TSTP Solution File: ALG438-1 by Otter---3.3

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : ALG438-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n028.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 12:46:40 EDT 2022

% Result   : Unknown 87.71s 87.82s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ALG438-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13  % Command  : otter-tptp-script %s
% 0.13/0.34  % Computer : n028.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Jul 27 03:46:03 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 87.63/87.77  ----- Otter 3.3f, August 2004 -----
% 87.63/87.77  The process was started by sandbox on n028.cluster.edu,
% 87.63/87.77  Wed Jul 27 03:46:03 2022
% 87.63/87.77  The command was "./otter".  The process ID is 20908.
% 87.63/87.77  
% 87.63/87.77  set(prolog_style_variables).
% 87.63/87.77  set(auto).
% 87.63/87.77     dependent: set(auto1).
% 87.63/87.77     dependent: set(process_input).
% 87.63/87.77     dependent: clear(print_kept).
% 87.63/87.77     dependent: clear(print_new_demod).
% 87.63/87.77     dependent: clear(print_back_demod).
% 87.63/87.77     dependent: clear(print_back_sub).
% 87.63/87.77     dependent: set(control_memory).
% 87.63/87.77     dependent: assign(max_mem, 12000).
% 87.63/87.77     dependent: assign(pick_given_ratio, 4).
% 87.63/87.77     dependent: assign(stats_level, 1).
% 87.63/87.77     dependent: assign(max_seconds, 10800).
% 87.63/87.77  clear(print_given).
% 87.63/87.77  
% 87.63/87.77  list(usable).
% 87.63/87.77  0 [] A=A.
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|V_p=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Opos__poly(V_p,T_a)| -c_Polynomial_Opos__poly(c_Polynomial_OpCons(V_a,V_p,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Opoly(c_Polynomial_Opcompose(V_p,V_q,T_a),V_x,T_a)=c_Polynomial_Opoly(V_p,c_Polynomial_Opoly(V_q,V_x,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__idom(T_a)| -c_Polynomial_Opos__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,T_a)=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_Polynomial_Opos__poly(c_Polynomial_OpCons(V_a,V_p,T_a),T_a)| -c_Polynomial_Opos__poly(V_p,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_Polynomial_Opos__poly(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a)| -c_Polynomial_Opos__poly(V_q,T_a)| -c_Polynomial_Opos__poly(V_p,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_Polynomial_Opos__poly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a)| -c_Polynomial_Opos__poly(V_q,T_a)| -c_Polynomial_Opos__poly(V_p,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)|c_Polynomial_Opos__poly(V_p,T_a)| -c_Polynomial_Opos__poly(c_Polynomial_OpCons(V_a,V_p,T_a),T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_lesse_quals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add(T_a)|c_lesse_quals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)| -c_lesse_quals(V_c,V_d,T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,V_d,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)| -c_lesse_quals(V_c,V_d,T_a)| -c_lesse_quals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)| -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_c,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_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_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(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).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(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).
% 87.63/87.77  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Opcompose(c_Polynomial_OpCons(V_a,V_p,T_a),V_q,T_a)=c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),c_HOL_Otimes__class_Otimes(V_q,c_Polynomial_Opcompose(V_p,V_q,T_a),tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)).
% 87.63/87.77  0 [] -class_Ring__and__Field_Ocomm__semiring__0(t_a)|c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(t_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__5__1(c_HOL_Ozero__class_Ozero(t_a)),t_a)=c_HOL_Ozero__class_Ozero(t_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Ocomm__semiring__0(t_a)|c_Polynomial_Opoly(c_Polynomial_OpCons(V_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__3__1(V_c),t_a)!=c_HOL_Ozero__class_Ozero(t_a)|V_c=c_HOL_Ozero__class_Ozero(t_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_Polynomial_Opos__poly(c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_lesse_quals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add(T_a)|c_lesse_quals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add(T_a)|c_lesse_quals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Ocomm__semiring__0(t_a)|c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(t_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a),V_x,t_a)=c_HOL_Ozero__class_Ozero(t_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Ocomm__semiring__0(t_a)|c_Polynomial_Opoly(c_Polynomial_OpCons(V_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a),V_x,t_a)!=c_HOL_Ozero__class_Ozero(t_a)|V_c=c_HOL_Ozero__class_Ozero(t_a).
% 87.63/87.77  0 [] -class_HOL_Ozero(T_a)|c_Polynomial_OpCons(V_a,V_p,T_a)!=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_p=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 87.63/87.77  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a)=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oidom(T_a)|c_Polynomial_Osmult(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a)=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 87.63/87.77  0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,tc_Polynomial_Opoly(T_a))=V_q.
% 87.63/87.77  0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))=V_p.
% 87.63/87.77  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_HOL_Otimes__class_Otimes(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 87.63/87.77  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,tc_Polynomial_Opoly(T_a))=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 87.63/87.77  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_HOL_Oplus__class_Oplus(V_p,c_Polynomial_Osmult(V_c,c_Polynomial_Osynthetic__div(V_p,V_c,T_a),T_a),tc_Polynomial_Opoly(T_a))=c_Polynomial_OpCons(c_Polynomial_Opoly(V_p,V_c,T_a),c_Polynomial_Osynthetic__div(V_p,V_c,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Odivision__ring(T_a)|c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Opordered__cancel__semiring(T_a)|c_lesse_quals(c_HOL_Otimes__class_Otimes(V_b,V_a,T_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).
% 87.63/87.77  0 [] -class_Ring__and__Field_Opordered__cancel__semiring(T_a)|c_lesse_quals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_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(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Opordered__cancel__semiring(T_a)|c_lesse_quals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_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).
% 87.63/87.77  0 [] -class_Ring__and__Field_Opordered__cancel__semiring(T_a)|c_lesse_quals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_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(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Opordered__cancel__semiring(T_a)|c_lesse_quals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_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).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_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(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_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).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Opordered__semiring(T_a)|c_lesse_quals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),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).
% 87.63/87.77  0 [] -class_Ring__and__Field_Opordered__semiring(T_a)|c_lesse_quals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),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).
% 87.63/87.77  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),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a).
% 87.63/87.77  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),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a).
% 87.63/87.77  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),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a).
% 87.63/87.77  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),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Opordered__cancel__semiring(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,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),V_a,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,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).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,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),V_a,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,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).
% 87.63/87.77  0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,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).
% 87.63/87.77  0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,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),V_a,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_lesse_quals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),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).
% 87.63/87.77  0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_lesse_quals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),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).
% 87.63/87.77  0 [] -class_Ring__and__Field_Omult__mono(T_a)|c_lesse_quals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),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).
% 87.63/87.77  0 [] -class_Ring__and__Field_Omult__mono(T_a)|c_lesse_quals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),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).
% 87.63/87.77  0 [] -class_Ring__and__Field_Omult__mono1(T_a)|c_lesse_quals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),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).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  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(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  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(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  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(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  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_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__comm__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_lesse_quals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_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(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  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(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 87.63/87.77  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),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,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),V_a,T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(V_x,V_y,T_a)!=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).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(V_x,V_y,T_a)!=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).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)| -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_lesse_quals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),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).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)| -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_lesse_quals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),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).
% 87.63/87.77  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)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_HOL_Ozero(T_a)|c_Polynomial_OpCons(V_a,V_p,T_a)!=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.77  0 [] -class_HOL_Ozero(T_a)|c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a)=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 87.63/87.77  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a)=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oidom(T_a)|c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a)=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oidom(T_a)|c_Polynomial_Osmult(V_a,V_p,T_a)!=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_p=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a)=c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a)=c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a)=c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(V_c,V_p,T_a)!=c_Polynomial_OpCons(V_a,V_p,T_a)|V_p=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 87.63/87.77  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)| -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)| -c_lesse_quals(V_b,V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(V_b,V_a,T_a)| -c_lesse_quals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_lesse_quals(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_lesse_quals(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_lesse_quals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_lesse_quals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(V_c,V_d,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__semiring(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__semiring(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 87.63/87.77  0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),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_HOL_Oord__class_Oless(V_c,V_d,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(V_c,V_d,T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)| -c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Odivision__ring(T_a)|c_HOL_Oinverse__class_Oinverse(V_a,T_a)!=c_HOL_Oinverse__class_Oinverse(V_b,T_a)|V_a=V_b|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Odivision__ring(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Odivision__ring(T_a)|c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)=V_a|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Odivision__ring(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Oinverse(V_a,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Odivision__ring(T_a)|c_HOL_Oinverse__class_Oinverse(V_a,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,V_d,T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 87.63/87.78  0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)| -c_lesse_quals(V_c,V_d,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__field(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 87.63/87.78  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_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_lesse_quals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.78  0 [] -class_Orderings_Olinorder(T_a)| -c_lesse_quals(V_x,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 87.63/87.78  0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_lesse_quals(V_x,V_y,T_a).
