TSTP Solution File: LCL852-1 by Otter---3.3

%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : LCL852-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Jul 27 13:05:37 EDT 2022

% Result   : Unknown 224.36s 224.49s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : LCL852-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12  % Command  : otter-tptp-script %s
% 0.12/0.33  % Computer : n010.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Jul 27 09:09:24 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 223.84/223.92  ----- Otter 3.3f, August 2004 -----
% 223.84/223.92  The process was started by sandbox on n010.cluster.edu,
% 223.84/223.92  Wed Jul 27 09:09:25 2022
% 223.84/223.92  The command was "./otter".  The process ID is 15296.
% 223.84/223.92  
% 223.84/223.92  set(prolog_style_variables).
% 223.84/223.92  set(auto).
% 223.84/223.92     dependent: set(auto1).
% 223.84/223.92     dependent: set(process_input).
% 223.84/223.92     dependent: clear(print_kept).
% 223.84/223.92     dependent: clear(print_new_demod).
% 223.84/223.92     dependent: clear(print_back_demod).
% 223.84/223.92     dependent: clear(print_back_sub).
% 223.84/223.92     dependent: set(control_memory).
% 223.84/223.92     dependent: assign(max_mem, 12000).
% 223.84/223.92     dependent: assign(pick_given_ratio, 4).
% 223.84/223.92     dependent: assign(stats_level, 1).
% 223.84/223.92     dependent: assign(max_seconds, 10800).
% 223.84/223.92  clear(print_given).
% 223.84/223.92  
% 223.84/223.92  list(usable).
% 223.84/223.92  0 [] A=A.
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 223.84/223.92  0 [] -c_lesse_quals(V_x,V_x,tc_nat)|c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)| -c_lesse_quals(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)| -c_lesse_quals(V_c,V_d,T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 223.84/223.92  0 [] c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_l),tc_nat)| -c_lesse_quals(V_k,V_l,tc_nat)| -c_lesse_quals(V_i,V_j,tc_nat).
% 223.84/223.92  0 [] c_Lambda_Osubstn(V_t,V_s,V_n)=c_Lambda_Osubst(V_t,c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_n).
% 223.84/223.92  0 [] -hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_b),V_d),V_b,tc_nat)))|hBOOL(hAPP(V_P,V_d)).
% 223.84/223.92  0 [] -hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_b),V_x),V_b,tc_nat)))|hBOOL(hAPP(V_P,V_x)).
% 223.84/223.92  0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ominus__class_Ominus(V_a,V_b,T_a)),V_b)=V_a.
% 223.84/223.92  0 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(V_i),V_s,V_k)=c_Lambda_OdB_OVar(V_i)|V_i=V_k|c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 223.84/223.92  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a).
% 223.84/223.92  0 [] V_n=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 223.84/223.92  0 [] c_Orderings_Oord__class_Omax(c_Suc(V_m),c_Suc(V_n),tc_nat)=c_Suc(c_Orderings_Oord__class_Omax(V_m,V_n,tc_nat)).
% 223.84/223.92  0 [] c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a)=hAPP(V_f3,V_dB).
% 223.84/223.92  0 [] c_Lambda_Obeta(c_Lambda_Osubst(V_r,V_t,V_i),c_Lambda_Osubst(V_s,V_t,V_i))| -c_Lambda_Obeta(V_r,V_s).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)| -c_lesse_quals(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(V_m,V_n,tc_nat)| -c_lesse_quals(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_m,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat)| -c_lesse_quals(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 223.84/223.92  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,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)| -c_lesse_quals(V_b,V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 223.84/223.92  0 [] c_List_Oreplicate(V_m,V_x,T_a)!=c_List_Oreplicate(V_n,V_y,T_a)|V_m=V_n.
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),V_m,tc_nat)=c_HOL_Ominus__class_Ominus(c_Suc(V_j),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),tc_nat)| -c_lesse_quals(V_k,V_j,tc_nat).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)| -c_HOL_Oord__class_Oless(V_y,V_z,T_a)| -c_HOL_Oord__class_Oless(V_x,V_z,T_a).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_lesse_quals(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_lesse_quals(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 223.84/223.92  0 [] hBOOL(hAPP(V_P,V_nat))| -hBOOL(hAPP(V_P,c_Suc(v_sko__Nat__Xnat__Xinduct__1(V_P))))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.92  0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Suc(V_n),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n))=c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n)=c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)).
