsum(B,C,D,A)),E)=c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),D),E,D,A,A),C,D,A).
% 277.97/278.06  ** KEPT (pick-wt=20): 5 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A)| -c_lesse_quals(B,D,A).
% 277.97/278.06  ** KEPT (pick-wt=18): 6 [] -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.
% 277.97/278.06  ** KEPT (pick-wt=24): 7 [] -class_OrderedGroup_Opordered__ab__semigroup__add(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A)| -c_lesse_quals(C,E,A)| -c_lesse_quals(B,D,A).
% 277.97/278.06  ** KEPT (pick-wt=18): 8 [] -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.
% 277.97/278.06  ** KEPT (pick-wt=18): 9 [] -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.
% 277.97/278.06  ** KEPT (pick-wt=24): 10 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_lesse_quals(E,D,A)| -c_lesse_quals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E),A).
% 277.97/278.06  ** KEPT (pick-wt=24): 11 [] -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)).
% 277.97/278.06  ** KEPT (pick-wt=24): 13 [copy,12,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)).
% 277.97/278.06  ** KEPT (pick-wt=45): 14 [] -class_Ring__and__Field_Opordered__ring(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D)),E),F,A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),E),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),F),A).
% 277.97/278.06  ** KEPT (pick-wt=45): 15 [] -class_Ring__and__Field_Opordered__ring(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F),A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D),F,A).
% 277.97/278.06  ** KEPT (pick-wt=45): 16 [] -class_Ring__and__Field_Opordered__ring(A)|c_lesse_quals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)),E)),F),A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)),F),A).
% 277.97/278.06  ** KEPT (pick-wt=45): 17 [] -class_Ring__and__Field_Opordered__ring(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F),A)| -c_lesse_quals(D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B)),C)),F),A).
% 277.97/278.06  ** KEPT (pick-wt=30): 18 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)).
% 277.97/278.06    Following clause subsumed by 18 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)).
% 277.97/278.06  ** KEPT (pick-wt=30): 20 [copy,19,flip.2] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(A),C),D)).
% 277.97/278.06    Following clause subsumed by 20 during input processing: 0 [flip.2] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(A),C),D)).
% 277.97/278.06  ** KEPT (pick-wt=24): 21 [] -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.
% 277.97/278.06  ** KEPT (pick-wt=21): 23 [copy,22,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)).
% 277.97/278.06  ** KEPT (pick-wt=21): 24 [] -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)).
% 277.97/278.06  ** KEPT (pick-wt=21): 25 [] -class_RealVector_Oreal__normed__algebra(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)).
% 277.97/278.06    Following clause subsumed by 25 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(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)).
% 277.97/278.06  ** KEPT (pick-wt=21): 26 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))=hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)).
% 277.97/278.06    Following clause subsumed by 26 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))=hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)).
% 277.97/278.06  ** KEPT (pick-wt=21): 27 [] -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).
% 277.97/278.06  ** KEPT (pick-wt=21): 28 [] -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).
% 277.97/278.06  ** KEPT (pick-wt=21): 29 [] -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)).
% 277.97/278.06  ** KEPT (pick-wt=19): 30 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A).
% 277.97/278.06  ** KEPT (pick-wt=19): 31 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.06  ** KEPT (pick-wt=16): 32 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 277.97/278.06  ** KEPT (pick-wt=14): 33 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 277.97/278.06  ** KEPT (pick-wt=14): 34 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 277.97/278.06  ** KEPT (pick-wt=13): 35 [] -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.
% 277.97/278.06  ** KEPT (pick-wt=13): 36 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B)=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.06  ** KEPT (pick-wt=11): 37 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B)=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.06  ** KEPT (pick-wt=11): 38 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 277.97/278.06    Following clause subsumed by 37 during input processing: 0 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B)=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.06  ** KEPT (pick-wt=11): 39 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B)=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.06  ** KEPT (pick-wt=13): 40 [] -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).
% 277.97/278.06  ** KEPT (pick-wt=12): 41 [] -class_OrderedGroup_Oordered__ab__group__add(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),B)!=B|B=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.06  ** KEPT (pick-wt=10): 43 [copy,42,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).
% 277.97/278.06    Following clause subsumed by 43 during input processing: 0 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.06  ** KEPT (pick-wt=10): 44 [] -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).
% 277.97/278.06  ** KEPT (pick-wt=16): 45 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A)| -c_lesse_quals(C,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A).
% 277.97/278.06    Following clause subsumed by 45 during input processing: 0 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A)| -c_lesse_quals(C,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A).
% 277.97/278.06  ** KEPT (pick-wt=16): 46 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A)| -c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),B,A).
% 277.97/278.06    Following clause subsumed by 46 during input processing: 0 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A)| -c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),B,A).
% 277.97/278.06  ** KEPT (pick-wt=18): 47 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),B).
% 277.97/278.07  ** KEPT (pick-wt=11): 48 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))=B.
% 277.97/278.07  ** KEPT (pick-wt=11): 49 [] -class_Lattices_Oboolean__algebra(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B))=B.
% 277.97/278.07    Following clause subsumed by 48 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.
% 277.97/278.07    Following clause subsumed by 48 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.
% 277.97/278.07    Following clause subsumed by 48 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.
% 277.97/278.07  ** KEPT (pick-wt=18): 50 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C).
% 277.97/278.07  ** KEPT (pick-wt=18): 51 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)!=hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),D)|B=C.
% 277.97/278.07  ** KEPT (pick-wt=18): 52 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B)!=hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)|C=D.
% 277.97/278.07  ** KEPT (pick-wt=16): 53 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A)| -c_lesse_quals(C,B,A).
% 277.97/278.07  ** KEPT (pick-wt=16): 54 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A).
% 277.97/278.07  ** KEPT (pick-wt=14): 55 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),B)!=hAPP(c_HOL_Ouminus__class_Ouminus(A),C)|B=C.
% 277.97/278.07  ** KEPT (pick-wt=14): 56 [] -class_Lattices_Oboolean__algebra(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),B)!=hAPP(c_HOL_Ouminus__class_Ouminus(A),C)|B=C.
% 277.97/278.07  ** KEPT (pick-wt=13): 57 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(C,B,A)| -c_lesse_quals(B,C,A).
% 277.97/278.07    Following clause subsumed by 57 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(C,B,A)| -c_lesse_quals(B,C,A).
% 277.97/278.07    Following clause subsumed by 57 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(B,C,A)| -c_lesse_quals(C,B,A).
% 277.97/278.07  ** KEPT (pick-wt=15): 58 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=15): 59 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.07  ** KEPT (pick-wt=23): 60 [] -class_OrderedGroup_Opordered__ab__group__add(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)!=hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E)|c_lesse_quals(C,B,A)| -c_lesse_quals(E,D,A).
% 277.97/278.07  ** KEPT (pick-wt=23): 61 [] -class_OrderedGroup_Opordered__ab__group__add(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)!=hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E)|c_lesse_quals(E,D,A)| -c_lesse_quals(C,B,A).
% 277.97/278.07  ** KEPT (pick-wt=14): 62 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_HOL_Ozero__class_Ozero(A)),B)=hAPP(c_HOL_Ouminus__class_Ouminus(A),B).
% 277.97/278.07  ** KEPT (pick-wt=18): 64 [copy,63,flip.2] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C).
% 277.97/278.07  ** KEPT (pick-wt=18): 66 [copy,65,flip.2] -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C).
% 277.97/278.07  ** KEPT (pick-wt=18): 68 [copy,67,flip.2] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C).
% 277.97/278.07    Following clause subsumed by 64 during input processing: 0 [flip.2] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C).
% 277.97/278.07  ** KEPT (pick-wt=15): 69 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A).
% 277.97/278.07  ** KEPT (pick-wt=15): 70 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=14): 71 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A).
% 277.97/278.07  ** KEPT (pick-wt=14): 72 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=14): 73 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),B,A).
% 277.97/278.07  ** KEPT (pick-wt=123): 74 [] -class_Ring__and__Field_Ocomm__ring(A)| -class_OrderedGroup_Omonoid__mult(A)|c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(A),c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),c_COMBB(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),tc_nat,A,tc_nat),A,tc_fun(A,A),tc_nat),c_Power_Opower__class_Opower(B,A),tc_nat,A,A),A,tc_fun(A,A),tc_nat),hAPP(c_Power_Opower__class_Opower(B,A),D),tc_nat,A,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat),tc_nat,A)=c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(B,A),A,tc_fun(A,A),tc_nat),c_COMBS(c_COMBB(c_HOL_Ominus__class_Ominus(A),c_COMBB(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),tc_nat,A,tc_nat),A,tc_fun(A,A),tc_nat),c_COMBB(c_Power_Opower__class_Opower(B,A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),tc_nat,A,tc_nat),tc_nat,A,A),tc_nat,A,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat),tc_nat,A).
% 277.97/278.07  ** KEPT (pick-wt=20): 75 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A).
% 277.97/278.07  ** KEPT (pick-wt=20): 76 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A)| -c_lesse_quals(C,D,A).
% 277.97/278.07  ** KEPT (pick-wt=20): 77 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A).
% 277.97/278.07  ** KEPT (pick-wt=20): 78 [] -class_OrderedGroup_Opordered__ab__semigroup__add(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A)| -c_lesse_quals(B,D,A).
% 277.97/278.07  ** KEPT (pick-wt=20): 79 [] -class_OrderedGroup_Opordered__ab__semigroup__add(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A)| -c_lesse_quals(C,D,A).
% 277.97/278.07  ** KEPT (pick-wt=15): 80 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),C)=B.
% 277.97/278.07  ** KEPT (pick-wt=35): 81 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(A),B),D)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E)).
% 277.97/278.07  ** KEPT (pick-wt=21): 82 [] -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).
% 277.97/278.07  ** KEPT (pick-wt=15): 83 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),C)=B.
% 277.97/278.07  ** KEPT (pick-wt=15): 85 [copy,84,flip.2] -class_Int_Onumber__ring(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),B)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,A)),B).
% 277.97/278.07  ** KEPT (pick-wt=15): 86 [] -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OMin,A))=hAPP(c_HOL_Ouminus__class_Ouminus(A),B).
% 277.97/278.07  ** KEPT (pick-wt=11): 88 [copy,87,flip.2] -class_Int_Onumber__ring(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A))=c_Int_Onumber__class_Onumber__of(c_Int_OMin,A).
% 277.97/278.07    Following clause subsumed by 88 during input processing: 0 [] -class_Int_Onumber__ring(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A))=c_Int_Onumber__class_Onumber__of(c_Int_OMin,A).
% 277.97/278.07  ** KEPT (pick-wt=21): 89 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B)!=c_HOL_Ozero__class_Ozero(tc_nat)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),A)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=A.
% 277.97/278.07  ** KEPT (pick-wt=19): 90 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OMin,A))=hAPP(c_HOL_Ouminus__class_Ouminus(A),B).
% 277.97/278.07  ** KEPT (pick-wt=7): 91 [] c_Int_OBit1(A)!=c_Int_OMin|A=c_Int_OMin.
% 277.97/278.07  ** KEPT (pick-wt=7): 93 [copy,92,flip.1] c_Int_OBit1(A)!=c_Int_OMin|c_Int_OMin=A.
% 277.97/278.07  ** KEPT (pick-wt=3): 94 [] c_Int_OPls!=c_Int_OMin.
% 277.97/278.07    Following clause subsumed by 94 during input processing: 0 [flip.1] c_Int_OPls!=c_Int_OMin.
% 277.97/278.07  ** KEPT (pick-wt=10): 95 [] -class_OrderedGroup_Omonoid__mult(A)|hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Oone__class_Oone(tc_nat))=B.
% 277.97/278.07  ** KEPT (pick-wt=10): 96 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Oone__class_Oone(tc_nat))=B.
% 277.97/278.07  ** KEPT (pick-wt=4): 98 [copy,97,flip.1] c_Int_OBit0(A)!=c_Int_OMin.
% 277.97/278.07    Following clause subsumed by 98 during input processing: 0 [] c_Int_OBit0(A)!=c_Int_OMin.
% 277.97/278.07  ** KEPT (pick-wt=21): 100 [copy,99,flip.2] -class_Ring__and__Field_Ofield(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C)=hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)).
% 277.97/278.07  ** KEPT (pick-wt=23): 101 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C))=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)).
% 277.97/278.07  ** KEPT (pick-wt=30): 102 [] -class_Ring__and__Field_Ofield(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)).
% 277.97/278.07  ** KEPT (pick-wt=30): 103 [] -class_RealVector_Oreal__normed__field(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)).
% 277.97/278.07  ** KEPT (pick-wt=23): 104 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C).
% 277.97/278.07  ** KEPT (pick-wt=21): 105 [] -class_RealVector_Oreal__normed__field(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C)=hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)).