% 87.63/87.78  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 87.63/87.78  0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a)| -c_lesse_quals(V_y,V_x,T_a).
% 87.63/87.78  0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_x,T_a)|c_lesse_quals(V_x,V_x,T_a).
% 87.63/87.78  0 [] -class_Orderings_Olinorder(T_a)| -c_lesse_quals(V_x,V_x,T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 87.63/87.78  0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|c_lesse_quals(V_y,V_x,T_a).
% 87.63/87.78  0 [] -class_Orderings_Opreorder(T_a)| -c_lesse_quals(V_y,V_x,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 87.63/87.78  0 [] -class_Orderings_Opreorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_z,T_a)| -c_HOL_Oord__class_Oless(V_y,V_z,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 87.63/87.78  0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_z,V_x,T_a)| -c_HOL_Oord__class_Oless(V_z,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Odivision__ring(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)=V_a.
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_h,T_a)=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),V_x,T_a)=c_Polynomial_Opoly(V_p,c_HOL_Oplus__class_Oplus(V_h,V_x,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(V_a,V_p,T_a),V_c,T_a)=c_Polynomial_OpCons(c_Polynomial_Opoly(V_p,V_c,T_a),c_Polynomial_Osynthetic__div(V_p,V_c,T_a),T_a).
% 87.63/87.78  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).
% 87.63/87.78  0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|V_x=V_y.
% 87.63/87.78  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).
% 87.63/87.78  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).
% 87.63/87.78  0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 87.63/87.78  0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 87.63/87.78  0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|V_x=V_y.
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__field(T_a)|c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Odivision__ring(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Oinverse(V_a,T_a)!=c_HOL_Oinverse__class_Oinverse(V_b,T_a)|V_a=V_b.
% 87.63/87.78  0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|V_x=V_y| -c_lesse_quals(V_x,V_y,T_a).
% 87.63/87.78  0 [] -class_Orderings_Oorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a)| -c_lesse_quals(V_x,V_y,T_a).
% 87.63/87.78  0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)|V_a=V_b| -c_lesse_quals(V_a,V_b,T_a).
% 87.63/87.78  0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_lesse_quals(V_a,V_b,T_a)|V_a=V_b.
% 87.63/87.78  0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y| -c_lesse_quals(V_x,V_y,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 87.63/87.78  0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a)| -c_lesse_quals(V_x,V_y,T_a).
% 87.63/87.78  0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_lesse_quals(V_b,V_a,T_a)|V_a=V_b.
% 87.63/87.78  0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|V_a=V_b| -c_lesse_quals(V_b,V_a,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),V_h,T_a)=c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oidom(T_a)|c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a)!=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_p=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__field(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__field(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__field(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__field(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__field(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Opoly(V_p,V_x,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  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_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a).
% 87.63/87.78  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),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__field(T_a)|c_lesse_quals(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__field(T_a)|c_lesse_quals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__field(T_a)|c_lesse_quals(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__field(T_a)|c_lesse_quals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 87.63/87.78  0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 87.63/87.78  0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 87.63/87.78  0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 87.63/87.78  0 [] -class_Orderings_Opreorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|c_lesse_quals(V_y,V_x,T_a)| -c_lesse_quals(V_x,V_y,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__field(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.78  0 [] -class_Orderings_Oorder(T_a)|c_lesse_quals(V_x,V_y,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 87.63/87.78  0 [] -class_Orderings_Opreorder(T_a)|c_lesse_quals(V_x,V_y,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c,T_a)=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 87.63/87.78  0 [] -class_Orderings_Opreorder(T_a)|c_lesse_quals(V_x,V_x,T_a).
% 87.63/87.78  0 [] -class_Orderings_Oorder(T_a)|c_lesse_quals(V_x,V_x,T_a).
% 87.63/87.78  0 [] -class_Orderings_Opreorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_z,T_a)| -c_HOL_Oord__class_Oless(V_y,V_z,T_a)| -c_lesse_quals(V_x,V_y,T_a).
% 87.63/87.78  0 [] -class_Orderings_Opreorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_z,T_a)| -c_lesse_quals(V_y,V_z,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 87.63/87.78  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).
% 87.63/87.78  0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_z,V_x,T_a)| -c_HOL_Oord__class_Oless(V_z,V_y,T_a)| -c_lesse_quals(V_y,V_x,T_a).
% 87.63/87.78  0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_z,V_x,T_a)| -c_lesse_quals(V_z,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 87.63/87.78  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).
% 87.63/87.78  0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 87.63/87.78  0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 87.63/87.78  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_y,V_x,T_a)|c_lesse_quals(V_x,V_y,T_a).
% 87.63/87.78  0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 87.63/87.78  0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Odivision__ring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ofield(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a)| -c_lesse_quals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a)| -c_lesse_quals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a)=c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_HOL_Oplus__class_Oplus(V_p,c_Polynomial_Osmult(V_c,V_q,T_a),tc_Polynomial_Opoly(T_a))!=c_Polynomial_OpCons(V_r,V_q,T_a)|V_q=c_Polynomial_Osynthetic__div(V_p,V_c,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_HOL_Oplus__class_Oplus(V_p,c_Polynomial_Osmult(V_c,V_q,T_a),tc_Polynomial_Opoly(T_a))!=c_Polynomial_OpCons(V_r,V_q,T_a)|V_r=c_Polynomial_Opoly(V_p,V_c,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_c,V_p,T_a),c_Polynomial_OpCons(V_a,V_p,T_a),tc_Polynomial_Opoly(T_a))!=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_p=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,V_p,T_a),V_h,T_a)=c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),c_Polynomial_OpCons(V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),tc_Polynomial_Opoly(T_a)).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_HOL_Otimes__class_Otimes(V_p,c_Polynomial_OpCons(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))=c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a,V_p,T_a),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a),tc_Polynomial_Opoly(T_a)).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a))=c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a,V_q,T_a),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a),tc_Polynomial_Opoly(T_a)).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Omult__zero(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Omult__zero(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)|V_y=V_z|V_w=V_x.
% 87.63/87.78  0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)|V_c=V_d|V_a=V_b.
% 87.63/87.78  0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(V_a,V_p,T_a),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a))=c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a).
% 87.63/87.78  0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)=c_HOL_Oplus__class_Oplus(V_b,V_a,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_x,V_y,T_a)=c_HOL_Oplus__class_Oplus(V_y,V_x,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)=c_HOL_Oplus__class_Oplus(V_c,V_a,T_a).
% 87.63/87.78  0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a)!=c_HOL_Oplus__class_Oplus(V_y,V_u,T_a)|c_HOL_Oplus__class_Oplus(V_x,V_z,T_a)=V_u.
% 87.63/87.78  0 [] -class_OrderedGroup_Ocancel__semigroup__add(T_a)|c_HOL_Oplus__class_Oplus(V_b,V_a,T_a)!=c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)|V_b=V_c.
% 87.63/87.78  0 [] -class_OrderedGroup_Ocancel__semigroup__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)!=c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)|V_b=V_c.
% 87.63/87.78  0 [] -class_OrderedGroup_Ocancel__ab__semigroup__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)!=c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)|V_b=V_c.
% 87.63/87.78  0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(V_x,V_y,T_a)!=c_HOL_Oplus__class_Oplus(V_x,V_z,T_a)|V_y=V_z.
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_r,tc_Polynomial_Opoly(T_a))=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_p,V_r,tc_Polynomial_Opoly(T_a)),c_HOL_Otimes__class_Otimes(V_q,V_r,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)).
% 87.63/87.78  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_a_H,T_a),V_b,T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a).
% 87.63/87.78  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_ya,T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a).
% 87.63/87.78  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oplus__class_Oplus(V_b,V_b_H,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a).
% 87.63/87.78  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ry,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a)=c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,V_rx,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a).
% 87.63/87.78  0 [] -class_OrderedGroup_Oab__semigroup__mult(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)=c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 87.63/87.78  0 [] -class_OrderedGroup_Oab__semigroup__idem__mult(T_a)|c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)=V_x.
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(V_a,c_Polynomial_OpCons(V_b,V_p,T_a),T_a)=c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_Polynomial_Osmult(V_a,V_p,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,T_a),T_a)!=c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,T_a),T_a)|V_c=V_d|V_r=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_HOL_Ozero(T_a)|c_Polynomial_OpCons(V_a,V_p,T_a)!=c_Polynomial_OpCons(V_b,V_q,T_a)|V_a=V_b.