% 223.84/223.92  0 [] hBOOL(hAPP(V_P,V_n))|hBOOL(hAPP(V_P,V_x))| -c_HOL_Oord__class_Oless(V_x,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(V_P),tc_nat)| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_m)),tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_i)),tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_m,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_x)),tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat)| -c_lesse_quals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)| -c_lesse_quals(V_k,V_j,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat)| -c_lesse_quals(V_k,V_j,tc_nat).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)| -c_lesse_quals(V_y,V_z,T_a)| -c_lesse_quals(V_x,V_z,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(c_Orderings_Oord__class_Omax(V_y,V_z,T_a),V_x,T_a)| -c_lesse_quals(V_z,V_x,T_a)| -c_lesse_quals(V_y,V_x,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a)| -c_lesse_quals(V_b,V_x,T_a)| -c_lesse_quals(V_a,V_x,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_y,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a).
% 223.84/223.92  0 [] -class_Orderings_Obot(T_a)|c_lesse_quals(c_Orderings_Obot__class_Obot(T_a),V_x,T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)| -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_lesse_quals(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)| -c_lesse_quals(V_b,V_c,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)| -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_lesse_quals(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)| -c_lesse_quals(V_b,V_a,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 223.84/223.92  0 [] hBOOL(hAPP(V_P,V_nat))| -hBOOL(hAPP(V_P,c_Suc(v_sko__List__Xupt__Xinduct__1(V_P))))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.92  0 [] c_Type_Otype_OAtom(V_nat)!=c_Type_Otype_OAtom(V_nat_H)|V_nat=V_nat_H.
% 223.84/223.92  0 [] c_lesse_quals(c_Suc(V_m),V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_lesse_quals(c_Suc(V_m),V_n,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(c_Suc(V_n),V_m,tc_nat)| -c_HOL_Oord__class_Oless(V_n,V_m,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)| -c_lesse_quals(c_Suc(V_n),V_m,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_y,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_z,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_i,V_k,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_m),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_j),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat)=c_Suc(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat))| -c_lesse_quals(V_n,V_m,tc_nat).
% 223.84/223.92  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_l)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n)| -c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_x).
% 223.84/223.92  0 [] -class_OrderedGroup_Osemigroup__add(T_a)|c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y),V_zs,T_a,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_y,V_zs,T_a,T_a)).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_l,tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] -class_Nat_Osemiring__char__0(T_a)|c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)!=c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)|V_m=V_n.
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_z,V_y,T_a)|c_lesse_quals(V_z,V_x,T_a)| -c_lesse_quals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a).
% 223.84/223.92  0 [] c_List_Odrop(V_n,c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_pwr,V_x),V_p)),hAPP(hAPP(V_pwr,V_x),V_q))=hAPP(hAPP(V_pwr,V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_p),V_q))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] c_Lambda_Oliftn(c_Suc(V_n),V_t,V_k)=c_Lambda_Olift(c_Lambda_Oliftn(V_n,V_t,V_k),V_k).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)!=c_HOL_Ozero__class_Ozero(T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)!=c_HOL_Ozero__class_Ozero(T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,V_y,T_a)=V_y| -c_lesse_quals(V_x,V_y,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,V_y,T_a)!=V_y|c_lesse_quals(V_x,V_y,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,V_y,T_a)=V_x| -c_lesse_quals(V_y,V_x,T_a).
% 223.84/223.92  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)),V_z).
% 223.84/223.92  0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_k)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)).
% 223.84/223.92  0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)).
% 223.84/223.92  0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)).
% 223.84/223.92  0 [] -class_OrderedGroup_Oab__semigroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)).
% 223.84/223.92  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_d).
% 223.84/223.92  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_b).
% 223.84/223.92  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_d)).
% 223.84/223.92  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat).
% 223.84/223.92  0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_u)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)=V_u.
% 223.84/223.92  0 [] c_lesse_quals(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_j),tc_nat)| -c_lesse_quals(V_i,V_j,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_m),tc_nat)| -c_lesse_quals(V_i,V_j,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(V_k,V_n,tc_nat)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),V_n,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(V_m,V_n,tc_nat)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),V_n,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat)| -c_lesse_quals(V_x,V_z,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat)| -c_lesse_quals(V_x,V_y,tc_nat).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)=c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(V_x,V_z,T_a),c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a).