% 277.97/278.07  ** KEPT (pick-wt=18): 106 [] -hBOOL(hAPP(A,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)),B)))|hBOOL(hAPP(A,C)).
% 277.97/278.07    Following clause subsumed by 106 during input processing: 0 [] -hBOOL(hAPP(A,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)),B)))|hBOOL(hAPP(A,C)).
% 277.97/278.07  ** KEPT (pick-wt=13): 108 [copy,107,flip.1] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)!=c_HOL_Oone__class_Oone(tc_nat)|A=c_HOL_Oone__class_Oone(tc_nat).
% 277.97/278.07  ** KEPT (pick-wt=13): 110 [copy,109,flip.1] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)!=c_HOL_Oone__class_Oone(tc_nat)|B=c_HOL_Oone__class_Oone(tc_nat).
% 277.97/278.07    Following clause subsumed by 108 during input processing: 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)!=c_HOL_Oone__class_Oone(tc_nat)|A=c_HOL_Oone__class_Oone(tc_nat).
% 277.97/278.07    Following clause subsumed by 110 during input processing: 0 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)!=c_HOL_Oone__class_Oone(tc_nat)|B=c_HOL_Oone__class_Oone(tc_nat).
% 277.97/278.07  ** KEPT (pick-wt=26): 111 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(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),A).
% 277.97/278.07  ** KEPT (pick-wt=22): 112 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(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)),A).
% 277.97/278.07  ** KEPT (pick-wt=26): 113 [] -class_Ring__and__Field_Oordered__ring__strict(A)|B=c_HOL_Ozero__class_Ozero(A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=26): 114 [] -class_Ring__and__Field_Oordered__ring__strict(A)|B=c_HOL_Ozero__class_Ozero(A)| -c_lesse_quals(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),A).
% 277.97/278.07  ** KEPT (pick-wt=26): 115 [] -class_Ring__and__Field_Oordered__idom(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),B,A)| -c_lesse_quals(C,c_HOL_Oone__class_Oone(A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.07  ** KEPT (pick-wt=26): 116 [] -class_Ring__and__Field_Oordered__idom(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A)| -c_lesse_quals(B,c_HOL_Oone__class_Oone(A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A).
% 277.97/278.07  ** KEPT (pick-wt=53): 118 [copy,117,flip.2] -class_Ring__and__Field_Ofield(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(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),E),C))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),E)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C))|C=c_HOL_Ozero__class_Ozero(A)|E=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.07  ** KEPT (pick-wt=36): 119 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(B,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A).
% 277.97/278.07  ** KEPT (pick-wt=36): 120 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),D,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),D,A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),B,A)| -c_lesse_quals(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A).
% 277.97/278.07  ** KEPT (pick-wt=12): 121 [] -class_Ring__and__Field_Oordered__idom(A)| -c_lesse_quals(hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=20): 122 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=20): 123 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=20): 124 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.07  ** KEPT (pick-wt=20): 125 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B),A).
% 277.97/278.07  ** KEPT (pick-wt=60): 126 [] -class_RealVector_Oreal__field(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))),F)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E)),F))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),F)),E)).
% 277.97/278.07  ** KEPT (pick-wt=29): 127 [] -class_Ring__and__Field_Oring__1(A)|hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),C)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A)),A),C)),hAPP(c_Power_Opower__class_Opower(B,A),C)).
% 277.97/278.07  ** KEPT (pick-wt=27): 128 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,D)),hAPP(c_Power_Opower__class_Opower(C,A),hAPP(c_Suc,D)),A).
% 277.97/278.07  ** KEPT (pick-wt=30): 129 [] -class_Ring__and__Field_Oordered__semidom(A)|hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,C))!=hAPP(c_Power_Opower__class_Opower(D,A),hAPP(c_Suc,C))|B=D| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),D,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.07  ** KEPT (pick-wt=22): 130 [] -class_Ring__and__Field_Oordered__idom(A)|B=c_HOL_Ozero__class_Ozero(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat)),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=35): 132 [copy,131,flip.2] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(A),B,A,tc_fun(A,A),D),E,D,A,A),C,D,A).
% 277.97/278.07    Following clause subsumed by 119 during input processing: 0 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lesse_quals(B,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),c_Int_Onumber__class_Onumber__of(D,A)),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(D,A)),A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(D,A)),C,A).
% 277.97/278.07    Following clause subsumed by 120 during input processing: 0 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(C,A)),D,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),D,A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),c_Int_Onumber__class_Onumber__of(C,A)),B,A)| -c_lesse_quals(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),c_Int_Onumber__class_Onumber__of(C,A)),A).
% 277.97/278.07    Following clause subsumed by 119 during input processing: 0 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lesse_quals(c_Int_Onumber__class_Onumber__of(B,A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D),A)| -c_lesse_quals(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D),A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D),C,A).
% 277.97/278.07    Following clause subsumed by 120 during input processing: 0 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),c_Int_Onumber__class_Onumber__of(D,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(D,A),A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(D,A)),C),B,A)| -c_lesse_quals(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(D,A)),C),A).
% 277.97/278.07  ** KEPT (pick-wt=19): 133 [] -class_Ring__and__Field_Oordered__idom(A)|c_Int_Onumber__class_Onumber__of(B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)| -c_lesse_quals(hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(B,tc_nat)),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=69): 134 [] -class_Ring__and__Field_Ocomm__ring(A)| -class_OrderedGroup_Omonoid__mult(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,C))),hAPP(c_Power_Opower__class_Opower(D,A),hAPP(c_Suc,C)))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(B,A),A,tc_fun(A,A),tc_nat),c_COMBB(c_Power_Opower__class_Opower(D,A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,A,tc_nat),tc_nat,A,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat),tc_nat,A)).
% 277.97/278.07  ** KEPT (pick-wt=24): 135 [] -class_Ring__and__Field_Ocomm__ring__1(A)|hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))=hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)).
% 277.97/278.07  ** KEPT (pick-wt=31): 136 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A).
% 277.97/278.07  ** KEPT (pick-wt=15): 137 [] -class_Ring__and__Field_Oordered__idom(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A).
% 277.97/278.07  ** KEPT (pick-wt=34): 138 [] -class_Ring__and__Field_Oordered__semidom(A)|hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))!=hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))|B=C| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.07  ** KEPT (pick-wt=34): 139 [] -class_Ring__and__Field_Ocomm__ring__1(A)|hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C))=hAPP(c_Power_Opower__class_Opower(B,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)).
% 277.97/278.07  ** KEPT (pick-wt=40): 140 [] -class_Ring__and__Field_Ofield(A)|c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(B,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_Power_Opower__class_Opower(B,A),C)),c_HOL_Oone__class_Oone(A))),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),c_HOL_Oone__class_Oone(A)))|B=c_HOL_Oone__class_Oone(A).
% 277.97/278.07  ** KEPT (pick-wt=32): 141 [] -class_Ring__and__Field_Oordered__idom(A)|B=c_HOL_Ozero__class_Ozero(A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=32): 142 [] -class_Ring__and__Field_Oordered__idom(A)|B=c_HOL_Ozero__class_Ozero(A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=30): 143 [] -class_Ring__and__Field_Oordered__idom(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=28): 144 [] -class_Ring__and__Field_Oordered__idom(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),A).
% 277.97/278.07  ** KEPT (pick-wt=20): 145 [] -class_Ring__and__Field_Oordered__idom(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(c_Power_Opower__class_Opower(B,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)),A).
% 277.97/278.07  ** KEPT (pick-wt=24): 146 [] -class_Ring__and__Field_Oordered__idom(A)|B=c_HOL_Ozero__class_Ozero(A)| -c_lesse_quals(hAPP(c_Power_Opower__class_Opower(B,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=23): 147 [] -class_Ring__and__Field_Ocomm__ring__1(A)|hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A)),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))=c_HOL_Oone__class_Oone(A).
% 277.97/278.07  ** KEPT (pick-wt=58): 149 [copy,148,flip.2] -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),A)),B)),C))=hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)).
% 277.97/278.07  ** KEPT (pick-wt=14): 150 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),B,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.07  ** KEPT (pick-wt=14): 151 [] -class_OrderedGroup_Oordered__ab__group__add(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A).
% 277.97/278.07  ** KEPT (pick-wt=14): 152 [] -class_OrderedGroup_Oordered__ab__group__add(A)|c_lesse_quals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=14): 153 [] -class_OrderedGroup_Oordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),B,A).
% 277.97/278.07  ** KEPT (pick-wt=14): 154 [] -class_OrderedGroup_Oordered__ab__group__add(A)|c_lesse_quals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),B,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.07  ** KEPT (pick-wt=16): 155 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,C,A).
% 277.97/278.07  ** KEPT (pick-wt=16): 156 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=24): 157 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(A),B),C)).
% 277.97/278.07  ** KEPT (pick-wt=6): 158 [] -class_Orderings_Opreorder(A)|c_lesse_quals(B,B,A).
% 277.97/278.07  ** KEPT (pick-wt=6): 159 [] -class_Orderings_Oorder(A)|c_lesse_quals(B,B,A).
% 277.97/278.07  ** KEPT (pick-wt=14): 160 [] -class_Orderings_Opreorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(D,C,A)| -c_lesse_quals(B,D,A).
% 277.97/278.07  ** KEPT (pick-wt=14): 161 [] -class_Orderings_Oorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(B,D,A)| -c_lesse_quals(D,C,A).
% 277.97/278.07  ** KEPT (pick-wt=10): 162 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)|c_lesse_quals(C,B,A).
% 277.97/278.07  ** KEPT (pick-wt=25): 164 [copy,163,flip.4] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber__ring(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B))=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,A)),B).
% 277.97/278.07  ** KEPT (pick-wt=22): 165 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=22): 166 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=22): 167 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)|c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=22): 168 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=25): 169 [] -class_Ring__and__Field_Omult__mono1(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(C,D,A).
% 277.97/278.07  ** KEPT (pick-wt=25): 170 [] -class_Ring__and__Field_Omult__mono(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(C,D,A).
% 277.97/278.07  ** KEPT (pick-wt=25): 171 [] -class_Ring__and__Field_Omult__mono(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(B,D,A).
% 277.97/278.07  ** KEPT (pick-wt=25): 172 [] -class_Ring__and__Field_Opordered__ring(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(D,C,A).
% 277.97/278.07  ** KEPT (pick-wt=25): 173 [] -class_Ring__and__Field_Opordered__ring(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(D,B,A).
% 277.97/278.07  ** KEPT (pick-wt=22): 174 [] -class_Ring__and__Field_Opordered__ring(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.07  ** KEPT (pick-wt=22): 175 [] -class_Ring__and__Field_Opordered__ring(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07    Following clause subsumed by 175 during input processing: 0 [] -class_Ring__and__Field_Opordered__ring(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=12): 176 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B),A).
% 277.97/278.07  ** KEPT (pick-wt=22): 177 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.07  ** KEPT (pick-wt=22): 178 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.07  ** KEPT (pick-wt=22): 179 [] -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.07  ** KEPT (pick-wt=22): 180 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A).
% 277.97/278.07  ** KEPT (pick-wt=22): 181 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A).
% 277.97/278.07  ** KEPT (pick-wt=22): 182 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A).
% 277.97/278.07  ** KEPT (pick-wt=22): 183 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A).
% 277.97/278.07  ** KEPT (pick-wt=34): 184 [] -class_Ring__and__Field_Opordered__semiring(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),D,A)| -c_lesse_quals(C,E,A)| -c_lesse_quals(B,D,A).
% 277.97/278.07  ** KEPT (pick-wt=34): 185 [] -class_Ring__and__Field_Opordered__semiring(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(C,E,A)| -c_lesse_quals(B,D,A).
% 277.97/278.07  ** KEPT (pick-wt=22): 186 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.08  ** KEPT (pick-wt=22): 187 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.08  ** KEPT (pick-wt=22): 188 [] -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.08  ** KEPT (pick-wt=22): 189 [] -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.08    Following clause subsumed by 188 during input processing: 0 [] -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.08    Following clause subsumed by 189 during input processing: 0 [] -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.08    Following clause subsumed by 189 during input processing: 0 [] -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A).
% 277.97/278.08  ** KEPT (pick-wt=14): 190 [] -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).
% 277.97/278.08  ** KEPT (pick-wt=14): 191 [] -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).
% 277.97/278.08  ** KEPT (pick-wt=14): 192 [] -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).
% 277.97/278.08    Following clause subsumed by 190 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).
% 277.97/278.08  ** KEPT (pick-wt=19): 194 [copy,193,factor_simp] -class_OrderedGroup_Opordered__comm__monoid__add(A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),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).