% 87.63/87.78  0 [] -class_HOL_Ozero(T_a)|c_Polynomial_OpCons(V_a,V_p,T_a)!=c_Polynomial_OpCons(V_b,V_q,T_a)|V_p=V_q.
% 87.63/87.78  0 [] -class_OrderedGroup_Oab__semigroup__idem__mult(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_x,V_y,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_ry,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)!=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).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ono__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)!=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).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ono__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)!=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).
% 87.63/87.78  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,V_a,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|V_x!=c_HOL_Oplus__class_Oplus(V_x,V_a,T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_p,T_a)=c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a,V_p,T_a),c_Polynomial_Osmult(V_b,V_p,T_a),tc_Polynomial_Opoly(T_a)).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(V_a,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a)=c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a,V_p,T_a),c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a)).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,V_y,T_a)=c_HOL_Otimes__class_Otimes(V_y,V_x,T_a).
% 87.63/87.78  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)=c_HOL_Otimes__class_Otimes(V_b,V_a,T_a).
% 87.63/87.78  0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)=c_HOL_Oplus__class_Oplus(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a).
% 87.63/87.78  0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a).
% 87.63/87.78  0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a)=c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),T_a).
% 87.63/87.78  0 [] -class_OrderedGroup_Oab__semigroup__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_d,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a)=c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Osemiring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_HOL_Otimes__class_Otimes(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))=c_Polynomial_Osmult(V_a,c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a))=c_Polynomial_Osmult(V_a,c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(V_a,c_Polynomial_Osmult(V_b,V_p,T_a),T_a)=c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_p,T_a).
% 87.63/87.78  0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a.
% 87.63/87.78  0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=V_a.
% 87.63/87.78  0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a.
% 87.63/87.78  0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|V_x=c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)=V_x.
% 87.63/87.78  0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=V_a.
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a.
% 87.63/87.78  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=V_a.
% 87.63/87.78  0 [] c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_a,c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))!=c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
% 87.63/87.78  0 [] class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1))| -class_OrderedGroup_Ocancel__comm__monoid__add(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Ocomm__ring__1(T_1).
% 87.63/87.78  0 [] class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_Ring__and__Field_Ofield(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_Ring__and__Field_Oidom(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_Int_Onumber__ring(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_HOL_Ozero(tc_Complex_Ocomplex).
% 87.63/87.78  0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oidom(T_1).
% 87.63/87.78  0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))| -class_OrderedGroup_Ocancel__comm__monoid__add(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1))| -class_OrderedGroup_Ocancel__comm__monoid__add(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oidom(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Ocomm__semiring__1(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Ocomm__semiring__0(T_1).
% 87.63/87.78  0 [] class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Ocomm__semiring__0(T_1).
% 87.63/87.78  0 [] class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(T_1))| -class_OrderedGroup_Ocomm__monoid__add(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Ocomm__semiring__0(T_1).
% 87.63/87.78  0 [] class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1))| -class_OrderedGroup_Ocomm__monoid__add(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(T_1))| -class_OrderedGroup_Oab__group__add(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Ocomm__semiring__0(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Ocomm__semiring__0(T_1).
% 87.63/87.78  0 [] class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(T_1))| -class_OrderedGroup_Ocomm__monoid__add(T_1).
% 87.63/87.78  0 [] class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oidom(T_1).
% 87.63/87.78  0 [] class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_Orderings_Oorder(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Oordered__idom(T_1).
% 87.63/87.78  0 [] class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1))| -class_Ring__and__Field_Ocomm__ring__1(T_1).
% 87.63/87.78  0 [] class_HOL_Ozero(tc_Polynomial_Opoly(T_1))| -class_HOL_Ozero(T_1).
% 87.63/87.78  end_of_list.
% 87.63/87.78  
% 87.63/87.78  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 87.63/87.78  
% 87.63/87.78  This ia a non-Horn set with equality.  The strategy will be
% 87.63/87.78  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 87.63/87.78  deletion, with positive clauses in sos and nonpositive
% 87.63/87.78  clauses in usable.
% 87.63/87.78  
% 87.63/87.78     dependent: set(knuth_bendix).
% 87.63/87.78     dependent: set(anl_eq).
% 87.63/87.78     dependent: set(para_from).
% 87.63/87.78     dependent: set(para_into).
% 87.63/87.78     dependent: clear(para_from_right).
% 87.63/87.78     dependent: clear(para_into_right).
% 87.63/87.78     dependent: set(para_from_vars).
% 87.63/87.78     dependent: set(eq_units_both_ways).
% 87.63/87.78     dependent: set(dynamic_demod_all).
% 87.63/87.78     dependent: set(dynamic_demod).
% 87.63/87.78     dependent: set(order_eq).
% 87.63/87.78     dependent: set(back_demod).
% 87.63/87.78     dependent: set(lrpo).
% 87.63/87.78     dependent: set(hyper_res).
% 87.63/87.78     dependent: set(unit_deletion).
% 87.63/87.78     dependent: set(factor).
% 87.63/87.78  
% 87.63/87.78  ------------> process usable:
% 87.63/87.78  ** KEPT (pick-wt=16): 1 [] -class_Ring__and__Field_Oordered__idom(A)|B=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Opos__poly(B,A)| -c_Polynomial_Opos__poly(c_Polynomial_OpCons(C,B,A),A).
% 87.63/87.78  ** KEPT (pick-wt=17): 2 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Opoly(c_Polynomial_Opcompose(B,C,A),D,A)=c_Polynomial_Opoly(B,c_Polynomial_Opoly(C,D,A),A).
% 87.63/87.78  ** KEPT (pick-wt=7): 3 [] -class_Ring__and__Field_Oordered__idom(A)| -c_Polynomial_Opos__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A).
% 87.63/87.78  ** KEPT (pick-wt=12): 4 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,A)=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 87.63/87.78  ** KEPT (pick-wt=11): 5 [] -class_Ring__and__Field_Oordered__idom(A)|c_Polynomial_Opos__poly(c_Polynomial_OpCons(B,C,A),A)| -c_Polynomial_Opos__poly(C,A).
% 87.63/87.78  ** KEPT (pick-wt=15): 6 [] -class_Ring__and__Field_Oordered__idom(A)|c_Polynomial_Opos__poly(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),A)| -c_Polynomial_Opos__poly(C,A)| -c_Polynomial_Opos__poly(B,A).
% 87.63/87.78  ** KEPT (pick-wt=15): 7 [] -class_Ring__and__Field_Oordered__idom(A)|c_Polynomial_Opos__poly(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),A)| -c_Polynomial_Opos__poly(C,A)| -c_Polynomial_Opos__poly(B,A).
% 87.63/87.78  ** KEPT (pick-wt=16): 8 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)|c_Polynomial_Opos__poly(C,A)| -c_Polynomial_Opos__poly(c_Polynomial_OpCons(B,C,A),A).
% 87.63/87.78  ** KEPT (pick-wt=16): 9 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A).
% 87.63/87.78  ** KEPT (pick-wt=16): 10 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_lesse_quals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A)| -c_lesse_quals(B,D,A).
% 87.63/87.78  ** KEPT (pick-wt=20): 11 [] -class_OrderedGroup_Opordered__ab__semigroup__add(A)|c_lesse_quals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A)| -c_lesse_quals(C,E,A)| -c_lesse_quals(B,D,A).
% 87.63/87.78  ** KEPT (pick-wt=20): 12 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A)| -c_HOL_Oord__class_Oless(C,E,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 87.63/87.78  ** KEPT (pick-wt=16): 13 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(D,B,A),c_HOL_Oplus__class_Oplus(D,C,A),A).
% 87.63/87.78  ** KEPT (pick-wt=16): 14 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,A).
% 87.63/87.78  ** KEPT (pick-wt=16): 15 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,A).
% 87.63/87.78  ** KEPT (pick-wt=16): 16 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A).
% 87.63/87.78  ** KEPT (pick-wt=16): 17 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 87.63/87.78  ** KEPT (pick-wt=16): 18 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 87.63/87.78  ** KEPT (pick-wt=20): 19 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(B,c_HOL_Oplus__class_Oplus(C,D,A),A)| -c_lesse_quals(E,D,A)| -c_lesse_quals(B,c_HOL_Oplus__class_Oplus(C,E,A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 20 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 21 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 87.63/87.78  ** KEPT (pick-wt=19): 22 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(B,C,A),A)=c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oinverse__class_Oinverse(C,A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 23 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)| -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A).
% 87.63/87.78  ** KEPT (pick-wt=20): 24 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 25 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 26 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.63/87.78  ** KEPT (pick-wt=27): 27 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Opcompose(c_Polynomial_OpCons(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A),c_HOL_Otimes__class_Otimes(D,c_Polynomial_Opcompose(C,D,A),tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)).