% 223.84/223.92  0 [] c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T,V_e,V_t,V_ts))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  0 [] hBOOL(hAPP(V_P,V_n))|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(V_P),tc_nat)| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|c_Lambda_Osubst(c_Lambda_OdB_OVar(V_x),V_s,V_x)=V_s.
% 223.84/223.92  0 [] c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a)=V_a.
% 223.84/223.92  0 [] hBOOL(hAPP(V_P,V_T))| -hBOOL(hAPP(V_P,c_Type_Osko__Type__Xtype__induct__1__1(V_P))).
% 223.84/223.92  0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.92  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,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),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).
% 223.84/223.92  0 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat)| -c_lesse_quals(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(V_m,V_l,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_l,tc_nat),tc_nat)| -c_lesse_quals(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)| -c_lesse_quals(V_m,V_n,tc_nat)| -c_lesse_quals(V_k,V_n,tc_nat)| -c_lesse_quals(V_k,V_m,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(V_m,V_n,tc_nat)| -c_lesse_quals(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)| -c_lesse_quals(V_k,V_n,tc_nat)| -c_lesse_quals(V_k,V_m,tc_nat).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat)=c_HOL_Ominus__class_Ominus(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)|V_xa=V_y.
% 223.84/223.92  0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|V_x_H=V_y_H.
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat)!=c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat)| -c_lesse_quals(V_k,V_n,tc_nat)| -c_lesse_quals(V_k,V_m,tc_nat)|V_m=V_n.
% 223.84/223.92  0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat).
% 223.84/223.92  0 [] c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(V_dB2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_x,V_a,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_x,V_b,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)| -c_HOL_Oord__class_Oless(V_z,V_x,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)| -c_HOL_Oord__class_Oless(V_z,V_y,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_z,T_a)| -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_z,T_a)| -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a).
% 223.84/223.92  0 [] c_Lambda_OdB_OAbs(V_r)=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 223.84/223.92  0 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat).
% 223.84/223.92  0 [] c_Lambda_OdB_OAbs(V_r)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|c_Lambda_OdB_OAbs(V_r)=V_s.
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),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).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)| -c_lesse_quals(V_k,V_n,tc_nat)| -c_lesse_quals(V_k,V_m,tc_nat).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat).
% 223.84/223.92  0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_a,V_xs,T_a,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a)).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),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).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_c,tc_nat),c_HOL_Ominus__class_Ominus(V_b,V_c,tc_nat),tc_nat)| -c_lesse_quals(V_c,V_a,tc_nat)| -c_HOL_Oord__class_Oless(V_a,V_b,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat)|c_Suc(V_m)=V_n| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] -c_lesse_quals(V_m,V_n,tc_nat)| -c_lesse_quals(c_Suc(V_n),V_m,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(c_Suc(V_n),V_m,tc_nat)|c_lesse_quals(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_y)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)|V_y=V_z.
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)|V_m=V_n.
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n)|V_m=V_n.
% 223.84/223.92  0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)|V_y=V_z.
% 223.84/223.92  0 [] -class_OrderedGroup_Ocancel__ab__semigroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)|V_b=V_c.
% 223.84/223.92  0 [] -class_OrderedGroup_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)|V_b=V_c.
% 223.84/223.92  0 [] -class_OrderedGroup_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)|V_b=V_c.
% 223.84/223.92  0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(V_r)|V_ss=c_List_Olist_ONil(tc_Lambda_OdB).
% 223.84/223.92  0 [] c_lesse_quals(V_m,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_k,tc_nat),tc_nat)| -c_lesse_quals(V_k,V_n,tc_nat).
% 223.84/223.92  0 [] hAPP(hAPP(V_pwr,hAPP(hAPP(V_mul,V_x),V_y)),V_q)=hAPP(hAPP(V_mul,hAPP(hAPP(V_pwr,V_x),V_q)),hAPP(hAPP(V_pwr,V_y),V_q))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_add,V_y),V_z))=hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_x),V_y)),hAPP(hAPP(V_mul,V_x),V_z))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,V_x),V_y)=hAPP(hAPP(V_mul,V_y),V_x)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_mul,V_y),V_z))=hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_x),V_y)),V_z)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,V_r1),V_x)=V_x| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,V_r0),V_x)=V_r0| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_add,V_x),V_y)=hAPP(hAPP(V_add,V_y),V_x)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_add,V_x),hAPP(hAPP(V_add,V_y),V_z))=hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_x),V_y)),V_z)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_add,V_r0),V_x)=V_x| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_c),V_d))=hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),V_d)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_add,V_a),V_c)=hAPP(hAPP(V_add,V_c),V_a)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),V_c)=hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),V_b)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_c),V_d))=hAPP(hAPP(V_add,V_c),hAPP(hAPP(V_add,V_a),V_d))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),V_c)=hAPP(hAPP(V_add,V_a),hAPP(hAPP(V_add,V_b),V_c))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_b)),hAPP(hAPP(V_add,V_c),V_d))=hAPP(hAPP(V_add,hAPP(hAPP(V_add,V_a),V_c)),hAPP(hAPP(V_add,V_b),V_d))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] c_Suc(V_x)!=c_Suc(V_y)|V_x=V_y.