% 277.97/278.08  ** KEPT (pick-wt=22): 195 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)| -class_OrderedGroup_Ocomm__monoid__add(A)|c_lesse_quals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_lesse_quals(B,D,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A).
% 277.97/278.08  ** KEPT (pick-wt=22): 196 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)| -class_OrderedGroup_Ocomm__monoid__add(A)|c_lesse_quals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_lesse_quals(B,C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),D,A).
% 277.97/278.08  ** KEPT (pick-wt=25): 197 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=c_HOL_Ozero__class_Ozero(A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)|B=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08  ** KEPT (pick-wt=25): 198 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=c_HOL_Ozero__class_Ozero(A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)|C=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08  ** KEPT (pick-wt=22): 199 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.08  ** KEPT (pick-wt=17): 200 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A).
% 277.97/278.08  ** KEPT (pick-wt=17): 201 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.08  ** KEPT (pick-wt=17): 202 [] -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.
% 277.97/278.08  ** KEPT (pick-wt=17): 203 [] -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).
% 277.97/278.08  ** KEPT (pick-wt=17): 204 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.08  ** KEPT (pick-wt=17): 205 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.08  ** KEPT (pick-wt=22): 206 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.08  ** KEPT (pick-wt=8): 207 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A).
% 277.97/278.08  ** KEPT (pick-wt=8): 208 [] -class_Ring__and__Field_Oordered__semidom(A)| -c_lesse_quals(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.08  ** KEPT (pick-wt=65): 210 [copy,209,flip.2] -class_RealVector_Oreal__normed__algebra(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),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E)))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)).
% 277.97/278.08  ** KEPT (pick-wt=40): 211 [] -class_Ring__and__Field_Oring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),B)),C)),E))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),E).
% 277.97/278.08    Following clause subsumed by 211 during input processing: 0 [flip.2] -class_Ring__and__Field_Oring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D).
% 277.97/278.08  ** KEPT (pick-wt=43): 212 [] -class_Ring__and__Field_Oring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D)=F.
% 277.97/278.08  ** KEPT (pick-wt=43): 213 [] -class_Ring__and__Field_Oring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F)|D=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B)),C)),F).
% 277.97/278.08  ** KEPT (pick-wt=38): 215 [copy,214,flip.3] -class_Ring__and__Field_Oring(A)| -class_Int_Onumber(A)|hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)).
% 277.97/278.08  ** KEPT (pick-wt=38): 216 [] -class_Ring__and__Field_Oring(A)| -class_Int_Onumber(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),c_Int_Onumber__class_Onumber__of(D,A))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(D,A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),c_Int_Onumber__class_Onumber__of(D,A))).
% 277.97/278.08  ** KEPT (pick-wt=17): 218 [copy,217,flip.2] -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A))),B)=hAPP(c_HOL_Ouminus__class_Ouminus(A),B).
% 277.97/278.08  ** KEPT (pick-wt=20): 219 [] -class_Ring__and__Field_Oordered__idom(A)|B=c_HOL_Ozero__class_Ozero(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(hAPP(c_Power_Opower__class_Opower(B,A),C),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.08  ** KEPT (pick-wt=23): 220 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(hAPP(c_Power_Opower__class_Opower(B,A),C),hAPP(c_Power_Opower__class_Opower(D,A),C),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(B,D,A).
% 277.97/278.08  ** KEPT (pick-wt=16): 221 [] -class_Ring__and__Field_Oordered__idom(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(c_Power_Opower__class_Opower(B,A),C),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.08  ** KEPT (pick-wt=16): 222 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(c_Power_Opower__class_Opower(B,A),C),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.08  ** KEPT (pick-wt=24): 223 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),A).
% 277.97/278.08  ** KEPT (pick-wt=24): 224 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),B),A).
% 277.97/278.08  ** KEPT (pick-wt=24): 225 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),A).
% 277.97/278.08  ** KEPT (pick-wt=24): 226 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),B),A).
% 277.97/278.08  ** KEPT (pick-wt=25): 227 [] -class_Ring__and__Field_Ofield(A)|hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C))=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))|C=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08  ** KEPT (pick-wt=24): 228 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.08  ** KEPT (pick-wt=24): 229 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.08  ** KEPT (pick-wt=27): 230 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(B,D,A).
% 277.97/278.08  ** KEPT (pick-wt=27): 231 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(D,B,A).
% 277.97/278.08  ** KEPT (pick-wt=25): 232 [] -class_Ring__and__Field_Ofield(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),C))=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)|C=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08  ** KEPT (pick-wt=24): 233 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.08  ** KEPT (pick-wt=24): 234 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),B),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.08  ** KEPT (pick-wt=24): 235 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)|c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.08  ** KEPT (pick-wt=24): 236 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),B),c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.08  ** KEPT (pick-wt=24): 237 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 277.97/278.08  ** KEPT (pick-wt=24): 238 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 277.97/278.08  ** KEPT (pick-wt=22): 240 [copy,239,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).
% 277.97/278.08  ** KEPT (pick-wt=16): 241 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(c_HOL_Oone__class_Oone(A),hAPP(c_Power_Opower__class_Opower(B,A),C),A)| -c_lesse_quals(c_HOL_Oone__class_Oone(A),B,A).
% 277.97/278.08  ** KEPT (pick-wt=16): 243 [copy,242,flip.1] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)!=A|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Oone__class_Oone(tc_nat).
% 277.97/278.08  ** KEPT (pick-wt=27): 244 [] -class_Ring__and__Field_Oordered__idom(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C))),A).
% 277.97/278.08  ** KEPT (pick-wt=21): 245 [] -class_Int_Onumber__ring(A)|hAPP(c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))=c_HOL_Oone__class_Oone(A).
% 277.97/278.08  ** KEPT (pick-wt=24): 246 [] -class_Int_Onumber__ring(A)|hAPP(c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,A),A),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)))=c_Int_Onumber__class_Onumber__of(c_Int_OMin,A).
% 277.97/278.08  ** KEPT (pick-wt=28): 247 [] -class_Ring__and__Field_Ocomm__ring__1(A)|hAPP(c_Power_Opower__class_Opower(hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A)),A),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)))=hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A)).
% 277.97/278.08  ** KEPT (pick-wt=51): 249 [copy,248,flip.2] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(B,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))),hAPP(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)))=c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat,A).
% 277.97/278.08  ** KEPT (pick-wt=77): 251 [copy,250,flip.3] -class_Power_Opower(A)| -class_OrderedGroup_Ocomm__monoid__add(A)|c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),c_COMBB(c_Power_Opower__class_Opower(B,A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,A,tc_nat),A,tc_fun(A,A),tc_nat),c_Power_Opower__class_Opower(D,A),tc_nat,A,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat),tc_nat,A)=c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(B,A),A,tc_fun(A,A),tc_nat),c_COMBB(c_Power_Opower__class_Opower(D,A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),tc_nat,A,tc_nat),tc_nat,A,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,C),tc_nat),tc_nat,A).
% 277.97/278.08  ** KEPT (pick-wt=84): 253 [copy,252,flip.3] -class_Ring__and__Field_Ocomm__semiring__0(A)| -class_OrderedGroup_Omonoid__mult(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(C,A),A,tc_fun(A,A),tc_nat),c_COMBB(c_Power_Opower__class_Opower(B,A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D),tc_nat,A,tc_nat),tc_nat,A,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,D),tc_nat),tc_nat,A))=c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(C,A),A,tc_fun(A,A),tc_nat),c_COMBB(c_Power_Opower__class_Opower(B,A),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,D)),tc_nat,A,tc_nat),tc_nat,A,A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,D),tc_nat),tc_nat,A).
% 277.97/278.08  ** KEPT (pick-wt=18): 254 [] -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.
% 277.97/278.08  ** KEPT (pick-wt=20): 255 [] -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.
% 277.97/278.08  ** KEPT (pick-wt=16): 256 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 277.97/278.08    Following clause subsumed by 256 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.
% 277.97/278.08  ** KEPT (pick-wt=16): 257 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B)|A=C.
% 277.97/278.08  ** KEPT (pick-wt=15): 258 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08  ** KEPT (pick-wt=11): 259 [] -class_Ring__and__Field_Ofield(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Oone__class_Oone(A))=B.
% 277.97/278.08  ** KEPT (pick-wt=35): 260 [] -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)).
% 277.97/278.08  ** KEPT (pick-wt=36): 262 [copy,261,flip.3] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D))|D=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08  ** KEPT (pick-wt=36): 264 [copy,263,flip.3] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),C)|D=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08  ** KEPT (pick-wt=9): 265 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A)=c_HOL_Oone__class_Oone(A).
% 277.97/278.08  ** KEPT (pick-wt=23): 266 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(c_Int_OBit1(B),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Int_Onumber__class_Onumber__of(B,A))),c_Int_Onumber__class_Onumber__of(B,A)).
% 277.97/278.08  ** KEPT (pick-wt=5): 267 [] c_Int_OBit1(A)!=c_Int_OBit0(B).
% 277.97/278.08  ** KEPT (pick-wt=29): 269 [copy,268,flip.5] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(B,A)!=c_HOL_Ozero__class_Ozero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),C)=c_Int_Onumber__class_Onumber__of(B,A).
% 277.97/278.08  ** KEPT (pick-wt=16): 270 [] -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A))=c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),A).
% 277.97/278.08  ** KEPT (pick-wt=30): 271 [] -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).
% 277.97/278.08  ** KEPT (pick-wt=58): 273 [copy,272,flip.2] -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),A)),B)),C))=hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)).
% 277.97/278.08  ** KEPT (pick-wt=30): 274 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(B,A)!=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D)=C|D=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08  ** KEPT (pick-wt=30): 275 [] -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)).
% 277.97/278.08  ** KEPT (pick-wt=30): 277 [copy,276,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)).
% 277.97/278.08  ** KEPT (pick-wt=30): 278 [] -class_RealVector_Oreal__normed__algebra(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)).
% 277.97/278.08    Following clause subsumed by 278 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(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)).
% 277.97/278.08  ** KEPT (pick-wt=30): 280 [copy,279,flip.2] -class_RealVector_Oreal__normed__algebra(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)).
% 277.97/278.08    Following clause subsumed by 280 during input processing: 0 [flip.2] -class_RealVector_Oreal__normed__algebra(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)).
% 277.97/278.08  ** KEPT (pick-wt=30): 281 [] -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)).
% 277.97/278.08  ** KEPT (pick-wt=25): 283 [copy,282,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)).
% 277.97/278.08  ** KEPT (pick-wt=25): 284 [] -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)).
% 277.97/278.08    Following clause subsumed by 283 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)).
% 277.97/278.08    Following clause subsumed by 283 during input processing: 0 [] -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)).
% 277.97/278.08  ** KEPT (pick-wt=25): 285 [] -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).
% 277.97/278.08  ** KEPT (pick-wt=25): 286 [] -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)).
% 277.97/278.08  ** KEPT (pick-wt=9): 287 [] -class_Int_Onumber__ring(A)|c_HOL_Oone__class_Oone(A)=c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A).
% 277.97/278.08  ** KEPT (pick-wt=18): 288 [] -class_Ring__and__Field_Ofield(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)!=c_HOL_Oone__class_Oone(A)|C=c_HOL_Ozero__class_Ozero(A)|B=C.
% 277.97/278.08  ** KEPT (pick-wt=23): 289 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|B=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|A=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.08  ** KEPT (pick-wt=19): 290 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(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).
% 277.97/278.08  ** KEPT (pick-wt=18): 291 [] -class_OrderedGroup_Omonoid__mult(A)|hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B).
% 277.97/278.08  ** KEPT (pick-wt=27): 292 [] -class_OrderedGroup_Ocomm__monoid__mult(A)|hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),D)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(B,A),D)),hAPP(c_Power_Opower__class_Opower(C,A),D)).
% 277.97/278.08  ** KEPT (pick-wt=27): 293 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),D)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(B,A),D)),hAPP(c_Power_Opower__class_Opower(C,A),D)).
% 277.97/278.08  ** KEPT (pick-wt=12): 294 [] -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Int_Onumber__class_Onumber__of(c_Int_OPls,A)),B)=B.
% 277.97/278.08  ** KEPT (pick-wt=12): 295 [] -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OPls,A))=B.
% 277.97/278.08  ** KEPT (pick-wt=20): 296 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,A)),B)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,A)),C)|B=C.
% 277.97/278.08  ** KEPT (pick-wt=10): 297 [] -class_OrderedGroup_Oab__semigroup__idem__mult(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)=B.
% 277.97/278.08  ** KEPT (pick-wt=21): 298 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Int_Onumber__class_Onumber__of(B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(B,tc_nat))=c_HOL_Oone__class_Oone(A).
% 277.97/278.08  ** KEPT (pick-wt=5): 299 [] hAPP(c_Suc,A)!=A.