% 87.63/87.78  ** KEPT (pick-wt=17): 28 [] -class_Ring__and__Field_Ocomm__semiring__0(t_a)|c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(t_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__5__1(c_HOL_Ozero__class_Ozero(t_a)),t_a)=c_HOL_Ozero__class_Ozero(t_a).
% 87.63/87.78  ** KEPT (pick-wt=19): 29 [] -class_Ring__and__Field_Ocomm__semiring__0(t_a)|c_Polynomial_Opoly(c_Polynomial_OpCons(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__3__1(A),t_a)!=c_HOL_Ozero__class_Ozero(t_a)|A=c_HOL_Ozero__class_Ozero(t_a).
% 87.63/87.78  ** KEPT (pick-wt=15): 30 [] -class_Ring__and__Field_Oordered__idom(A)|c_Polynomial_Opos__poly(c_Polynomial_OpCons(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.63/87.78  ** KEPT (pick-wt=16): 31 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_lesse_quals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A)| -c_lesse_quals(C,D,A).
% 87.63/87.78  ** KEPT (pick-wt=16): 32 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_HOL_Oplus__class_Oplus(D,B,A),c_HOL_Oplus__class_Oplus(D,C,A),A).
% 87.63/87.78  ** KEPT (pick-wt=16): 33 [] -class_OrderedGroup_Opordered__ab__semigroup__add(A)|c_lesse_quals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A)| -c_lesse_quals(B,D,A).
% 87.63/87.78  ** KEPT (pick-wt=16): 34 [] -class_OrderedGroup_Opordered__ab__semigroup__add(A)|c_lesse_quals(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A)| -c_lesse_quals(C,D,A).
% 87.63/87.78  ** KEPT (pick-wt=15): 35 [] -class_Ring__and__Field_Ocomm__semiring__0(t_a)|c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(t_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a),A,t_a)=c_HOL_Ozero__class_Ozero(t_a).
% 87.63/87.78  ** KEPT (pick-wt=18): 36 [] -class_Ring__and__Field_Ocomm__semiring__0(t_a)|c_Polynomial_Opoly(c_Polynomial_OpCons(A,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a),B,t_a)!=c_HOL_Ozero__class_Ozero(t_a)|A=c_HOL_Ozero__class_Ozero(t_a).
% 87.63/87.78  ** KEPT (pick-wt=15): 37 [] -class_HOL_Ozero(A)|c_Polynomial_OpCons(B,C,A)!=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|C=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 87.63/87.78  ** KEPT (pick-wt=12): 38 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Osmult(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A)=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 87.63/87.78  ** KEPT (pick-wt=12): 39 [] -class_Ring__and__Field_Oidom(A)|c_Polynomial_Osmult(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A)=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 87.63/87.78  ** KEPT (pick-wt=11): 40 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A))=B.
% 87.63/87.78  ** KEPT (pick-wt=11): 41 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A))=B.
% 87.63/87.78  ** KEPT (pick-wt=13): 42 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A))=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 87.63/87.78  ** KEPT (pick-wt=13): 43 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,tc_Polynomial_Opoly(A))=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 87.63/87.78  ** KEPT (pick-wt=24): 44 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_HOL_Oplus__class_Oplus(B,c_Polynomial_Osmult(C,c_Polynomial_Osynthetic__div(B,C,A),A),tc_Polynomial_Opoly(A))=c_Polynomial_OpCons(c_Polynomial_Opoly(B,C,A),c_Polynomial_Osynthetic__div(B,C,A),A).
% 87.63/87.78  ** KEPT (pick-wt=21): 45 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Otimes__class_Otimes(D,B,A),A).
% 87.63/87.78  ** KEPT (pick-wt=21): 46 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 87.63/87.78  ** KEPT (pick-wt=21): 47 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 87.63/87.78  ** KEPT (pick-wt=21): 48 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A).
% 87.63/87.78  ** KEPT (pick-wt=25): 49 [] -class_Ring__and__Field_Odivision__ring(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(B,C,A),A)=c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(C,A),c_HOL_Oinverse__class_Oinverse(B,A),A)|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 87.63/87.78  ** KEPT (pick-wt=20): 50 [] -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lesse_quals(c_HOL_Otimes__class_Otimes(B,C,A),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).
% 87.63/87.78    Following clause subsumed by 50 during input processing: 0 [] -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lesse_quals(c_HOL_Otimes__class_Otimes(B,C,A),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).
% 87.63/87.78  ** KEPT (pick-wt=20): 51 [] -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lesse_quals(c_HOL_Otimes__class_Otimes(B,C,A),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).
% 87.63/87.78    Following clause subsumed by 50 during input processing: 0 [] -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lesse_quals(c_HOL_Otimes__class_Otimes(B,C,A),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).
% 87.63/87.78    Following clause subsumed by 51 during input processing: 0 [] -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lesse_quals(c_HOL_Otimes__class_Otimes(B,C,A),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).
% 87.63/87.78  ** KEPT (pick-wt=20): 52 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(c_HOL_Otimes__class_Otimes(B,C,A),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).
% 87.63/87.78  ** KEPT (pick-wt=20): 53 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(c_HOL_Otimes__class_Otimes(B,C,A),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).
% 87.63/87.78  ** KEPT (pick-wt=10): 54 [] -class_Ring__and__Field_Oordered__ring__strict(A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=22): 55 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Otimes__class_Otimes(D,B,A),A).
% 87.63/87.78  ** KEPT (pick-wt=22): 56 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 87.63/87.78  ** KEPT (pick-wt=30): 57 [] -class_Ring__and__Field_Opordered__semiring(A)|c_lesse_quals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),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).
% 87.63/87.78  ** KEPT (pick-wt=30): 58 [] -class_Ring__and__Field_Opordered__semiring(A)|c_lesse_quals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),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).
% 87.63/87.78  ** KEPT (pick-wt=20): 59 [] -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),c_HOL_Otimes__class_Otimes(C,B,A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 60 [] -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),c_HOL_Otimes__class_Otimes(B,C,A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 61 [] -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),c_HOL_Otimes__class_Otimes(C,B,A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 62 [] -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),c_HOL_Otimes__class_Otimes(B,C,A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 63 [] -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.63/87.78  ** KEPT (pick-wt=20): 64 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 65 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.63/87.78  ** KEPT (pick-wt=10): 66 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,B,A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 67 [] -class_Ring__and__Field_Opordered__ring(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78    Following clause subsumed by 67 during input processing: 0 [] -class_Ring__and__Field_Opordered__ring(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 68 [] -class_Ring__and__Field_Opordered__ring(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.63/87.78  ** KEPT (pick-wt=21): 69 [] -class_Ring__and__Field_Opordered__ring(A)|c_lesse_quals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(D,B,A).
% 87.63/87.78  ** KEPT (pick-wt=21): 70 [] -class_Ring__and__Field_Opordered__ring(A)|c_lesse_quals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(D,C,A).
% 87.63/87.78  ** KEPT (pick-wt=21): 71 [] -class_Ring__and__Field_Omult__mono(A)|c_lesse_quals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(B,D,A).
% 87.63/87.78  ** KEPT (pick-wt=21): 72 [] -class_Ring__and__Field_Omult__mono(A)|c_lesse_quals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(C,D,A).
% 87.63/87.78  ** KEPT (pick-wt=21): 73 [] -class_Ring__and__Field_Omult__mono1(A)|c_lesse_quals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(C,D,A).
% 87.63/87.78  ** KEPT (pick-wt=20): 74 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 87.63/87.78  ** KEPT (pick-wt=20): 75 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.63/87.78    Following clause subsumed by 74 during input processing: 0 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 76 [] -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(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 77 [] -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(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 78 [] -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(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 79 [] -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_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 80 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 81 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 82 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.63/87.78  ** KEPT (pick-wt=20): 83 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=21): 84 [] -class_Ring__and__Field_Oordered__comm__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(C,D,A).
% 87.63/87.78  ** KEPT (pick-wt=21): 85 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(D,B,A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=21): 86 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 87.63/87.78  ** KEPT (pick-wt=21): 87 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 87.63/87.78    Following clause subsumed by 85 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(D,B,A).
% 87.63/87.78  ** KEPT (pick-wt=21): 88 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=21): 89 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.63/87.78  ** KEPT (pick-wt=21): 90 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(C,D,A).
% 87.63/87.78    Following clause subsumed by 88 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(D,C,A).
% 87.63/87.78    Following clause subsumed by 89 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.63/87.78  ** KEPT (pick-wt=21): 91 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A).