% 223.84/223.92  0 [] c_Suc(V_nat)!=c_Suc(V_nat_H)|V_nat=V_nat_H.
% 223.84/223.92  0 [] -class_OrderedGroup_Oab__semigroup__add(T_a)|c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,V_a,T_a,T_a)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_a,V_xs,T_a,T_a).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 223.84/223.92  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_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).
% 223.84/223.92  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(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 223.84/223.92  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(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_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).
% 223.84/223.92  0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.92  0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Omonoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_zs,T_a,T_a))=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_x,V_zs,T_a,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_y,V_z,T_a)| -c_lesse_quals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_x,V_z,T_a)| -c_lesse_quals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)| -c_lesse_quals(V_z,V_y,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)| -c_lesse_quals(V_z,V_x,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)| -c_lesse_quals(V_x,V_b,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)| -c_lesse_quals(V_x,V_a,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_b,V_x,T_a)| -c_lesse_quals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_a,V_x,T_a)| -c_lesse_quals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a).
% 223.84/223.92  0 [] c_lesse_quals(V_j,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),tc_nat)| -c_lesse_quals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),V_i,tc_nat)| -c_lesse_quals(V_j,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),tc_nat).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_z,V_y,T_a)|c_HOL_Oord__class_Oless(V_z,V_x,T_a)| -c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a).
% 223.84/223.92  0 [] c_InductTermi_OIT(c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r)),V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))| -c_InductTermi_OIT(V_s)| -c_InductTermi_OIT(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_r,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)).
% 223.84/223.92  0 [] c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b)=V_a.
% 223.84/223.92  0 [] c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_i),V_s,V_k)=c_Lambda_OdB_OVar(V_i)|V_i=V_k|c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 223.84/223.92  0 [] c_InductTermi_OIT(v_s____).
% 223.84/223.92  0 [] c_Lambda_OdB_OAbs(V_dB)!=c_Lambda_OdB_OAbs(V_dB_H)|V_dB=V_dB_H.
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),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).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 223.84/223.92  0 [] V_m=V_n|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat).
% 223.84/223.92  0 [] V_m=V_n| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat).
% 223.84/223.92  0 [] V_n=V_m| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat).
% 223.84/223.92  0 [] c_Lambda_OdB_OAbs(V_r)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_ss=c_List_Olist_ONil(tc_Lambda_OdB).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat))| -c_lesse_quals(V_k,V_j,tc_nat).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_k,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),V_i)| -c_lesse_quals(V_k,V_j,tc_nat).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat)| -c_lesse_quals(V_k,V_j,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_j,V_k,tc_nat).
% 223.84/223.92  0 [] c_Type_Otype_Otype__rec(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),T_a)=hAPP(V_f1,V_nat).
% 223.84/223.92  0 [] c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB))| -c_Lambda_Obeta(V_r,V_s).
% 223.84/223.92  0 [] c_List_Olist_ONil(T_a)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a).
% 223.84/223.92  0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.92  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).
% 223.84/223.92  0 [] -c_HOL_Oord__class_Oless(V_x,V_x,tc_nat).
% 223.84/223.92  0 [] -c_HOL_Oord__class_Oless(V_n,V_n,tc_nat).
% 223.84/223.92  0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 223.84/223.92  0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 223.84/223.92  0 [] -c_lesse_quals(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_i),tc_nat)|c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_i),V_i,tc_nat)=V_k.
% 223.84/223.92  0 [] c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k)=c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_n))|c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 223.84/223.92  0 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t),c_Lambda_Osubst(V_s,V_t,c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),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).