% 277.97/278.08    Following clause subsumed by 299 during input processing: 0 [flip.1] hAPP(c_Suc,A)!=A.
% 277.97/278.08  ** KEPT (pick-wt=25): 300 [] -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).
% 277.97/278.08  ** KEPT (pick-wt=25): 301 [] -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).
% 277.97/278.08  ** KEPT (pick-wt=34): 302 [] -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).
% 277.97/278.08  ** KEPT (pick-wt=30): 303 [] 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).
% 277.97/278.08  ** KEPT (pick-wt=31): 304 [] -class_Ring__and__Field_Oordered__idom(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08  ** KEPT (pick-wt=31): 305 [] -class_Ring__and__Field_Oordered__idom(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08  ** KEPT (pick-wt=17): 306 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),B)=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.08  ** KEPT (pick-wt=21): 307 [] -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)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),B)=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.08  ** KEPT (pick-wt=11): 308 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(A).
% 277.97/278.08  ** KEPT (pick-wt=11): 309 [] -class_Power_Opower(A)|hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(A).
% 277.97/278.08  ** KEPT (pick-wt=29): 311 [copy,310,flip.4] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(C,A))),c_Int_Onumber__class_Onumber__of(C,A))=B|c_Int_Onumber__class_Onumber__of(C,A)=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08    Following clause subsumed by 311 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(C,A))),c_Int_Onumber__class_Onumber__of(C,A))=B|c_Int_Onumber__class_Onumber__of(C,A)=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08  ** KEPT (pick-wt=14): 312 [] -class_Ring__and__Field_Oring__1__no__zero__divisors(A)|hAPP(c_Power_Opower__class_Opower(B,A),C)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08  ** KEPT (pick-wt=20): 313 [] -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)|hAPP(c_Power_Opower__class_Opower(B,A),C)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08  ** KEPT (pick-wt=20): 314 [] -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).
% 277.97/278.08  ** KEPT (pick-wt=37): 315 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E))=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)).
% 277.97/278.08  ** KEPT (pick-wt=29): 316 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),A),D)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_Power_Opower__class_Opower(B,A),D)),hAPP(c_Power_Opower__class_Opower(C,A),D)).
% 277.97/278.08  ** KEPT (pick-wt=19): 318 [copy,317,flip.3] -class_Ring__and__Field_Ofield(A)|B=c_HOL_Ozero__class_Ozero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)),B)=C.
% 277.97/278.08    Following clause subsumed by 318 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)|B=c_HOL_Ozero__class_Ozero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)),B)=C.
% 277.97/278.08    Following clause subsumed by 318 during input processing: 0 [flip.3] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),C)=B|C=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08    Following clause subsumed by 318 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),C)=B|C=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08  ** KEPT (pick-wt=23): 319 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(A))!=c_Int_Onumber__class_Onumber__of(C,A)|c_Int_Onumber__class_Onumber__of(C,A)=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08  ** KEPT (pick-wt=23): 320 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(B,A)!=c_HOL_Ozero__class_Ozero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),c_HOL_Ozero__class_Ozero(A))=c_Int_Onumber__class_Onumber__of(B,A).
% 277.97/278.08    Following clause subsumed by 284 during input processing: 0 [] -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)).
% 277.97/278.08    Following clause subsumed by 283 during input processing: 0 [] -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))).
% 277.97/278.08  ** KEPT (pick-wt=35): 321 [] -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)).
% 277.97/278.08  ** KEPT (pick-wt=7): 323 [copy,322,flip.2] -class_Ring__and__Field_Ozero__ne_q__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 277.97/278.08  ** KEPT (pick-wt=24): 324 [] -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_Int_Onumber__class_Onumber__of(B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|hAPP(c_Power_Opower__class_Opower(C,A),c_Int_Onumber__class_Onumber__of(B,tc_nat))!=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08  ** KEPT (pick-wt=25): 326 [copy,325,flip.4] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,A))),c_Int_Onumber__class_Onumber__of(B,A))=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.08  ** KEPT (pick-wt=19): 327 [] -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).
% 277.97/278.08  ** KEPT (pick-wt=19): 328 [] -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).
% 277.97/278.08    Following clause subsumed by 328 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).
% 277.97/278.08  ** KEPT (pick-wt=18): 329 [] -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.
% 277.97/278.08  ** KEPT (pick-wt=18): 330 [] -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.
% 277.97/278.08  ** KEPT (pick-wt=30): 331 [] -class_OrderedGroup_Omonoid__mult(A)|hAPP(c_Power_Opower__class_Opower(B,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C))=hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(B,A),C),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)).
% 277.97/278.08    Following clause subsumed by 269 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(B,A)!=c_HOL_Ozero__class_Ozero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),C)=c_Int_Onumber__class_Onumber__of(B,A).
% 277.97/278.08  ** KEPT (pick-wt=26): 332 [] -class_RealVector_Oreal__normed__algebra(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).
% 277.97/278.09  ** KEPT (pick-wt=26): 333 [] -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).
% 277.97/278.09  ** KEPT (pick-wt=21): 334 [] hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|B=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.09  ** KEPT (pick-wt=21): 335 [] hAPP(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=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.09    Following clause subsumed by 323 during input processing: 0 [] -class_Ring__and__Field_Ozero__ne_q__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 277.97/278.09  ** KEPT (pick-wt=37): 336 [] -class_OrderedGroup_Omonoid__mult(A)|hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(B,A),C),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))).
% 277.97/278.09  ** KEPT (pick-wt=17): 337 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OPls,A))=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=11): 338 [] -class_OrderedGroup_Omonoid__mult(A)|hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),A),B)=c_HOL_Oone__class_Oone(A).
% 277.97/278.09  ** KEPT (pick-wt=28): 339 [] -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.
% 277.97/278.09  ** KEPT (pick-wt=15): 340 [] -class_Ring__and__Field_Ofield(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A))=B.
% 277.97/278.09    Following clause subsumed by 340 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A))=B.
% 277.97/278.09  ** KEPT (pick-wt=8): 341 [] c_Int_OBit0(A)!=c_Int_OBit0(B)|A=B.
% 277.97/278.09  ** KEPT (pick-wt=7): 342 [] c_Int_OBit0(A)!=c_Int_OPls|A=c_Int_OPls.
% 277.97/278.09    Following clause subsumed by 309 during input processing: 0 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(A).
% 277.97/278.09  ** KEPT (pick-wt=4): 343 [] c_Int_OBit1(A)!=c_Int_OPls.
% 277.97/278.09    Following clause subsumed by 291 during input processing: 0 [] -class_OrderedGroup_Omonoid__mult(A)| -class_Int_Onumber(A)|hAPP(c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),c_Int_Onumber__class_Onumber__of(B,A)).
% 277.97/278.09  ** KEPT (pick-wt=28): 344 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,C),hAPP(c_Suc,D),tc_nat),tc_nat,A)=c_Finite__Set_Osetsum(c_COMBB(B,c_Suc,tc_nat,A,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,A).
% 277.97/278.09  ** KEPT (pick-wt=15): 345 [] -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).
% 277.97/278.09    Following clause subsumed by 345 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).
% 277.97/278.09  ** KEPT (pick-wt=15): 346 [] -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).
% 277.97/278.09    Following clause subsumed by 343 during input processing: 0 [flip.1] c_Int_OBit1(A)!=c_Int_OPls.
% 277.97/278.09  ** KEPT (pick-wt=23): 347 [] -class_OrderedGroup_Omonoid__mult(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(B,A),C)),B)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_Power_Opower__class_Opower(B,A),C)).
% 277.97/278.09  ** KEPT (pick-wt=20): 348 [] 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.
% 277.97/278.09  ** KEPT (pick-wt=20): 349 [] 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.
% 277.97/278.09    Following clause subsumed by 349 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).
% 277.97/278.09    Following clause subsumed by 318 during input processing: 0 [flip.4] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),C)=c_Int_Onumber__class_Onumber__of(B,A)|C=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=22): 350 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A))),B).
% 277.97/278.09  ** KEPT (pick-wt=10): 351 [] hAPP(c_Suc,A)!=hAPP(c_Suc,B)|A=B.
% 277.97/278.09    Following clause subsumed by 351 during input processing: 0 [] hAPP(c_Suc,A)!=hAPP(c_Suc,B)|A=B.
% 277.97/278.09  ** KEPT (pick-wt=29): 353 [copy,352,flip.4] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(C,A))),c_Int_Onumber__class_Onumber__of(C,A))=B|c_Int_Onumber__class_Onumber__of(C,A)=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09    Following clause subsumed by 353 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(C,A))),c_Int_Onumber__class_Onumber__of(C,A))=B|c_Int_Onumber__class_Onumber__of(C,A)=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=19): 355 [copy,354,flip.3] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B)),B)=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=19): 356 [] hAPP(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).
% 277.97/278.09  ** KEPT (pick-wt=23): 357 [] hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|B=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|A=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.09    Following clause subsumed by 306 during input processing: 0 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(B,tc_nat))=c_HOL_Ozero__class_Ozero(A)|c_Int_Onumber__class_Onumber__of(B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.09    Following clause subsumed by 307 during input processing: 0 [] -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)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(B,tc_nat))=c_HOL_Ozero__class_Ozero(A)|c_Int_Onumber__class_Onumber__of(B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.09  ** KEPT (pick-wt=39): 358 [] 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.
% 277.97/278.09    Following clause subsumed by 358 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.
% 277.97/278.09  ** KEPT (pick-wt=43): 359 [] -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.
% 277.97/278.09    Following clause subsumed by 359 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.
% 277.97/278.09  ** KEPT (pick-wt=38): 360 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(B,A),C)),hAPP(c_Power_Opower__class_Opower(B,A),C))).
% 277.97/278.09    Following clause subsumed by 318 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),C)=c_Int_Onumber__class_Onumber__of(B,A)|C=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=53): 362 [copy,361,flip.2] -class_Ring__and__Field_Ofield(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Otimes__class_Otimes(A),E),C))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),E)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C))|C=c_HOL_Ozero__class_Ozero(A)|E=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=21): 364 [copy,363,flip.3] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),C)=B|C=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09    Following clause subsumed by 364 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),C)=B|C=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=12): 365 [] -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).
% 277.97/278.09  ** KEPT (pick-wt=12): 366 [] -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).
% 277.97/278.09  ** KEPT (pick-wt=12): 367 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B)=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09    Following clause subsumed by 367 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B)=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=12): 368 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09    Following clause subsumed by 368 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09    Following clause subsumed by 365 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).
% 277.97/278.09  ** KEPT (pick-wt=12): 369 [] -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).
% 277.97/278.09  ** KEPT (pick-wt=12): 370 [] -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).
% 277.97/278.09  ** KEPT (pick-wt=12): 371 [] -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).
% 277.97/278.09  ** KEPT (pick-wt=12): 372 [] -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).
% 277.97/278.09  ** KEPT (pick-wt=26): 373 [] -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)),C)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A))),C).
% 277.97/278.09  ** KEPT (pick-wt=26): 374 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),c_HOL_Oone__class_Oone(A))),B).
% 277.97/278.09  ** KEPT (pick-wt=38): 375 [] -class_Ring__and__Field_Osemiring(A)| -class_Int_Onumber(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_Int_Onumber__class_Onumber__of(D,A))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(D,A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),c_Int_Onumber__class_Onumber__of(D,A))).
% 277.97/278.09  ** KEPT (pick-wt=18): 376 [] -class_Ring__and__Field_Oordered__idom(A)|hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=8): 378 [copy,377,flip.2] -class_Int_Onumber__ring(A)|c_HOL_Ozero__class_Ozero(A)=c_Int_Onumber__class_Onumber__of(c_Int_OPls,A).
% 277.97/278.09  ** KEPT (pick-wt=6): 379 [] hAPP(c_Suc,A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.09    Following clause subsumed by 379 during input processing: 0 [] hAPP(c_Suc,A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.09    Following clause subsumed by 355 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,A))),c_Int_Onumber__class_Onumber__of(B,A))=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=23): 380 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(B,A)!=c_HOL_Ozero__class_Ozero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),c_Int_Onumber__class_Onumber__of(B,A))=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=20): 381 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_Power_Opower__class_Opower(B,A),C))=hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,C)).
% 277.97/278.09  ** KEPT (pick-wt=20): 382 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(B,A),C)),B)=hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,C)).
% 277.97/278.09  ** KEPT (pick-wt=30): 383 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)!=c_Int_Onumber__class_Onumber__of(D,A)|B=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(D,A)),C)|C=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=15): 384 [] -class_Ring__and__Field_Osemiring__1(A)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=15): 385 [] -class_Ring__and__Field_Oordered__idom(A)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=31): 386 [] -class_Ring__and__Field_Ofield(A)|hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C),A),D)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_Power_Opower__class_Opower(B,A),D)),hAPP(c_Power_Opower__class_Opower(C,A),D))|C=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=25): 387 [] -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).