% 87.63/87.78    Following clause subsumed by 88 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=21): 92 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A)| -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 93 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_lesse_quals(c_HOL_Oplus__class_Oplus(B,C,A),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).
% 87.63/87.78  ** KEPT (pick-wt=15): 94 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=15): 95 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 96 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.63/87.78  ** KEPT (pick-wt=15): 97 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.63/87.78  ** KEPT (pick-wt=15): 98 [] -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),c_HOL_Oplus__class_Oplus(B,B,A),A).
% 87.63/87.78  ** KEPT (pick-wt=20): 99 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.63/87.78  ** KEPT (pick-wt=15): 100 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.63/87.78  ** KEPT (pick-wt=15): 101 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A).
% 87.63/87.78  ** KEPT (pick-wt=18): 102 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 87.63/87.78  ** KEPT (pick-wt=15): 103 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=15): 104 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.78  ** KEPT (pick-wt=15): 105 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.79  ** KEPT (pick-wt=15): 106 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.79  ** KEPT (pick-wt=23): 107 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oplus__class_Oplus(B,C,A)!=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).
% 87.63/87.79  ** KEPT (pick-wt=23): 108 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oplus__class_Oplus(B,C,A)!=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).
% 87.63/87.79  ** KEPT (pick-wt=20): 109 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)| -class_OrderedGroup_Ocomm__monoid__add(A)|c_lesse_quals(B,c_HOL_Oplus__class_Oplus(C,D,A),A)| -c_lesse_quals(B,C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),D,A).
% 87.63/87.79  ** KEPT (pick-wt=20): 110 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)| -class_OrderedGroup_Ocomm__monoid__add(A)|c_lesse_quals(B,c_HOL_Oplus__class_Oplus(C,D,A),A)| -c_lesse_quals(B,D,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A).
% 87.63/87.79  ** KEPT (pick-wt=17): 112 [copy,111,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)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 87.63/87.79  ** KEPT (pick-wt=20): 113 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.79  ** KEPT (pick-wt=14): 114 [] -class_HOL_Ozero(A)|c_Polynomial_OpCons(B,C,A)!=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B=c_HOL_Ozero__class_Ozero(A).
% 87.63/87.79  ** KEPT (pick-wt=13): 115 [] -class_HOL_Ozero(A)|c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A)=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 87.63/87.79  ** KEPT (pick-wt=11): 116 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 87.63/87.79  ** KEPT (pick-wt=11): 117 [] -class_Ring__and__Field_Oidom(A)|c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 87.63/87.79  ** KEPT (pick-wt=19): 118 [] -class_Ring__and__Field_Oidom(A)|c_Polynomial_Osmult(B,C,A)!=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|C=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B=c_HOL_Ozero__class_Ozero(A).
% 87.63/87.79  ** KEPT (pick-wt=17): 119 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Opoly(c_Polynomial_Osmult(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_Polynomial_Opoly(C,D,A),A).
% 87.63/87.79  ** KEPT (pick-wt=21): 120 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(B,C,tc_Polynomial_Opoly(A)),D,A)=c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(B,D,A),c_Polynomial_Opoly(C,D,A),A).
% 87.63/87.79  ** KEPT (pick-wt=21): 121 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,A)=c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(B,D,A),c_Polynomial_Opoly(C,D,A),A).
% 87.63/87.79  ** KEPT (pick-wt=16): 122 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Osmult(B,C,A)!=c_Polynomial_OpCons(D,C,A)|C=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 87.63/87.79  ** KEPT (pick-wt=20): 123 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.63/87.79  ** KEPT (pick-wt=20): 124 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)| -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A)| -c_lesse_quals(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 87.63/87.79  ** KEPT (pick-wt=21): 125 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A)| -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.79  ** KEPT (pick-wt=21): 126 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_lesse_quals(D,C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.79  ** KEPT (pick-wt=21): 127 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A).
% 87.63/87.79  ** KEPT (pick-wt=21): 128 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_lesse_quals(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.63/87.79  ** KEPT (pick-wt=21): 129 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_lesse_quals(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A).
% 87.63/87.79  ** KEPT (pick-wt=21): 130 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_lesse_quals(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 87.63/87.79  ** KEPT (pick-wt=30): 131 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_HOL_Oord__class_Oless(C,E,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 87.63/87.79  ** KEPT (pick-wt=21): 132 [] -class_Ring__and__Field_Oordered__semiring(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A).
% 87.63/87.79  ** KEPT (pick-wt=21): 133 [] -class_Ring__and__Field_Oordered__semiring(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 87.63/87.79  ** KEPT (pick-wt=21): 134 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A).
% 87.63/87.79  ** KEPT (pick-wt=21): 135 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 87.63/87.79  ** KEPT (pick-wt=30): 136 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(C,E,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 87.63/87.79  ** KEPT (pick-wt=30): 137 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(C,E,A)| -c_lesse_quals(B,D,A).
% 87.63/87.79  ** KEPT (pick-wt=30): 138 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)| -c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(B,D,A).
% 87.63/87.79  ** KEPT (pick-wt=20): 139 [] -class_Ring__and__Field_Odivision__ring(A)|c_HOL_Oinverse__class_Oinverse(B,A)!=c_HOL_Oinverse__class_Oinverse(C,A)|B=C|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 87.63/87.79  ** KEPT (pick-wt=11): 140 [] -class_Ring__and__Field_Odivision__ring(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 87.63/87.79  ** KEPT (pick-wt=9): 141 [] -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 87.63/87.79  ** KEPT (pick-wt=13): 142 [] -class_Ring__and__Field_Odivision__ring(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(B,A),A)=B|B=c_HOL_Ozero__class_Ozero(A).
% 87.63/87.79  ** KEPT (pick-wt=14): 143 [] -class_Ring__and__Field_Odivision__ring(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(B,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 87.63/87.79  ** KEPT (pick-wt=12): 144 [] -class_Ring__and__Field_Odivision__ring(A)|c_HOL_Oinverse__class_Oinverse(B,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 87.63/87.79  ** KEPT (pick-wt=20): 145 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A)| -c_HOL_Oord__class_Oless(C,E,A)| -c_lesse_quals(B,D,A).
% 87.63/87.79  ** KEPT (pick-wt=20): 146 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A)| -c_lesse_quals(C,E,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 87.63/87.79  ** KEPT (pick-wt=16): 147 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Oinverse(B,A),A).
% 87.63/87.79  ** KEPT (pick-wt=16): 148 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Oinverse(B,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.63/87.79  ** KEPT (pick-wt=14): 149 [] -class_Ring__and__Field_Oordered__field(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Oinverse(B,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.63/87.79  ** KEPT (pick-wt=16): 150 [] -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_Oinverse__class_Oinverse(B,A),c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.79  ** KEPT (pick-wt=16): 151 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.79  ** KEPT (pick-wt=10): 152 [] -class_Orderings_Olinorder(A)| -c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 87.63/87.79  ** KEPT (pick-wt=10): 153 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_lesse_quals(C,B,A).
% 87.63/87.79    Following clause subsumed by 153 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)|c_HOL_Oord__class_Oless(C,B,A).
% 87.63/87.79    Following clause subsumed by 152 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(C,B,A).
% 87.63/87.79    Following clause subsumed by 153 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,B,A)|c_lesse_quals(B,B,A).
% 87.63/87.79    Following clause subsumed by 152 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_lesse_quals(B,B,A)| -c_HOL_Oord__class_Oless(B,B,A).
% 87.63/87.79    Following clause subsumed by 153 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_lesse_quals(C,B,A).
% 87.63/87.79  ** KEPT (pick-wt=10): 154 [] -class_Orderings_Opreorder(A)| -c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 87.63/87.79  ** KEPT (pick-wt=14): 155 [] -class_Orderings_Opreorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 87.63/87.79  ** KEPT (pick-wt=14): 156 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(D,C,A).
% 87.63/87.79  ** KEPT (pick-wt=11): 157 [] -class_Ring__and__Field_Odivision__ring(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(B,A),A)=B.
% 87.63/87.79  ** KEPT (pick-wt=12): 158 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,A)=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 87.63/87.79  ** KEPT (pick-wt=17): 159 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(B,C,A),D,A)=c_Polynomial_Opoly(B,c_HOL_Oplus__class_Oplus(C,D,A),A).
% 87.63/87.79  ** KEPT (pick-wt=20): 160 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(B,C,A),D,A)=c_Polynomial_OpCons(c_Polynomial_Opoly(C,D,A),c_Polynomial_Osynthetic__div(C,D,A),A).
% 87.63/87.79  ** KEPT (pick-wt=13): 161 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(C,B,A)| -c_lesse_quals(B,C,A).
% 87.63/87.79  ** KEPT (pick-wt=13): 162 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)|C=B.