% 223.84/223.92  0 [] c_lesse_quals(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(V_m,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_x),tc_nat).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat)),V_m)=c_Orderings_Oord__class_Omax(V_n,V_m,tc_nat).
% 223.84/223.92  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.
% 223.84/223.92  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).
% 223.84/223.92  0 [] V_m=V_n| -c_lesse_quals(V_n,V_m,tc_nat)| -c_lesse_quals(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)|V_m=V_n.
% 223.84/223.92  0 [] hBOOL(hAPP(hAPP(V_P,V_n),V_m))|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)|V_m=V_n|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_y,V_x,tc_nat)|c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)|V_x=V_y.
% 223.84/223.92  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).
% 223.84/223.92  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.
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,V_x,T_a)=V_x.
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)| -c_HOL_Oord__class_Oless(V_c,V_d,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_l),tc_nat)| -c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(V_x,V_y,tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_y,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_rs=V_ss.
% 223.84/223.92  0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_r=V_s.
% 223.84/223.92  0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(V_r)|V_s=c_Lambda_OdB_OAbs(V_r).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(V_m,c_Suc(c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),tc_nat)=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),c_Suc(V_j),tc_nat)| -c_lesse_quals(V_k,V_j,tc_nat).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 223.84/223.92  0 [] c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat)| -c_lesse_quals(V_i,V_j,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(V_m,V_n,tc_nat)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat)| -c_lesse_quals(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)|hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s)=V_t.
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_rx),V_ry))=hAPP(hAPP(V_mul,V_rx),hAPP(hAPP(V_mul,V_lx),V_ry))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_rx),V_ry))=hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),V_ry)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_rx)=hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_ly),V_rx))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_rx)=hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),V_ly)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry))=hAPP(hAPP(V_mul,V_rx),hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),V_ry))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry))=hAPP(hAPP(V_mul,V_lx),hAPP(hAPP(V_mul,V_ly),hAPP(hAPP(V_mul,V_rx),V_ry)))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_ly)),hAPP(hAPP(V_mul,V_rx),V_ry))=hAPP(hAPP(V_mul,hAPP(hAPP(V_mul,V_lx),V_rx)),hAPP(hAPP(V_mul,V_ly),V_ry))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,V_a),V_r1)=V_a| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,V_r1),V_a)=V_a| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,V_a),V_r0)=V_r0| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,V_r0),V_a)=V_r0| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_b)),V_c)=hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_c)),hAPP(hAPP(V_mul,V_b),V_c))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,V_a),V_b)=hAPP(hAPP(V_mul,V_b),V_a)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_add,V_a),V_r0)=V_a| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_add,V_r0),V_a)=V_a| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_add,V_m),V_m)=hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_r1),V_r1)),V_m)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_add,V_m),hAPP(hAPP(V_mul,V_a),V_m))=hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_r1)),V_m)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_m)),V_m)=hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_r1)),V_m)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_add,hAPP(hAPP(V_mul,V_a),V_m)),hAPP(hAPP(V_mul,V_b),V_m))=hAPP(hAPP(V_mul,hAPP(hAPP(V_add,V_a),V_b)),V_m)| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] -hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_xc),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f1,V_xc))).
% 223.84/223.92  0 [] -hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f1,V_nat))).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat),c_Suc(V_k),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat).
% 223.84/223.92  0 [] c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))| -c_InductTermi_OIT(V_r).
% 223.84/223.92  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d)).
% 223.84/223.92  0 [] c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(V_dB),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,V_y,T_a)=c_Orderings_Oord__class_Omax(V_y,V_x,T_a).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_Power_Opower__class_Opower(V_a,V_n,T_a)!=c_Power_Opower__class_Opower(V_b,V_n,T_a)|V_a=V_b| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -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).
% 223.84/223.92  0 [] c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k)=c_Lambda_OdB_OVar(V_i)| -c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(c_Suc(V_n),c_Suc(V_n),tc_nat).
% 223.84/223.92  0 [] c_List_Odrop(V_i,c_List_Oreplicate(V_k,V_x,T_a),T_a)=c_List_Oreplicate(c_HOL_Ominus__class_Ominus(V_k,V_i,tc_nat),V_x,T_a).
% 223.84/223.92  0 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a)=c_List_Olist_ONil(T_a).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(V_n,c_HOL_Ominus__class_Ominus(V_n,V_i,tc_nat),tc_nat)=V_i| -c_lesse_quals(V_i,V_n,tc_nat).