% 277.97/278.09    Following clause subsumed by 378 during input processing: 0 [] -class_Int_Onumber__ring(A)|c_HOL_Ozero__class_Ozero(A)=c_Int_Onumber__class_Onumber__of(c_Int_OPls,A).
% 277.97/278.09  ** KEPT (pick-wt=14): 389 [copy,388,flip.3] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=29): 390 [] -class_Ring__and__Field_Oordered__idom(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=18): 391 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)=hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)).
% 277.97/278.09  ** KEPT (pick-wt=36): 392 [] -class_Ring__and__Field_Ofield(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)!=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E)|E=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C).
% 277.97/278.09  ** KEPT (pick-wt=36): 393 [] -class_Ring__and__Field_Ofield(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)|C=c_HOL_Ozero__class_Ozero(A)|E=c_HOL_Ozero__class_Ozero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),E)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C).
% 277.97/278.09  ** KEPT (pick-wt=22): 394 [] -class_OrderedGroup_Omonoid__mult(A)|hAPP(c_Power_Opower__class_Opower(B,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))=hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(B,A),C),A),D).
% 277.97/278.09    Following clause subsumed by 355 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B)),B)=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=17): 395 [] 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).
% 277.97/278.09  ** KEPT (pick-wt=15): 396 [] -class_Ring__and__Field_Osemiring__1(A)|hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))=c_HOL_Oone__class_Oone(A).
% 277.97/278.09  ** KEPT (pick-wt=13): 397 [] 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).
% 277.97/278.09  ** KEPT (pick-wt=13): 398 [] 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).
% 277.97/278.09  ** KEPT (pick-wt=15): 399 [] -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).
% 277.97/278.09  ** KEPT (pick-wt=23): 400 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(B,A)!=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),c_HOL_Ozero__class_Ozero(A))|c_Int_Onumber__class_Onumber__of(B,A)=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=23): 401 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(B,A)!=c_HOL_Ozero__class_Ozero(A)|c_Int_Onumber__class_Onumber__of(B,A)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),c_HOL_Ozero__class_Ozero(A)).
% 277.97/278.09  ** KEPT (pick-wt=23): 402 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(B,A)!=c_HOL_Ozero__class_Ozero(A)|c_HOL_Ozero__class_Ozero(A)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),c_Int_Onumber__class_Onumber__of(B,A)).
% 277.97/278.09  ** KEPT (pick-wt=27): 403 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(B,A),C)),hAPP(c_Power_Opower__class_Opower(B,A),D))=hAPP(c_Power_Opower__class_Opower(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)).
% 277.97/278.09  ** KEPT (pick-wt=16): 405 [copy,404,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).
% 277.97/278.09  ** KEPT (pick-wt=12): 407 [copy,406,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.09    Following clause subsumed by 407 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.09  ** KEPT (pick-wt=13): 408 [] -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A)),B)=B.
% 277.97/278.09  ** KEPT (pick-wt=13): 409 [] -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A))=B.
% 277.97/278.09  ** KEPT (pick-wt=17): 410 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)!=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|A=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.09  ** KEPT (pick-wt=17): 411 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)!=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|B=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.09  ** KEPT (pick-wt=7): 413 [copy,412,flip.1] c_Int_OBit0(A)!=c_Int_OPls|c_Int_OPls=A.
% 277.97/278.09  ** KEPT (pick-wt=6): 414 [] c_HOL_Ozero__class_Ozero(tc_nat)!=hAPP(c_Suc,A).
% 277.97/278.09    Following clause subsumed by 414 during input processing: 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=hAPP(c_Suc,A).
% 277.97/278.09  ** KEPT (pick-wt=15): 415 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|hAPP(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),A),hAPP(c_Suc,B))=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=22): 416 [] -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A))),c_Int_Onumber__class_Onumber__of(B,A))=c_Int_Onumber__class_Onumber__of(c_Int_OBit0(B),A).
% 277.97/278.09  ** KEPT (pick-wt=11): 417 [] -class_OrderedGroup_Omonoid__mult(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oone__class_Oone(A))=B.
% 277.97/278.09  ** KEPT (pick-wt=11): 418 [] -class_OrderedGroup_Omonoid__mult(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B)=B.
% 277.97/278.09  ** KEPT (pick-wt=11): 419 [] -class_OrderedGroup_Ocomm__monoid__mult(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B)=B.
% 277.97/278.09  ** KEPT (pick-wt=11): 420 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B)=B.
% 277.97/278.09  ** KEPT (pick-wt=11): 421 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oone__class_Oone(A))=B.
% 277.97/278.09    Following clause subsumed by 420 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B)=B.
% 277.97/278.09  ** KEPT (pick-wt=27): 423 [copy,422,flip.3] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B),A),C)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),hAPP(c_Power_Opower__class_Opower(B,A),C)).
% 277.97/278.09  ** KEPT (pick-wt=37): 424 [] -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)).
% 277.97/278.09    Following clause subsumed by 424 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)).
% 277.97/278.09  ** KEPT (pick-wt=8): 425 [] c_Int_OBit1(A)!=c_Int_OBit1(B)|A=B.
% 277.97/278.09  ** KEPT (pick-wt=22): 426 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(B,A),C),A),D)=hAPP(c_Power_Opower__class_Opower(B,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)).
% 277.97/278.09    Following clause subsumed by 381 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_Power_Opower__class_Opower(B,A),C))=hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,C)).
% 277.97/278.09  ** KEPT (pick-wt=20): 428 [copy,427,flip.2] -class_OrderedGroup_Omonoid__mult(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(B,A),C)),B)=hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,C)).
% 277.97/278.09  ** KEPT (pick-wt=20): 430 [copy,429,flip.2] -class_Power_Opower(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_Power_Opower__class_Opower(B,A),C))=hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,C)).
% 277.97/278.09    Following clause subsumed by 381 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_Power_Opower__class_Opower(B,A),C))=hAPP(c_Power_Opower__class_Opower(B,A),hAPP(c_Suc,C)).
% 277.97/278.09  ** KEPT (pick-wt=15): 431 [] -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).
% 277.97/278.09  ** KEPT (pick-wt=13): 432 [] -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).
% 277.97/278.09    Following clause subsumed by 431 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).
% 277.97/278.09  ** KEPT (pick-wt=25): 433 [] -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)).
% 277.97/278.09  ** KEPT (pick-wt=25): 434 [] -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)).
% 277.97/278.09  ** KEPT (pick-wt=25): 436 [copy,435,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)).
% 277.97/278.09  ** KEPT (pick-wt=25): 437 [] -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)).
% 277.97/278.09  ** KEPT (pick-wt=25): 438 [] -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)).
% 277.97/278.09    Following clause subsumed by 436 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)).
% 277.97/278.09  ** KEPT (pick-wt=25): 439 [] -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).
% 277.97/278.09  ** KEPT (pick-wt=25): 440 [] -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)).
% 277.97/278.09    Following clause subsumed by 436 during input processing: 0 [] -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)).
% 277.97/278.09  ** KEPT (pick-wt=27): 442 [copy,441,flip.2] -class_OrderedGroup_Omonoid__mult(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(B,A),C)),hAPP(c_Power_Opower__class_Opower(B,A),D))=hAPP(c_Power_Opower__class_Opower(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)).
% 277.97/278.09  ** KEPT (pick-wt=17): 443 [] -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)|hAPP(c_Power_Opower__class_Opower(B,A),c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=15): 444 [] -class_Ring__and__Field_Ofield(A)|B=c_HOL_Ozero__class_Ozero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),B)=c_HOL_Oone__class_Oone(A).
% 277.97/278.09    Following clause subsumed by 444 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),B)=c_HOL_Oone__class_Oone(A)|B=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09    Following clause subsumed by 444 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),B)=c_HOL_Oone__class_Oone(A)|B=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=38): 446 [copy,445,flip.3] -class_Ring__and__Field_Osemiring(A)| -class_Int_Onumber(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 277.97/278.09  ** KEPT (pick-wt=30): 447 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Ozero__class_Ozero(A)|c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_nat),tc_nat,A)=c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A).
% 277.97/278.09  ** KEPT (pick-wt=23): 448 [] -class_OrderedGroup_Omonoid__mult(A)|hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),B).
% 277.97/278.09  ** KEPT (pick-wt=14): 449 [] -class_Int_Oring__char__0(A)| -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(B,A)!=c_Int_Onumber__class_Onumber__of(C,A)|B=C.
% 277.97/278.09  ** KEPT (pick-wt=35): 451 [copy,450,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).
% 277.97/278.09  ** KEPT (pick-wt=40): 453 [copy,452,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)).
% 277.97/278.09  ** KEPT (pick-wt=23): 454 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(c_Int_OBit0(B),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,A))),c_Int_Onumber__class_Onumber__of(B,A)).
% 277.97/278.09  ** KEPT (pick-wt=12): 455 [] -class_Ring__and__Field_Ofield(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Ozero__class_Ozero(A)),B)=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09    Following clause subsumed by 389 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09    Following clause subsumed by 389 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=12): 456 [] -class_RealVector_Oreal__normed__field(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Ozero__class_Ozero(A)),B)=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=31): 457 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(c_Power_Opower__class_Opower(B,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Power_Opower__class_Opower(B,A),C)),hAPP(c_Power_Opower__class_Opower(B,A),C)).
% 277.97/278.09  ** KEPT (pick-wt=21): 458 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|A=c_HOL_Ozero__class_Ozero(tc_nat)|A=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 277.97/278.09  ** KEPT (pick-wt=21): 459 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|B=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 277.97/278.09  ** KEPT (pick-wt=19): 460 [] -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),A)),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B).
% 277.97/278.09  ** KEPT (pick-wt=19): 461 [] -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),A))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B).
% 277.97/278.09  ** KEPT (pick-wt=31): 462 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(A),B),D)|C=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=31): 463 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(A),C),D)|B=c_HOL_Ozero__class_Ozero(A).
% 277.97/278.09  ** KEPT (pick-wt=5): 464 [] c_Int_OBit0(A)!=c_Int_OBit1(B).
% 277.97/278.09  ** KEPT (pick-wt=27): 465 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),D)=hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),C).
% 277.97/278.09  ** KEPT (pick-wt=11): 466 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 277.97/278.09  ** KEPT (pick-wt=11): 467 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 278.08/278.10  ** KEPT (pick-wt=11): 468 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 278.08/278.10  ** KEPT (pick-wt=13): 470 [copy,469,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.
% 278.08/278.10  ** KEPT (pick-wt=11): 471 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 278.08/278.10  ** KEPT (pick-wt=11): 472 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 278.08/278.10  ** KEPT (pick-wt=11): 473 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 278.08/278.10    Following clause subsumed by 471 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.
% 278.08/278.10    Following clause subsumed by 313 during input processing: 0 [] -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)|hAPP(c_Power_Opower__class_Opower(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat))!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 278.08/278.10  ** KEPT (pick-wt=30): 474 [] -class_Ring__and__Field_Ofield(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)).
% 278.08/278.10  ** KEPT (pick-wt=30): 475 [] -class_RealVector_Oreal__normed__field(A)|hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)).
% 278.08/278.10  ** KEPT (pick-wt=155): 477 [copy,476,flip.1] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_m))),tc_Complex_Ocomplex),v_i)),c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_COMBB(v_a,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_m,tc_nat),tc_nat,tc_Complex_Ocomplex))!=c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_COMBB(v_a,c_COMBB(c_Suc,hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),v_m)),tc_Complex_Ocomplex),c_COMBB(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_i),c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat,tc_nat,tc_nat),tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_m,tc_nat),tc_nat,tc_Complex_Ocomplex).
% 278.08/278.10  ** KEPT (pick-wt=6): 478 [] class_Lattices_Oboolean__algebra(tc_fun(A,B))| -class_Lattices_Oboolean__algebra(B).
% 278.08/278.10  ** KEPT (pick-wt=6): 479 [] class_Orderings_Opreorder(tc_fun(A,B))| -class_Orderings_Opreorder(B).
% 278.08/278.10  ** KEPT (pick-wt=6): 480 [] class_Orderings_Oorder(tc_fun(A,B))| -class_Orderings_Oorder(B).
% 278.08/278.10  ** KEPT (pick-wt=7): 481 [] A=B| -c_fe_qual(A,B,C).
% 278.08/278.10  219 back subsumes 130.
% 278.08/278.10    Following clause subsumed by 464 during input processing: 0 [copy,267,flip.1] c_Int_OBit0(A)!=c_Int_OBit1(B).