% 87.63/87.79    Following clause subsumed by 161 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(C,B,A)| -c_lesse_quals(B,C,A).
% 87.63/87.79    Following clause subsumed by 161 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(B,C,A)| -c_lesse_quals(C,B,A).
% 87.63/87.79    Following clause subsumed by 162 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|C=B|c_HOL_Oord__class_Oless(C,B,A).
% 87.63/87.79    Following clause subsumed by 162 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A).
% 87.63/87.79    Following clause subsumed by 162 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A).
% 87.63/87.79  ** KEPT (pick-wt=13): 163 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)|C=B.
% 87.63/87.79  ** KEPT (pick-wt=18): 164 [] -class_Ring__and__Field_Oordered__field(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|B=c_HOL_Ozero__class_Ozero(A)| -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Ozero__class_Ozero(A),A).
% 87.63/87.79  ** KEPT (pick-wt=14): 165 [] -class_Ring__and__Field_Odivision__ring(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(B,A)!=c_HOL_Oinverse__class_Oinverse(C,A)|B=C.
% 87.63/87.79  ** KEPT (pick-wt=13): 166 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|B=C| -c_lesse_quals(B,C,A).
% 87.63/87.79    Following clause subsumed by 166 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,C,A).
% 87.63/87.79    Following clause subsumed by 166 during input processing: 0 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|B=C| -c_lesse_quals(B,C,A).
% 87.63/87.79    Following clause subsumed by 166 during input processing: 0 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,C,A)|B=C.
% 87.63/87.79  ** KEPT (pick-wt=13): 167 [] -class_Orderings_Olinorder(A)|B=C| -c_lesse_quals(B,C,A)|c_HOL_Oord__class_Oless(B,C,A).
% 87.63/87.79    Following clause subsumed by 167 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,C,A).
% 87.63/87.79  ** KEPT (pick-wt=13): 168 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,C,A)|C=B.
% 87.63/87.79    Following clause subsumed by 168 during input processing: 0 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|C=B| -c_lesse_quals(B,C,A).
% 87.63/87.79  ** KEPT (pick-wt=18): 169 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A),C,A)=c_Polynomial_OpCons(B,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),A).
% 87.63/87.79  ** KEPT (pick-wt=11): 170 [] -class_Ring__and__Field_Oidom(A)|c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,A)=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=11): 171 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,A)=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=15): 172 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(B,C,A)!=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 87.71/87.79  ** KEPT (pick-wt=18): 173 [] -class_Ring__and__Field_Oordered__field(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)|B=c_HOL_Ozero__class_Ozero(A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Oinverse(B,A),A).
% 87.71/87.79  ** KEPT (pick-wt=19): 174 [] -class_Ring__and__Field_Oordered__field(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(C,A),c_HOL_Oinverse__class_Oinverse(B,A),A).
% 87.71/87.79  ** KEPT (pick-wt=19): 175 [] -class_Ring__and__Field_Oordered__field(A)|c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oinverse__class_Oinverse(C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 87.71/87.79  ** KEPT (pick-wt=19): 176 [] -class_Ring__and__Field_Oordered__field(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(C,A),c_HOL_Oinverse__class_Oinverse(B,A),A).
% 87.71/87.79  ** KEPT (pick-wt=19): 177 [] -class_Ring__and__Field_Oordered__field(A)|c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oinverse__class_Oinverse(C,A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(C,B,A).
% 87.71/87.79    Following clause subsumed by 171 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Opoly(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,A)=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=16): 178 [] -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_HOL_Oinverse__class_Oinverse(B,A),A).
% 87.71/87.79  ** KEPT (pick-wt=16): 179 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Oinverse(B,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 87.71/87.79  ** KEPT (pick-wt=19): 180 [] -class_Ring__and__Field_Oordered__field(A)|c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Oinverse__class_Oinverse(C,A),c_HOL_Oinverse__class_Oinverse(B,A),A).
% 87.71/87.79  ** KEPT (pick-wt=19): 181 [] -class_Ring__and__Field_Oordered__field(A)|c_lesse_quals(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oinverse__class_Oinverse(C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(C,B,A).
% 87.71/87.79  ** KEPT (pick-wt=19): 182 [] -class_Ring__and__Field_Oordered__field(A)|c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(c_HOL_Oinverse__class_Oinverse(C,A),c_HOL_Oinverse__class_Oinverse(B,A),A).
% 87.71/87.79  ** KEPT (pick-wt=19): 183 [] -class_Ring__and__Field_Oordered__field(A)|c_lesse_quals(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oinverse__class_Oinverse(C,A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(C,B,A).
% 87.71/87.79  ** KEPT (pick-wt=6): 184 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 87.71/87.79  ** KEPT (pick-wt=6): 185 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 87.71/87.79  ** KEPT (pick-wt=6): 186 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 87.71/87.79  ** KEPT (pick-wt=14): 187 [] -class_Orderings_Opreorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_lesse_quals(C,B,A)| -c_lesse_quals(B,C,A).
% 87.71/87.79  ** KEPT (pick-wt=16): 188 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Ozero__class_Ozero(A),A).
% 87.71/87.79  ** KEPT (pick-wt=16): 189 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 87.71/87.79  ** KEPT (pick-wt=14): 190 [] -class_Ring__and__Field_Oordered__field(A)|c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 87.71/87.79  ** KEPT (pick-wt=10): 191 [] -class_Orderings_Oorder(A)|c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(B,C,A).
% 87.71/87.79  ** KEPT (pick-wt=10): 192 [] -class_Orderings_Opreorder(A)|c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(B,C,A).
% 87.71/87.79  ** KEPT (pick-wt=12): 193 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,A)=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 87.71/87.79  ** KEPT (pick-wt=6): 194 [] -class_Orderings_Opreorder(A)|c_lesse_quals(B,B,A).
% 87.71/87.79  ** KEPT (pick-wt=6): 195 [] -class_Orderings_Oorder(A)|c_lesse_quals(B,B,A).
% 87.71/87.79  ** KEPT (pick-wt=14): 196 [] -class_Orderings_Opreorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_lesse_quals(B,D,A).
% 87.71/87.79  ** KEPT (pick-wt=14): 197 [] -class_Orderings_Opreorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(D,C,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 87.71/87.79  ** KEPT (pick-wt=14): 198 [] -class_Orderings_Opreorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(D,C,A)| -c_lesse_quals(B,D,A).
% 87.71/87.79  ** KEPT (pick-wt=14): 199 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_lesse_quals(D,C,A).
% 87.71/87.79  ** KEPT (pick-wt=14): 200 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,D,A)| -c_HOL_Oord__class_Oless(D,C,A).
% 87.71/87.79  ** KEPT (pick-wt=14): 201 [] -class_Orderings_Oorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(B,D,A)| -c_lesse_quals(D,C,A).
% 87.71/87.79  ** KEPT (pick-wt=10): 202 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 87.71/87.79    Following clause subsumed by 202 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 87.71/87.79  ** KEPT (pick-wt=10): 203 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)|c_lesse_quals(C,B,A).
% 87.71/87.79  ** KEPT (pick-wt=10): 204 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 87.71/87.79  ** KEPT (pick-wt=10): 205 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 87.71/87.79  ** KEPT (pick-wt=33): 207 [copy,206,flip.2] -class_Ring__and__Field_Odivision__ring(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oplus__class_Oplus(B,C,A),A),c_HOL_Oinverse__class_Oinverse(C,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oinverse__class_Oinverse(C,A),A)|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=33): 209 [copy,208,flip.2] -class_Ring__and__Field_Ofield(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oinverse__class_Oinverse(B,A),A),c_HOL_Oinverse__class_Oinverse(C,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oinverse__class_Oinverse(C,A),A)|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=20): 210 [] -class_Ring__and__Field_Oordered__ring__strict(A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A),A).
% 87.71/87.79  ** KEPT (pick-wt=20): 211 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A),c_HOL_Ozero__class_Ozero(A),A).
% 87.71/87.79  ** KEPT (pick-wt=16): 212 [] -class_Ring__and__Field_Oordered__ring__strict(A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),c_HOL_Ozero__class_Ozero(A),A).
% 87.71/87.79  ** KEPT (pick-wt=16): 213 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A).
% 87.71/87.79  ** KEPT (pick-wt=20): 214 [] -class_Ring__and__Field_Oordered__ring__strict(A)|B=c_HOL_Ozero__class_Ozero(A)| -c_lesse_quals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,C,A),c_HOL_Otimes__class_Otimes(B,B,A),A),c_HOL_Ozero__class_Ozero(A),A).