% 223.84/223.92  0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OAbs(V_r).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_x),V_s,V_x)=c_Lambda_Oliftn(V_x,V_s,c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.92  0 [] V_m=c_Suc(V_n)|c_lesse_quals(V_m,V_n,tc_nat)| -c_lesse_quals(V_m,c_Suc(V_n),tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat).
% 223.84/223.92  0 [] -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Orderings_Oord__class_Omax(V_x,V_y,T_a)),V_z)=c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z),T_a).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a)!=c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a)|V_a=V_b| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)=c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a)=c_Orderings_Oord__class_Omax(V_y,c_Orderings_Oord__class_Omax(V_x,V_z,T_a),T_a).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a).
% 223.84/223.92  0 [] c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t))| -c_Lambda_Obeta(V_s,V_t).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)=c_Orderings_Oord__class_Omax(V_x,V_y,T_a).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_n,tc_nat)=V_m.
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_n,tc_nat)=V_m.
% 223.84/223.92  0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_b,T_a)=V_a.
% 223.84/223.92  0 [] c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),T_a)=hAPP(V_f1,V_nat).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)| -c_HOL_Oord__class_Oless(V_c,V_d,T_a)| -c_lesse_quals(V_a,V_b,T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)| -c_lesse_quals(V_c,V_d,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_n,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat).
% 223.84/223.92  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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 223.84/223.92  0 [] V_T=hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(V_T,V_e,V_t)),c_Type_Osko__Type__Xtyping__elims__3__2(V_T,V_e,V_t))| -c_Type_Otyping(V_e,c_Lambda_OdB_OAbs(V_t),V_T).
% 223.84/223.92  0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,V_n,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oring__1__no__zero__divisors(T_a)|c_Power_Opower__class_Opower(V_a,V_n,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a.
% 223.84/223.92  0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|V_x!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_x=V_y.
% 223.84/223.92  0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=V_b.
% 223.84/223.92  0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=V_b.
% 223.84/223.92  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x)=V_x.
% 223.84/223.92  0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 223.84/223.92  0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|V_x=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Ozero__class_Ozero(T_a)).
% 223.84/223.92  0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))=V_a.
% 223.84/223.92  0 [] -class_OrderedGroup_Omonoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 223.84/223.92  0 [] -class_OrderedGroup_Omonoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))=V_a.
% 223.84/223.92  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))=V_a.
% 223.84/223.92  0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 223.84/223.92  0 [] c_lesse_quals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 223.84/223.92  0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 223.84/223.92  0 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k)=V_t.
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] c_Suc(V_m)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] c_Suc(V_nat_H)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=V_n.
% 223.84/223.92  0 [] V_n=c_HOL_Ozero__class_Ozero(tc_nat)| -c_lesse_quals(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=V_m.
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] V_x!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_a)|V_a=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=V_m|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_m).
% 223.84/223.92  0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_nat_H).
% 223.84/223.92  0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_xs,T_a,T_a)=c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a).
% 223.84/223.92  0 [] -c_lesse_quals(V_i,V_j,tc_nat)|V_j=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_j,V_i,tc_nat)),V_i).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat))=V_m| -c_lesse_quals(V_n,V_m,tc_nat).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)),V_n)=V_m| -c_lesse_quals(V_n,V_m,tc_nat).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_pwr,V_x),V_q))=hAPP(hAPP(V_pwr,V_x),c_Suc(V_q))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_mul,hAPP(hAPP(V_pwr,V_x),V_q)),V_x)=hAPP(hAPP(V_pwr,V_x),c_Suc(V_q))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_pwr,V_x),c_Suc(V_q))=hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_pwr,V_x),V_q))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(V_pwr,V_x),c_Suc(V_n))=hAPP(hAPP(V_mul,V_x),hAPP(hAPP(V_pwr,V_x),V_n))| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat))=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat)| -c_lesse_quals(V_k,V_j,tc_nat).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat)),V_i)=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_k,tc_nat)| -c_lesse_quals(V_k,V_j,tc_nat).
% 223.84/223.92  0 [] c_List_Odrop(V_n,c_List_Odrop(V_m,V_xs,T_a),T_a)=c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_xs,T_a).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_lesse_quals(c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a),T_a).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 223.84/223.92  0 [] c_List_Oreplicate(V_n,V_x,T_a)!=c_List_Olist_ONil(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a)=hAPP(hAPP(V_f3,V_dB),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB,T_a)).