% 278.08/278.10  318 back subsumes 311.
% 278.08/278.10  355 back subsumes 326.
% 278.08/278.10  364 back subsumes 353.
% 278.08/278.10    Following clause subsumed by 414 during input processing: 0 [copy,379,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)!=hAPP(c_Suc,A).
% 278.08/278.10  389 back subsumes 258.
% 278.08/278.10    Following clause subsumed by 379 during input processing: 0 [copy,414,flip.1] hAPP(c_Suc,A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 278.08/278.10    Following clause subsumed by 267 during input processing: 0 [copy,464,flip.1] c_Int_OBit1(A)!=c_Int_OBit0(B).
% 278.08/278.10  515 back subsumes 514.
% 278.08/278.10  
% 278.08/278.10  ------------> process sos:
% 278.08/278.10  ** KEPT (pick-wt=3): 557 [] A=A.
% 278.08/278.10  ** KEPT (pick-wt=14): 558 [] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 278.08/278.10  ** KEPT (pick-wt=23): 559 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),C)),B).
% 278.08/278.10  ** KEPT (pick-wt=11): 560 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,A)),c_HOL_Oone__class_Oone(tc_nat))=A.
% 278.08/278.10  ---> New Demodulator: 561 [new_demod,560] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,A)),c_HOL_Oone__class_Oone(tc_nat))=A.
% 278.08/278.10  ** KEPT (pick-wt=21): 563 [copy,562,flip.1] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))),B)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),hAPP(c_Suc,B)).
% 278.08/278.10  ---> New Demodulator: 564 [new_demod,563] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))),B)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),hAPP(c_Suc,B)).
% 278.08/278.10  ** KEPT (pick-wt=9): 565 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),A)=c_HOL_Ozero__class_Ozero(tc_nat).
% 278.08/278.10  ** KEPT (pick-wt=9): 566 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 278.08/278.10  ---> New Demodulator: 567 [new_demod,566] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 278.08/278.10  ** KEPT (pick-wt=10): 568 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=c_HOL_Ozero__class_Ozero(tc_nat).
% 278.08/278.10  ---> New Demodulator: 569 [new_demod,568] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=c_HOL_Ozero__class_Ozero(tc_nat).
% 278.08/278.10  ** KEPT (pick-wt=4): 570 [] c_Int_OBit1(c_Int_OMin)=c_Int_OMin.
% 278.08/278.10  ---> New Demodulator: 571 [new_demod,570] c_Int_OBit1(c_Int_OMin)=c_Int_OMin.
% 278.08/278.10    Following clause subsumed by 557 during input processing: 0 [demod,571] c_Int_OMin=c_Int_OMin.
% 278.08/278.10  ** KEPT (pick-wt=17): 572 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,A)),hAPP(c_Suc,B))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B).
% 278.08/278.10  ---> New Demodulator: 573 [new_demod,572] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,A)),hAPP(c_Suc,B))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B).
% 278.08/278.10  ** KEPT (pick-wt=27): 574 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,A)),B)),hAPP(c_Suc,C))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B)),C).
% 278.08/278.10  ---> New Demodulator: 575 [new_demod,574] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,A)),B)),hAPP(c_Suc,C))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B)),C).
% 278.08/278.10  ** KEPT (pick-wt=23): 576 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C).
% 278.08/278.10  ---> New Demodulator: 577 [new_demod,576] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C).
% 278.08/278.11  ** KEPT (pick-wt=23): 578 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),C).
% 278.08/278.11  ---> New Demodulator: 579 [new_demod,578] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),C).
% 278.08/278.11  ** KEPT (pick-wt=23): 580 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)).
% 278.08/278.11  ** KEPT (pick-wt=13): 581 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),A)=B.
% 278.08/278.11  ---> New Demodulator: 582 [new_demod,581] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),A)=B.
% 278.08/278.11  ** KEPT (pick-wt=13): 583 [] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),B)=A.
% 278.08/278.11  ---> New Demodulator: 584 [new_demod,583] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),B)=A.
% 278.08/278.11  ** KEPT (pick-wt=11): 586 [copy,585,flip.1] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 278.08/278.11  ---> New Demodulator: 587 [new_demod,586] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=9): 588 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)=A.
% 278.08/278.11  ---> New Demodulator: 589 [new_demod,588] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)=A.
% 278.08/278.11  ** KEPT (pick-wt=9): 590 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))=A.
% 278.08/278.11  ---> New Demodulator: 591 [new_demod,590] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))=A.
% 278.08/278.11  ** KEPT (pick-wt=28): 592 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)).
% 278.08/278.11  ** KEPT (pick-wt=28): 594 [copy,593,flip.1] hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(tc_nat),B),C)).
% 278.08/278.11  ---> New Demodulator: 595 [new_demod,594] hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(tc_nat),B),C)).
% 278.08/278.11    Following clause subsumed by 557 during input processing: 0 [demod,591] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=6): 596 [] c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat))=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 278.08/278.11  ---> New Demodulator: 597 [new_demod,596] c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat))=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=7): 598 [] c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 278.08/278.11  ---> New Demodulator: 599 [new_demod,598] c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 278.08/278.11    Following clause subsumed by 557 during input processing: 0 [demod,599] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=33): 600 [] hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A)),c_HOL_Oone__class_Oone(tc_nat)))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=14): 602 [copy,601,flip.1] c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)).
% 278.08/278.11  ---> New Demodulator: 603 [new_demod,602] c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)).
% 278.08/278.11  ** KEPT (pick-wt=47): 605 [copy,604,demod,603,603,603] hAPP(c_Suc,hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)))))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),A)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=43): 607 [copy,606,demod,603] hAPP(c_Suc,hAPP(c_Suc,hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)))))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat)),A)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=25): 609 [copy,608,flip.1] hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=28): 611 [copy,610,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))),A))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=7): 613 [copy,612,flip.1] hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 278.08/278.11  ---> New Demodulator: 614 [new_demod,613] hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=6): 616 [copy,615,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 278.08/278.11  ---> New Demodulator: 617 [new_demod,616] c_HOL_Ozero__class_Ozero(tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=15): 619 [copy,618,demod,617] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 278.08/278.11  ---> New Demodulator: 620 [new_demod,619] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=11): 622 [copy,621,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))=hAPP(c_Suc,A).
% 278.08/278.11  ---> New Demodulator: 623 [new_demod,622] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))=hAPP(c_Suc,A).
% 278.08/278.11  ** KEPT (pick-wt=11): 625 [copy,624,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)=hAPP(c_Suc,A).
% 278.08/278.11  ---> New Demodulator: 626 [new_demod,625] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)=hAPP(c_Suc,A).
% 278.08/278.11  ** KEPT (pick-wt=39): 628 [copy,627,demod,617] c_FFT__Mirabelle_ODFT(A,B,v_i)=c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_COMBB(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat),A,tc_nat),tc_nat,tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=39): 630 [copy,629,demod,617] c_FFT__Mirabelle_OIDFT(A,B,v_i)=c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat),A,tc_nat),tc_nat,tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=7): 632 [copy,631,demod,617,flip.1] c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)=c_FFT__Mirabelle_Oroot(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)).
% 278.08/278.11  ---> New Demodulator: 633 [new_demod,632] c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)=c_FFT__Mirabelle_Oroot(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)).
% 278.08/278.11  ** KEPT (pick-wt=4): 635 [copy,634,flip.1] c_Int_OBit0(c_Int_OPls)=c_Int_OPls.
% 278.08/278.11  ---> New Demodulator: 636 [new_demod,635] c_Int_OBit0(c_Int_OPls)=c_Int_OPls.
% 278.08/278.11  ** KEPT (pick-wt=28): 637 [] 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)).
% 278.08/278.11  ** KEPT (pick-wt=28): 639 [copy,638,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)).
% 278.08/278.11  ---> New Demodulator: 640 [new_demod,639] 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)).
% 278.08/278.11  ** KEPT (pick-wt=23): 641 [] 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)).
% 278.08/278.11  ---> New Demodulator: 642 [new_demod,641] 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)).
% 278.08/278.11  ** KEPT (pick-wt=15): 644 [copy,643,demod,603,623] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),A)=hAPP(c_Suc,hAPP(c_Suc,A)).
% 278.08/278.11  ---> New Demodulator: 645 [new_demod,644] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),A)=hAPP(c_Suc,hAPP(c_Suc,A)).
% 278.08/278.11  ** KEPT (pick-wt=15): 647 [copy,646,demod,603,623] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))=hAPP(c_Suc,hAPP(c_Suc,A)).
% 278.08/278.11  ---> New Demodulator: 648 [new_demod,647] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)))=hAPP(c_Suc,hAPP(c_Suc,A)).
% 278.08/278.11  ** KEPT (pick-wt=15): 650 [copy,649,demod,617] c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)=hAPP(c_Suc,hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)))).
% 278.08/278.11  ---> New Demodulator: 651 [new_demod,650] c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)=hAPP(c_Suc,hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)))).
% 278.08/278.11  ** KEPT (pick-wt=17): 653 [copy,652,demod,617,617] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),A)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),B).
% 278.08/278.11  ** KEPT (pick-wt=17): 655 [copy,654,demod,617,617] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)).
% 278.08/278.11  ** KEPT (pick-wt=11): 657 [copy,656,demod,633] hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),tc_Complex_Ocomplex),A)=c_FFT__Mirabelle_Oroot(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)).
% 278.08/278.11  ** KEPT (pick-wt=22): 659 [copy,658,demod,651,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))))),A)=hAPP(c_Suc,hAPP(c_Suc,hAPP(c_Suc,A))).
% 278.08/278.11  ---> New Demodulator: 660 [new_demod,659] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))))),A)=hAPP(c_Suc,hAPP(c_Suc,hAPP(c_Suc,A))).
% 278.08/278.11  ** KEPT (pick-wt=20): 661 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(c_Suc,B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)).
% 278.08/278.11  ---> New Demodulator: 662 [new_demod,661] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(c_Suc,B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)).
% 278.08/278.11  ** KEPT (pick-wt=20): 663 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(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)).
% 278.08/278.11  ** KEPT (pick-wt=17): 664 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,A)),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_Suc,B)).
% 278.08/278.11  ---> New Demodulator: 665 [new_demod,664] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,A)),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_Suc,B)).
% 278.08/278.11  ** KEPT (pick-wt=18): 667 [copy,666,demod,617,617,617,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)))=hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)).
% 278.08/278.11  ---> New Demodulator: 668 [new_demod,667] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)))=hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)).
% 278.08/278.11  ** KEPT (pick-wt=39): 670 [copy,669,demod,603,623,603,623] hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),A)),tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),C)))=hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)).
% 278.08/278.11  ---> New Demodulator: 671 [new_demod,670] hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),A)),tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))),C)))=hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)).
% 278.08/278.11  ** KEPT (pick-wt=17): 673 [copy,672,demod,665] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_Suc,B))=hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)).
% 278.08/278.11  ---> New Demodulator: 674 [new_demod,673] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_Suc,B))=hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)).
% 278.08/278.11    Following clause subsumed by 557 during input processing: 0 [demod,674] hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)).
% 278.08/278.11  ** KEPT (pick-wt=13): 675 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 278.08/278.11  ** KEPT (pick-wt=27): 677 [copy,676,demod,617,617,662,665,674,617] hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))))=hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)).
% 278.08/278.11  ---> New Demodulator: 678 [new_demod,677] hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))))=hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)).
% 278.08/278.11  ** KEPT (pick-wt=12): 680 [copy,679,demod,617,617] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 278.08/278.11  ---> New Demodulator: 681 [new_demod,680] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=12): 683 [copy,682,demod,617,617] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),A)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 278.08/278.11  ---> New Demodulator: 684 [new_demod,683] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),A)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=18): 686 [copy,685,demod,617,617,617,665,674,flip.1] hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)))=hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)).
% 278.08/278.11  ---> New Demodulator: 687 [new_demod,686] hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)))=hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)).
% 278.08/278.11  ** KEPT (pick-wt=7): 689 [copy,688,demod,617] c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 278.08/278.11  ---> New Demodulator: 690 [new_demod,689] c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=8): 692 [copy,691,demod,599,617] c_HOL_Oone__class_Oone(tc_nat)=hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)).
% 278.08/278.11  ---> New Demodulator: 693 [new_demod,692] c_HOL_Oone__class_Oone(tc_nat)=hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)).
% 278.08/278.11    Following clause subsumed by 557 during input processing: 0 [demod,636] c_Int_OPls=c_Int_OPls.
% 278.08/278.11    Following clause subsumed by 557 during input processing: 0 [demod,617,617,674,687,617] hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))=hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)).
% 278.08/278.11    Following clause subsumed by 557 during input processing: 0 [demod,603,693,693,674,665,674,687,617] hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)))=hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))).