% 87.71/87.79  ** KEPT (pick-wt=20): 215 [] -class_Ring__and__Field_Oordered__ring__strict(A)|B=c_HOL_Ozero__class_Ozero(A)| -c_lesse_quals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),c_HOL_Ozero__class_Ozero(A),A).
% 87.71/87.79  ** KEPT (pick-wt=20): 216 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A)|C=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=20): 217 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A)|B=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=20): 218 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Opoly(c_Polynomial_OpCons(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(D,c_Polynomial_Opoly(C,D,A),A),A).
% 87.71/87.79  ** KEPT (pick-wt=21): 219 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_HOL_Oplus__class_Oplus(B,c_Polynomial_Osmult(C,D,A),tc_Polynomial_Opoly(A))!=c_Polynomial_OpCons(E,D,A)|D=c_Polynomial_Osynthetic__div(B,C,A).
% 87.71/87.79  ** KEPT (pick-wt=21): 220 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_HOL_Oplus__class_Oplus(B,c_Polynomial_Osmult(C,D,A),tc_Polynomial_Opoly(A))!=c_Polynomial_OpCons(E,D,A)|E=c_Polynomial_Opoly(B,C,A).
% 87.71/87.79  ** KEPT (pick-wt=22): 221 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(B,C,A),c_Polynomial_OpCons(D,C,A),tc_Polynomial_Opoly(A))!=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|C=c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 87.71/87.79  ** KEPT (pick-wt=27): 223 [copy,222,flip.2] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(B,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(C,B,A),A),c_Polynomial_OpCons(D,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(C,B,A),A),tc_Polynomial_Opoly(A))=c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(D,C,A),B,A).
% 87.71/87.79  ** KEPT (pick-wt=19): 224 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A)=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=27): 225 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_HOL_Otimes__class_Otimes(B,c_Polynomial_OpCons(C,D,A),tc_Polynomial_Opoly(A))=c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(C,B,A),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),A),tc_Polynomial_Opoly(A)).
% 87.71/87.79  ** KEPT (pick-wt=27): 226 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(B,C,A),D,tc_Polynomial_Opoly(A))=c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(B,D,A),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),A),tc_Polynomial_Opoly(A)).
% 87.71/87.79  ** KEPT (pick-wt=10): 227 [] -class_Ring__and__Field_Oring__no__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=10): 228 [] -class_Ring__and__Field_Oring__no__zero__divisors(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=10): 229 [] -class_Ring__and__Field_Omult__zero(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=10): 230 [] -class_Ring__and__Field_Omult__zero(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=10): 231 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=10): 232 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79    Following clause subsumed by 232 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=10): 233 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79    Following clause subsumed by 233 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=10): 234 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79    Following clause subsumed by 231 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=31): 235 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A)|C=E|B=D.
% 87.71/87.79    Following clause subsumed by 235 during input processing: 0 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A)|C=E|B=D.
% 87.71/87.79  ** KEPT (pick-wt=25): 237 [copy,236,flip.2] -class_OrderedGroup_Ocomm__monoid__add(A)|c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,tc_Polynomial_Opoly(A)),A)=c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(B,D,A),c_Polynomial_OpCons(C,E,A),tc_Polynomial_Opoly(A)).
% 87.71/87.79  ** KEPT (pick-wt=11): 238 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oplus__class_Oplus(B,C,A)=c_HOL_Oplus__class_Oplus(C,B,A).
% 87.71/87.79  ** KEPT (pick-wt=11): 239 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(B,C,A)=c_HOL_Oplus__class_Oplus(C,B,A).
% 87.71/87.79    Following clause subsumed by 239 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(B,C,A)=c_HOL_Oplus__class_Oplus(C,B,A).
% 87.71/87.79  ** KEPT (pick-wt=20): 240 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A)!=c_HOL_Oplus__class_Oplus(C,E,A)|c_HOL_Oplus__class_Oplus(B,D,A)=E.
% 87.71/87.79  ** KEPT (pick-wt=14): 241 [] -class_OrderedGroup_Ocancel__semigroup__add(A)|c_HOL_Oplus__class_Oplus(B,C,A)!=c_HOL_Oplus__class_Oplus(D,C,A)|B=D.
% 87.71/87.79  ** KEPT (pick-wt=14): 242 [] -class_OrderedGroup_Ocancel__semigroup__add(A)|c_HOL_Oplus__class_Oplus(B,C,A)!=c_HOL_Oplus__class_Oplus(B,D,A)|C=D.
% 87.71/87.79  ** KEPT (pick-wt=14): 243 [] -class_OrderedGroup_Ocancel__ab__semigroup__add(A)|c_HOL_Oplus__class_Oplus(B,C,A)!=c_HOL_Oplus__class_Oplus(B,D,A)|C=D.
% 87.71/87.79  ** KEPT (pick-wt=16): 244 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(B,C,A)!=c_HOL_Oplus__class_Oplus(B,D,A)|C=D.
% 87.71/87.79  ** KEPT (pick-wt=23): 245 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,E,A),A).
% 87.71/87.79  ** KEPT (pick-wt=20): 247 [copy,246,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 87.71/87.79  ** KEPT (pick-wt=20): 248 [] -class_Ring__and__Field_Ocomm__semiring(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 87.71/87.79  ** KEPT (pick-wt=20): 249 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 87.71/87.79  ** KEPT (pick-wt=25): 250 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,tc_Polynomial_Opoly(A)),D,tc_Polynomial_Opoly(A))=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,tc_Polynomial_Opoly(A)),c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),tc_Polynomial_Opoly(A)).
% 87.71/87.79  ** KEPT (pick-wt=20): 251 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 87.71/87.79    Following clause subsumed by 251 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 87.71/87.79  ** KEPT (pick-wt=20): 252 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 87.71/87.79    Following clause subsumed by 252 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 87.71/87.79    Following clause subsumed by 247 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 87.71/87.79  ** KEPT (pick-wt=17): 254 [copy,253,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A).
% 87.71/87.79  ** KEPT (pick-wt=17): 255 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A)=c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(B,D,A),A).
% 87.71/87.79    Following clause subsumed by 254 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A).
% 87.71/87.79    Following clause subsumed by 254 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A).
% 87.71/87.79  ** KEPT (pick-wt=17): 256 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,D,A),C,A).
% 87.71/87.79  ** KEPT (pick-wt=17): 257 [] -class_OrderedGroup_Oab__semigroup__mult(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A).
% 87.71/87.79  ** KEPT (pick-wt=8): 258 [] -class_OrderedGroup_Oab__semigroup__idem__mult(A)|c_HOL_Otimes__class_Otimes(B,B,A)=B.
% 87.71/87.79  ** KEPT (pick-wt=20): 259 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Osmult(B,c_Polynomial_OpCons(C,D,A),A)=c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(B,C,A),c_Polynomial_Osmult(B,D,A),A).
% 87.71/87.79  ** KEPT (pick-wt=19): 260 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A)!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=19): 261 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=26): 262 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A)!=c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,E,A),A)|D=E|C=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=14): 263 [] -class_HOL_Ozero(A)|c_Polynomial_OpCons(B,C,A)!=c_Polynomial_OpCons(D,E,A)|B=D.
% 87.71/87.79  ** KEPT (pick-wt=14): 264 [] -class_HOL_Ozero(A)|c_Polynomial_OpCons(B,C,A)!=c_Polynomial_OpCons(D,E,A)|C=E.
% 87.71/87.79  ** KEPT (pick-wt=14): 265 [] -class_OrderedGroup_Oab__semigroup__idem__mult(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(B,C,A),A)=c_HOL_Otimes__class_Otimes(B,C,A).
% 87.71/87.79    Following clause subsumed by 255 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)=c_HOL_Otimes__class_Otimes(D,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),E,A),A).
% 87.71/87.79    Following clause subsumed by 254 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(D,E,A),A),A).
% 87.71/87.79  ** KEPT (pick-wt=23): 266 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A).
% 87.71/87.79  ** KEPT (pick-wt=17): 267 [] -class_Ring__and__Field_Oring__no__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=17): 268 [] -class_Ring__and__Field_Ono__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79    Following clause subsumed by 268 during input processing: 0 [] -class_Ring__and__Field_Ono__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=13): 269 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oplus__class_Oplus(B,B,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=14): 271 [copy,270,flip.3] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(B,C,A)!=B|C=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.79  ** KEPT (pick-wt=21): 272 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(B,D,A),c_Polynomial_Osmult(C,D,A),tc_Polynomial_Opoly(A)).
% 87.71/87.79  ** KEPT (pick-wt=22): 273 [] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Osmult(B,c_HOL_Oplus__class_Oplus(C,D,tc_Polynomial_Opoly(A)),A)=c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(B,C,A),c_Polynomial_Osmult(B,D,A),tc_Polynomial_Opoly(A)).