% 278.08/278.11    Following clause subsumed by 557 during input processing: 0 [demod,617,690] c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 278.08/278.11    Following clause subsumed by 557 during input processing: 0 [demod,617,617,665,674,687,617] hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))=hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)).
% 278.08/278.11  ** KEPT (pick-wt=23): 695 [copy,694,demod,640,640] 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)).
% 278.08/278.11    Following clause subsumed by 695 during input processing: 0 [demod,640,640] 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)).
% 278.08/278.11  ** KEPT (pick-wt=14): 697 [copy,696,demod,617,617,617] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 278.08/278.11  ---> New Demodulator: 698 [new_demod,697] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=13): 699 [] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A).
% 278.08/278.11  ** KEPT (pick-wt=23): 700 [] 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)).
% 278.08/278.11  ---> New Demodulator: 701 [new_demod,700] 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)).
% 278.08/278.11  ** KEPT (pick-wt=23): 702 [] 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)).
% 278.08/278.11  ** KEPT (pick-wt=14): 703 [] hAPP(c_COMBB(A,B,C,D,E),F)=hAPP(A,hAPP(B,F)).
% 278.08/278.11  ---> New Demodulator: 704 [new_demod,703] hAPP(c_COMBB(A,B,C,D,E),F)=hAPP(A,hAPP(B,F)).
% 278.08/278.11  ** KEPT (pick-wt=16): 705 [] hAPP(c_COMBS(A,B,C,D,E),F)=hAPP(hAPP(A,F),hAPP(B,F)).
% 278.08/278.11    Following clause subsumed by 557 during input processing: 0 [demod,617,603,693,693,674,665,674,698] hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)))=hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))).
% 278.08/278.11  ** KEPT (pick-wt=38): 707 [copy,706,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)).
% 278.08/278.11  ---> New Demodulator: 708 [new_demod,707] 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)).
% 278.08/278.11  ** KEPT (pick-wt=20): 710 [copy,709,demod,603,693,693,674,665,674,698,662,662,681] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A).
% 278.08/278.11  ---> New Demodulator: 711 [new_demod,710] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A).
% 278.08/278.11  ** KEPT (pick-wt=19): 713 [copy,712,demod,603,693,693,674,665,674,698] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)))),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A).
% 278.08/278.11  ** KEPT (pick-wt=10): 715 [copy,714,demod,617,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))=A.
% 278.08/278.11  ---> New Demodulator: 716 [new_demod,715] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))=A.
% 278.08/278.11    Following clause subsumed by 557 during input processing: 0 [demod,617,716] A=A.
% 278.08/278.11  ** KEPT (pick-wt=10): 718 [copy,717,demod,617] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),A)=A.
% 278.08/278.11  ---> New Demodulator: 719 [new_demod,718] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),A)=A.
% 278.08/278.11  ** KEPT (pick-wt=2): 720 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 721 [] class_Ring__and__Field_Opordered__cancel__semiring(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 722 [] class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 723 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 724 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 725 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 726 [] class_Ring__and__Field_Opordered__semiring(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 727 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 728 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 729 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 730 [] class_Ring__and__Field_Ocomm__semiring__0(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 731 [] class_OrderedGroup_Oab__semigroup__mult(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 732 [] class_OrderedGroup_Ocomm__monoid__mult(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 733 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 734 [] class_Ring__and__Field_Ocomm__semiring(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 735 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 736 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 737 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 738 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 739 [] class_Ring__and__Field_Omult__mono1(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 740 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 741 [] class_Ring__and__Field_Omult__mono(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 742 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 743 [] class_Ring__and__Field_Osemiring(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 744 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 745 [] class_Orderings_Opreorder(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 746 [] class_Orderings_Olinorder(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 747 [] class_Orderings_Oorder(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 748 [] class_Power_Opower(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 749 [] class_Int_Onumber(tc_nat).
% 278.08/278.11  ** KEPT (pick-wt=2): 750 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 751 [] class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 752 [] class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 753 [] class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 754 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 755 [] class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 756 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 757 [] class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 758 [] class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 759 [] class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 760 [] class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 761 [] class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 762 [] class_Ring__and__Field_Opordered__semiring(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 763 [] class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 764 [] class_Ring__and__Field_Oordered__semidom(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 765 [] class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 766 [] class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 767 [] class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 768 [] class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 769 [] class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 770 [] class_Ring__and__Field_Opordered__ring(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 771 [] class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 772 [] class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 773 [] class_Ring__and__Field_Ozero__ne_q__one(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 774 [] class_Ring__and__Field_Oordered__idom(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 775 [] class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 776 [] class_Ring__and__Field_Osemiring__1(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 777 [] class_Ring__and__Field_Osemiring__0(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 778 [] class_Ring__and__Field_Omult__mono1(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 779 [] class_OrderedGroup_Oab__group__add(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 780 [] class_Ring__and__Field_Omult__zero(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 781 [] class_Ring__and__Field_Omult__mono(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 782 [] class_Ring__and__Field_Ocomm__ring(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 783 [] class_OrderedGroup_Omonoid__mult(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 784 [] class_Ring__and__Field_Osemiring(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 785 [] class_OrderedGroup_Omonoid__add(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 786 [] class_OrderedGroup_Ogroup__add(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 787 [] class_Ring__and__Field_Oring__1(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 788 [] class_Ring__and__Field_Oring(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 789 [] class_Ring__and__Field_Oidom(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 790 [] class_Orderings_Opreorder(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 791 [] class_Orderings_Olinorder(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 792 [] class_Orderings_Oorder(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 793 [] class_Int_Oring__char__0(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 794 [] class_Int_Onumber__ring(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 795 [] class_Power_Opower(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 796 [] class_Int_Onumber(tc_Int_Oint).
% 278.08/278.11  ** KEPT (pick-wt=2): 797 [] class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 798 [] class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 799 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 800 [] class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 801 [] class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 802 [] class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 803 [] class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 804 [] class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 805 [] class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 806 [] class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 807 [] class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 808 [] class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 809 [] class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 810 [] class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 811 [] class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 812 [] class_Ring__and__Field_Ozero__ne_q__one(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 813 [] class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 814 [] class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 815 [] class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 816 [] class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 817 [] class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 818 [] class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 819 [] class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 820 [] class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 821 [] class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex).
% 278.08/278.11  ** KEPT (pick-wt=2): 822 [] class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex).
% 278.08/278.12  ** KEPT (pick-wt=2): 823 [] class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex).
% 278.08/278.12  ** KEPT (pick-wt=2): 824 [] class_RealVector_Oreal__field(tc_Complex_Ocomplex).
% 278.08/278.12  ** KEPT (pick-wt=2): 825 [] class_Ring__and__Field_Ofield(tc_Complex_Ocomplex).
% 278.08/278.12  ** KEPT (pick-wt=2): 826 [] class_Ring__and__Field_Oring(tc_Complex_Ocomplex).
% 278.08/278.12  ** KEPT (pick-wt=2): 827 [] class_Ring__and__Field_Oidom(tc_Complex_Ocomplex).
% 278.08/278.12  ** KEPT (pick-wt=2): 828 [] class_Int_Oring__char__0(tc_Complex_Ocomplex).
% 278.08/278.12  ** KEPT (pick-wt=2): 829 [] class_Int_Onumber__ring(tc_Complex_Ocomplex).
% 278.08/278.12  ** KEPT (pick-wt=2): 830 [] class_Power_Opower(tc_Complex_Ocomplex).
% 278.08/278.12  ** KEPT (pick-wt=2): 831 [] class_Int_Onumber(tc_Complex_Ocomplex).
% 278.08/278.12    Following clause subsumed by 705 during input processing: 0 [] hAPP(c_COMBS(A,B,C,D,E),F)=hAPP(hAPP(A,F),hAPP(B,F)).
% 278.08/278.12    Following clause subsumed by 558 during input processing: 0 [] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 278.08/278.12    Following clause subsumed by 557 during input processing: 0 [demod,704] hAPP(A,hAPP(B,F))=hAPP(A,hAPP(B,F)).
% 278.08/278.12  ** KEPT (pick-wt=4): 832 [] c_fe_qual(A,A,B).
% 278.08/278.12    Following clause subsumed by 557 during input processing: 0 [copy,557,flip.1] A=A.
% 278.08/278.12  557 back subsumes 537.
% 278.08/278.12  557 back subsumes 493.
% 278.08/278.12  557 back subsumes 492.
% 278.08/278.12  557 back subsumes 485.
% 278.08/278.12  557 back subsumes 484.
% 278.08/278.12  ** KEPT (pick-wt=14): 833 [copy,558,flip.1] hAPP(hAPP(A,B),C)=hAPP(c_COMBC(A,C,D,E,F),B).
% 278.08/278.12    Following clause subsumed by 559 during input processing: 0 [copy,559,flip.1] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),C)),B).
% 278.08/278.12  >>>> Starting back demodulation with 561.
% 278.08/278.12  >>>> Starting back demodulation with 564.
% 278.08/278.12  ** KEPT (pick-wt=10): 834 [copy,565,flip.1,demod,617,flip.1] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),A)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 278.08/278.12  ---> New Demodulator: 835 [new_demod,834] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),A)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 278.08/278.12  >>>> Starting back demodulation with 567.
% 278.08/278.12  >>>> Starting back demodulation with 569.
% 278.08/278.12  >>>> Starting back demodulation with 571.
% 278.08/278.12  >>>> Starting back demodulation with 573.
% 278.08/278.12  >>>> Starting back demodulation with 575.
% 278.08/278.12  >>>> Starting back demodulation with 577.
% 278.08/278.12  >>>> Starting back demodulation with 579.
% 278.08/278.12  ** KEPT (pick-wt=23): 836 [copy,580,flip.1] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B)),C).
% 278.08/278.12  >>>> Starting back demodulation with 582.
% 278.08/278.12      >> back demodulating 106 with 582.
% 278.08/278.12  >>>> Starting back demodulation with 584.
% 278.08/278.12  >>>> Starting back demodulation with 587.
% 278.08/278.12  >>>> Starting back demodulation with 589.
% 278.08/278.12      >> back demodulating 586 with 589.
% 278.08/278.12  >>>> Starting back demodulation with 591.
% 278.08/278.12  ** KEPT (pick-wt=28): 837 [copy,592,flip.1] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),C)),B).
% 278.08/278.12  >>>> Starting back demodulation with 595.
% 278.08/278.12  >>>> Starting back demodulation with 597.
% 278.08/278.12  >>>> Starting back demodulation with 599.
% 278.08/278.12  >>>> Starting back demodulation with 603.
% 278.08/278.12      >> back demodulating 600 with 603.
% 278.08/278.12      >> back demodulating 477 with 603.
% 278.08/278.12      >> back demodulating 457 with 603.
% 278.08/278.12      >> back demodulating 396 with 603.
% 278.08/278.12      >> back demodulating 391 with 603.
% 278.08/278.12      >> back demodulating 390 with 603.
% 278.08/278.12      >> back demodulating 385 with 603.
% 278.08/278.12      >> back demodulating 384 with 603.
% 278.08/278.12      >> back demodulating 376 with 603.
% 278.08/278.12      >> back demodulating 360 with 603.
% 278.08/278.12      >> back demodulating 336 with 603.
% 278.08/278.12      >> back demodulating 331 with 603.
% 278.08/278.12      >> back demodulating 305 with 603.
% 278.08/278.12      >> back demodulating 304 with 603.
% 278.08/278.12      >> back demodulating 291 with 603.
% 278.08/278.12      >> back demodulating 273 with 603.
% 278.08/278.12      >> back demodulating 249 with 603.
% 278.08/278.12      >> back demodulating 247 with 603.
% 278.08/278.12      >> back demodulating 246 with 603.
% 278.08/278.12      >> back demodulating 245 with 603.
% 278.08/278.12      >> back demodulating 244 with 603.
% 278.08/278.12      >> back demodulating 149 with 603.
% 278.08/278.12      >> back demodulating 147 with 603.
% 278.08/278.12      >> back demodulating 146 with 603.
% 278.08/278.12      >> back demodulating 145 with 603.
% 278.08/278.12      >> back demodulating 144 with 603.
% 278.08/278.12      >> back demodulating 143 with 603.
% 278.08/278.12      >> back demodulating 142 with 603.
% 278.08/278.12      >> back demodulating 141 with 603.
% 278.08/278.12      >> back demodulating 139 with 603.
% 278.08/278.12      >> back demodulating 138 with 603.
% 278.08/278.12      >> back demodulating 137 with 603.
% 278.08/278.12      >> back demodulating 136 with 603.
% 278.08/278.12      >> back demodulating 135 with 603.
% 278.08/278.12  >>>> Starting back demodulation with 614.