% 87.71/87.79  ** KEPT (pick-wt=25): 274 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(B,C,A),A).
% 87.71/87.79    Following clause subsumed by 274 during input processing: 0 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(B,C,A),A).
% 87.71/87.79  ** KEPT (pick-wt=11): 275 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,C,A)=c_HOL_Otimes__class_Otimes(C,B,A).
% 87.71/87.80  ** KEPT (pick-wt=11): 276 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 87.71/87.80    Following clause subsumed by 275 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,C,A)=c_HOL_Otimes__class_Otimes(C,B,A).
% 87.71/87.80  ** KEPT (pick-wt=17): 277 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A).
% 87.71/87.80  ** KEPT (pick-wt=17): 278 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A).
% 87.71/87.80  ** KEPT (pick-wt=17): 280 [copy,279,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A).
% 87.71/87.80  ** KEPT (pick-wt=17): 281 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A).
% 87.71/87.80  ** KEPT (pick-wt=17): 282 [] -class_OrderedGroup_Oab__semigroup__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A).
% 87.71/87.80    Following clause subsumed by 280 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A).
% 87.71/87.80  ** KEPT (pick-wt=17): 283 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),C,A).
% 87.71/87.80  ** KEPT (pick-wt=17): 284 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A).
% 87.71/87.80    Following clause subsumed by 280 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A).
% 87.71/87.80  ** KEPT (pick-wt=26): 286 [copy,285,flip.2] -class_Ring__and__Field_Osemiring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A),E,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,A),E,A),A).
% 87.71/87.80  ** KEPT (pick-wt=19): 288 [copy,287,flip.2] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Osmult(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),A)=c_HOL_Otimes__class_Otimes(C,c_Polynomial_Osmult(B,D,A),tc_Polynomial_Opoly(A)).
% 87.71/87.80  ** KEPT (pick-wt=19): 290 [copy,289,flip.2] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Osmult(B,c_HOL_Otimes__class_Otimes(C,D,tc_Polynomial_Opoly(A)),A)=c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(B,C,A),D,tc_Polynomial_Opoly(A)).
% 87.71/87.80  ** KEPT (pick-wt=17): 292 [copy,291,flip.2] -class_Ring__and__Field_Ocomm__semiring__0(A)|c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_Polynomial_Osmult(B,c_Polynomial_Osmult(C,D,A),A).
% 87.71/87.80  ** KEPT (pick-wt=9): 293 [] -class_OrderedGroup_Omonoid__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 87.71/87.80  ** KEPT (pick-wt=9): 294 [] -class_OrderedGroup_Omonoid__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A)=B.
% 87.71/87.80  ** KEPT (pick-wt=9): 295 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 87.71/87.80  ** KEPT (pick-wt=11): 297 [copy,296,flip.3] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 87.71/87.80  ** KEPT (pick-wt=9): 298 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A)=B.
% 87.71/87.80  ** KEPT (pick-wt=9): 299 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A)=B.
% 87.71/87.80  ** KEPT (pick-wt=9): 300 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 87.71/87.80    Following clause subsumed by 298 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A)=B.
% 87.71/87.80  ** KEPT (pick-wt=31): 302 [copy,301,flip.1] c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))!=c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_a,c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
% 87.71/87.80  ** KEPT (pick-wt=5): 303 [] class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(A))| -class_OrderedGroup_Ocancel__comm__monoid__add(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 304 [] class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Ocomm__ring__1(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 305 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 306 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 307 [] class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 308 [] class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 309 [] class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 310 [] class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 311 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 312 [] class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oidom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 313 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(A))| -class_OrderedGroup_Ocancel__comm__monoid__add(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 314 [] class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 315 [] class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 316 [] class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(A))| -class_OrderedGroup_Ocancel__comm__monoid__add(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 317 [] class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 318 [] class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 319 [] class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oidom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 320 [] class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 321 [] class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Ocomm__semiring__1(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 322 [] class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Ocomm__semiring__0(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 323 [] class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Ocomm__semiring__0(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 324 [] class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(A))| -class_OrderedGroup_Ocomm__monoid__add(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 325 [] class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 326 [] class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Ocomm__semiring__0(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 327 [] class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(A))| -class_OrderedGroup_Ocomm__monoid__add(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 328 [] class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 329 [] class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 330 [] class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(A))| -class_OrderedGroup_Oab__group__add(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 331 [] class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Ocomm__semiring__0(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 332 [] class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 333 [] class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Ocomm__semiring__0(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 334 [] class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(A))| -class_OrderedGroup_Ocomm__monoid__add(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 335 [] class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oidom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 336 [] class_Orderings_Opreorder(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 337 [] class_Orderings_Olinorder(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 338 [] class_Orderings_Oorder(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Oordered__idom(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 339 [] class_Int_Onumber__ring(tc_Polynomial_Opoly(A))| -class_Ring__and__Field_Ocomm__ring__1(A).
% 87.71/87.80  ** KEPT (pick-wt=5): 340 [] class_HOL_Ozero(tc_Polynomial_Opoly(A))| -class_HOL_Ozero(A).
% 87.71/87.80  35 back subsumes 28.
% 87.71/87.80  36 back subsumes 29.
% 87.71/87.80  141 back subsumes 140.
% 87.71/87.80  144 back subsumes 143.
% 87.71/87.80  149 back subsumes 148.
% 87.71/87.80  190 back subsumes 189.
% 87.71/87.80  363 back subsumes 359.
% 87.71/87.80  367 back subsumes 361.
% 87.71/87.80  402 back subsumes 401.
% 87.71/87.80  
% 87.71/87.80  ------------> process sos:
% 87.71/87.80  ** KEPT (pick-wt=3): 425 [] A=A.
% 87.71/87.80  ** KEPT (pick-wt=2): 426 [] class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 427 [] class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 428 [] class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 429 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 430 [] class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 431 [] class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 432 [] class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 433 [] class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 434 [] class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 435 [] class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 436 [] class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 437 [] class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 438 [] class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 439 [] class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 440 [] class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 441 [] class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 442 [] class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 443 [] class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 444 [] class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 445 [] class_Ring__and__Field_Ofield(tc_Complex_Ocomplex).
% 87.71/87.80  ** KEPT (pick-wt=2): 446 [] class_Ring__and__Field_Oidom(tc_Complex_Ocomplex).
% 87.71/87.82  ** KEPT (pick-wt=2): 447 [] class_Int_Onumber__ring(tc_Complex_Ocomplex).
% 87.71/87.82  ** KEPT (pick-wt=2): 448 [] class_HOL_Ozero(tc_Complex_Ocomplex).
% 87.71/87.82    Following clause subsumed by 425 during input processing: 0 [copy,425,flip.1] A=A.
% 87.71/87.82  425 back subsumes 413.
% 87.71/87.82  425 back subsumes 412.
% 87.71/87.82  425 back subsumes 411.
% 87.71/87.82  425 back subsumes 410.
% 87.71/87.82  425 back subsumes 409.
% 87.71/87.82  425 back subsumes 408.
% 87.71/87.82  
% 87.71/87.82  ======= end of input processing =======
% 87.71/87.82  
% 87.71/87.82  =========== start of search ===========
% 87.71/87.82  
% 87.71/87.82  
% 87.71/87.82  Resetting weight limit to 2.
% 87.71/87.82  
% 87.71/87.82  
% 87.71/87.82  Resetting weight limit to 2.
% 87.71/87.82  
% 87.71/87.82  sos_size=23
% 87.71/87.82  
% 87.71/87.82  Search stopped because sos empty.
% 87.71/87.82  
% 87.71/87.82  
% 87.71/87.82  Search stopped because sos empty.
% 87.71/87.82  
% 87.71/87.82  ============ end of search ============
% 87.71/87.82  
% 87.71/87.82  -------------- statistics -------------
% 87.71/87.82  clauses given                 24
% 87.71/87.82  clauses generated           1704
% 87.71/87.82  clauses kept                 433
% 87.71/87.82  clauses forward subsumed      97
% 87.71/87.82  clauses back subsumed         15
% 87.71/87.82  Kbytes malloced             5859
% 87.71/87.82  
% 87.71/87.82  ----------- times (seconds) -----------
% 87.71/87.82  user CPU time          0.07          (0 hr, 0 min, 0 sec)
% 87.71/87.82  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 87.71/87.82  wall-clock time       88             (0 hr, 1 min, 28 sec)
% 87.71/87.82  
% 87.71/87.82  Process 20908 finished Wed Jul 27 03:47:31 2022
% 87.71/87.82  Otter interrupted
% 87.71/87.82  PROOF NOT FOUND
%------------------------------------------------------------------------------