% 278.08/278.12      >> back demodulating 547 with 614.
% 278.08/278.12      >> back demodulating 546 with 614.
% 278.08/278.12      >> back demodulating 539 with 614.
% 278.08/278.12      >> back demodulating 538 with 614.
% 278.08/278.12      >> back demodulating 459 with 614.
% 278.08/278.12      >> back demodulating 458 with 614.
% 278.08/278.12      >> back demodulating 447 with 614.
% 278.08/278.12      >> back demodulating 411 with 614.
% 278.08/278.12      >> back demodulating 410 with 614.
% 278.08/278.12      >> back demodulating 357 with 614.
% 278.08/278.12      >> back demodulating 356 with 614.
% 278.08/278.12      >> back demodulating 335 with 614.
% 278.08/278.12      >> back demodulating 334 with 614.
% 278.08/278.12      >> back demodulating 290 with 614.
% 278.08/278.12      >> back demodulating 289 with 614.
% 278.08/278.12  >>>> Starting back demodulation with 617.
% 278.08/278.12      >> back demodulating 613 with 617.
% 278.08/278.12      >> back demodulating 611 with 617.
% 278.08/278.12      >> back demodulating 609 with 617.
% 278.08/278.12      >> back demodulating 607 with 617.
% 278.08/278.12      >> back demodulating 605 with 617.
% 278.08/278.12      >> back demodulating 568 with 617.
% 278.08/278.12      >> back demodulating 566 with 617.
% 278.08/278.12      >> back demodulating 565 with 617.
% 278.08/278.12      >> back demodulating 553 with 617.
% 278.08/278.12      >> back demodulating 545 with 617.
% 278.08/278.12      >> back demodulating 544 with 617.
% 278.08/278.12      >> back demodulating 541 with 617.
% 278.08/278.12      >> back demodulating 443 with 617.
% 278.08/278.12      >> back demodulating 414 with 617.
% 278.08/278.12      >> back demodulating 407 with 617.
% 278.08/278.12      >> back demodulating 398 with 617.
% 278.08/278.12      >> back demodulating 397 with 617.
% 278.08/278.12      >> back demodulating 395 with 617.
% 278.08/278.12      >> back demodulating 379 with 617.
% 278.08/278.12      >> back demodulating 349 with 617.
% 278.08/278.12      >> back demodulating 348 with 617.
% 278.08/278.12      >> back demodulating 324 with 617.
% 278.08/278.12      >> back demodulating 309 with 617.
% 278.08/278.12      >> back demodulating 308 with 617.
% 278.08/278.12      >> back demodulating 307 with 617.
% 278.08/278.12      >> back demodulating 306 with 617.
% 278.08/278.12      >> back demodulating 303 with 617.
% 278.08/278.12      >> back demodulating 298 with 617.
% 278.08/278.12      >> back demodulating 253 with 617.
% 278.08/278.12      >> back demodulating 251 with 617.
% 278.08/278.12      >> back demodulating 243 with 617.
% 278.08/278.12      >> back demodulating 140 with 617.
% 278.08/278.12      >> back demodulating 134 with 617.
% 278.08/278.12      >> back demodulating 133 with 617.
% 278.08/278.12      >> back demodulating 121 with 617.
% 278.08/278.12      >> back demodulating 89 with 617.
% 278.08/278.12      >> back demodulating 74 with 617.
% 278.08/278.12  >>>> Starting back demodulation with 620.
% 278.08/278.12  >>>> Starting back demodulation with 623.
% 278.08/278.12      >> back demodulating 602 with 623.
% 278.08/278.12  >>>> Starting back demodulation with 626.
% 278.08/278.12  ** KEPT (pick-wt=39): 915 [copy,628,flip.1] c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_COMBB(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat),A,tc_nat),tc_nat,tc_Complex_Ocomplex)=c_FFT__Mirabelle_ODFT(A,B,v_i).
% 278.08/278.12  ** KEPT (pick-wt=39): 916 [copy,630,flip.1] c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(B),tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat),B,tc_nat),tc_nat,tc_Complex_Ocomplex)=c_FFT__Mirabelle_OIDFT(B,A,v_i).
% 278.08/278.12  >>>> Starting back demodulation with 633.
% 278.08/278.12      >> back demodulating 596 with 633.
% 278.08/278.12  >>>> Starting back demodulation with 636.
% 278.08/278.12  ** KEPT (pick-wt=28): 919 [copy,637,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),C),B))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B).
% 278.08/278.12  >>>> Starting back demodulation with 640.
% 278.08/278.12  >>>> Starting back demodulation with 642.
% 278.08/278.12  >>>> Starting back demodulation with 645.
% 278.08/278.12  >>>> Starting back demodulation with 648.
% 278.08/278.12  >>>> Starting back demodulation with 651.
% 278.08/278.12      >> back demodulating 448 with 651.
% 278.08/278.12    Following clause subsumed by 557 during input processing: 0 [copy,653,flip.1,demod,684,684] c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 278.08/278.12    Following clause subsumed by 557 during input processing: 0 [copy,655,flip.1,demod,681,681] c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 278.08/278.12  ** KEPT (pick-wt=11): 921 [copy,657,flip.1] c_FFT__Mirabelle_Oroot(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))=hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),tc_Complex_Ocomplex),A).
% 278.08/278.12  >>>> Starting back demodulation with 660.
% 278.08/278.12  >>>> Starting back demodulation with 662.
% 278.08/278.12  ** KEPT (pick-wt=20): 922 [copy,663,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,B)),A).
% 278.08/278.12  >>>> Starting back demodulation with 665.
% 278.08/278.12      >> back demodulating 659 with 665.
% 278.08/278.12      >> back demodulating 644 with 665.
% 278.08/278.12  >>>> Starting back demodulation with 668.
% 278.08/278.12  >>>> Starting back demodulation with 671.
% 278.08/278.12  >>>> Starting back demodulation with 674.
% 278.08/278.12      >> back demodulating 667 with 674.
% 278.08/278.12      >> back demodulating 664 with 674.
% 278.08/278.12      >> back demodulating 647 with 674.
% 278.08/278.12    Following clause subsumed by 675 during input processing: 0 [copy,675,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 278.08/278.12  >>>> Starting back demodulation with 678.
% 278.08/278.12  >>>> Starting back demodulation with 681.
% 278.08/278.12      >> back demodulating 677 with 681.
% 278.08/278.12      >> back demodulating 655 with 681.
% 278.08/278.12  >>>> Starting back demodulation with 684.
% 278.08/278.12      >> back demodulating 653 with 684.
% 278.08/278.12  >>>> Starting back demodulation with 687.
% 278.08/278.12  >>>> Starting back demodulation with 690.
% 278.08/278.12  >>>> Starting back demodulation with 693.
% 278.08/278.12      >> back demodulating 670 with 693.
% 278.08/278.12      >> back demodulating 625 with 693.
% 278.08/278.12      >> back demodulating 622 with 693.
% 278.08/278.12      >> back demodulating 598 with 693.
% 278.08/278.12      >> back demodulating 590 with 693.
% 278.08/278.12      >> back demodulating 588 with 693.
% 278.08/278.12      >> back demodulating 563 with 693.
% 278.08/278.12      >> back demodulating 560 with 693.
% 278.08/278.12      >> back demodulating 110 with 693.
% 278.08/278.12      >> back demodulating 108 with 693.
% 278.08/278.12      >> back demodulating 96 with 693.
% 278.08/278.12      >> back demodulating 95 with 693.
% 278.08/278.12    Following clause subsumed by 695 during input processing: 0 [copy,695,flip.1] 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)).
% 278.08/278.12  >>>> Starting back demodulation with 698.
% 278.08/278.12      >> back demodulating 686 with 698.
% 278.08/278.12    Following clause subsumed by 699 during input processing: 0 [copy,699,flip.1] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A).
% 278.08/278.12  >>>> Starting back demodulation with 701.
% 278.08/278.12    Following clause subsumed by 702 during input processing: 0 [copy,702,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)).
% 278.08/278.12  >>>> Starting back demodulation with 704.
% 278.08/278.12  ** KEPT (pick-wt=16): 935 [copy,705,flip.1] hAPP(hAPP(A,B),hAPP(C,B))=hAPP(c_COMBS(A,C,D,E,F),B).
% 278.08/278.12  >>>> Starting back demodulation with 708.
% 278.08/278.12  >>>> Starting back demodulation with 711.
% 278.08/278.12  ** KEPT (pick-wt=19): 936 [copy,713,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)))),A).
% 281.78/281.85  >>>> Starting back demodulation with 716.
% 281.78/281.85      >> back demodulating 710 with 716.
% 281.78/281.85      >> back demodulating 697 with 716.
% 281.78/281.85  >>>> Starting back demodulation with 719.
% 281.78/281.85    Following clause subsumed by 558 during input processing: 0 [copy,833,flip.1] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 281.78/281.85  >>>> Starting back demodulation with 835.
% 281.78/281.85    Following clause subsumed by 580 during input processing: 0 [copy,836,flip.1] hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)).
% 281.78/281.85    Following clause subsumed by 592 during input processing: 0 [copy,837,flip.1] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)).
% 281.78/281.85  >>>> Starting back demodulation with 884.
% 281.78/281.85  >>>> Starting back demodulation with 886.
% 281.78/281.85  >>>> Starting back demodulation with 914.
% 281.78/281.85    Following clause subsumed by 628 during input processing: 0 [copy,915,flip.1] c_FFT__Mirabelle_ODFT(A,B,v_i)=c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_COMBB(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat),A,tc_nat),tc_nat,tc_Complex_Ocomplex).
% 281.78/281.85    Following clause subsumed by 630 during input processing: 0 [copy,916,flip.1] c_FFT__Mirabelle_OIDFT(A,B,v_i)=c_Finite__Set_Osetsum(c_COMBS(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),c_COMBB(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),tc_Complex_Ocomplex),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),v_i),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat),A,tc_nat),tc_nat,tc_Complex_Ocomplex).
% 281.78/281.85  >>>> Starting back demodulation with 918.
% 281.78/281.85    Following clause subsumed by 637 during input processing: 0 [copy,919,flip.1] 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)).
% 281.78/281.85    Following clause subsumed by 657 during input processing: 0 [copy,921,flip.1] hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),tc_Complex_Ocomplex),A)=c_FFT__Mirabelle_Oroot(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)).
% 281.78/281.85    Following clause subsumed by 663 during input processing: 0 [copy,922,flip.1] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(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)).
% 281.78/281.85  >>>> Starting back demodulation with 924.
% 281.78/281.85  >>>> Starting back demodulation with 926.
% 281.78/281.85  >>>> Starting back demodulation with 928.
% 281.78/281.85  >>>> Starting back demodulation with 930.
% 281.78/281.85  >>>> Starting back demodulation with 932.
% 281.78/281.85    Following clause subsumed by 705 during input processing: 0 [copy,935,flip.1] hAPP(c_COMBS(A,B,C,D,E),F)=hAPP(hAPP(A,F),hAPP(B,F)).
% 281.78/281.85    Following clause subsumed by 713 during input processing: 0 [copy,936,flip.1] hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)))),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A).
% 281.78/281.85  
% 281.78/281.85  ======= end of input processing =======
% 281.78/281.85  
% 281.78/281.85  =========== start of search ===========
% 281.78/281.85  
% 281.78/281.85  
% 281.78/281.85  Resetting weight limit to 2.
% 281.78/281.85  
% 281.78/281.85  
% 281.78/281.85  Resetting weight limit to 2.
% 281.78/281.85  
% 281.78/281.85  sos_size=248
% 281.78/281.85  
% 281.78/281.85  Search stopped in tp_alloc by max_mem option.
% 281.78/281.85  
% 281.78/281.85  Search stopped in tp_alloc by max_mem option.
% 281.78/281.85  
% 281.78/281.85  ============ end of search ============
% 281.78/281.85  
% 281.78/281.85  -------------- statistics -------------
% 281.78/281.85  clauses given                250
% 281.78/281.85  clauses generated         302640
% 281.78/281.85  clauses kept                 781
% 281.78/281.85  clauses forward subsumed     199
% 281.78/281.85  clauses back subsumed         11
% 281.78/281.85  Kbytes malloced            11718
% 281.78/281.85  
% 281.78/281.85  ----------- times (seconds) -----------
% 281.78/281.85  user CPU time          3.84          (0 hr, 0 min, 3 sec)
% 281.78/281.85  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 281.78/281.85  wall-clock time      282             (0 hr, 4 min, 42 sec)
% 281.78/281.85  
% 281.78/281.85  Process 23144 finished Wed Jul 27 05:58:37 2022
% 281.78/281.85  Otter interrupted
% 281.78/281.85  PROOF NOT FOUND
%------------------------------------------------------------------------------