% 223.84/223.92  0 [] c_List_Olist_ONil(T_a)!=c_List_Oreplicate(V_n,V_x,T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(V_m,V_n,tc_nat)| -c_lesse_quals(c_Suc(V_m),V_n,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(V_m,c_Suc(V_n),tc_nat)| -c_lesse_quals(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 223.84/223.92  0 [] -c_lesse_quals(c_Suc(V_n),V_n,tc_nat).
% 223.84/223.92  0 [] c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubst(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)| -c_lesse_quals(V_k,V_n,tc_nat)| -c_lesse_quals(V_k,V_m,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_k,tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_k,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_lesse_quals(V_k,V_n,tc_nat)| -c_lesse_quals(V_k,V_m,tc_nat).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),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).
% 223.84/223.92  0 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(V_j),V_u,V_i)=c_Lambda_OdB_OVar(V_j)| -c_HOL_Oord__class_Oless(V_j,V_i,tc_nat).
% 223.84/223.92  0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f3,V_dB))).
% 223.84/223.92  0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_xa),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f3,V_xa))).
% 223.84/223.92  0 [] c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j))| -c_InductTermi_OIT(V_r).
% 223.84/223.92  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 223.84/223.92  0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat).
% 223.84/223.92  0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat).
% 223.84/223.92  0 [] -class_Ring__and__Field_Oring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a)=c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)| -c_lesse_quals(V_n,V_m,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat)| -c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat).
% 223.84/223.92  0 [] c_Suc(V_n)!=V_n.
% 223.84/223.92  0 [] V_n!=c_Suc(V_n).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 223.84/223.92  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(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 223.84/223.92  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(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_lesse_quals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 223.84/223.92  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).
% 223.84/223.92  0 [] c_lesse_quals(V_n,V_n,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(V_i,V_k,tc_nat)| -c_lesse_quals(V_j,V_k,tc_nat)| -c_lesse_quals(V_i,V_j,tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(V_x,V_x,tc_nat).
% 223.84/223.92  0 [] -class_Orderings_Oorder(T_a)|c_lesse_quals(V_x,V_x,T_a).
% 223.84/223.92  0 [] -class_Orderings_Opreorder(T_a)|c_lesse_quals(V_x,V_x,T_a).
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_lesse_quals(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)| -c_lesse_quals(V_c,V_d,T_a)| -c_lesse_quals(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a).
% 223.84/223.92  0 [] hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat)))| -c_HOL_Oord__class_Oless(V_a,V_b,tc_nat)| -hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(V_a,V_b,tc_nat))).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.92  0 [] V_n=V_m| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)| -c_lesse_quals(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))=V_n| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 223.84/223.92  0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|c_lesse_quals(V_y_H,V_x_H,T_a)| -c_lesse_quals(V_y,V_x,T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|c_lesse_quals(V_y,V_x,T_a)| -c_lesse_quals(V_y_H,V_x_H,T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 223.84/223.92  0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)| -c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat))=V_m|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_n,c_Suc(V_i),tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 223.84/223.92  0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  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).
% 223.84/223.92  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.
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)|V_m=V_n| -c_lesse_quals(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] V_m=V_n|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_lesse_quals(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)|V_m=V_n| -c_lesse_quals(V_m,V_n,tc_nat).
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  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.
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  0 [] c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB1)),c_Lambda_OdB_OdB__size(V_dB2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.92  0 [] c_lesse_quals(V_n,V_m,tc_nat)| -c_lesse_quals(c_Suc(V_n),c_Suc(V_m),tc_nat).
% 223.84/223.92  0 [] c_lesse_quals(c_Suc(V_n),c_Suc(V_m),tc_nat)| -c_lesse_quals(V_n,V_m,tc_nat).
% 223.84/223.92  0 [] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(V_dB))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  0 [] c_lesse_quals(V_n,V_m,tc_nat)|c_lesse_quals(V_m,V_n,tc_nat).
% 223.84/223.92  0 [] -class_Orderings_Olinorder(T_a)|c_lesse_quals(V_y,V_x,T_a)|c_lesse_quals(V_x,V_y,T_a).
% 223.84/223.92  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).
% 223.84/223.92  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).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] hBOOL(hAPP(V_P,V_nat))|hBOOL(hAPP(V_P,v_sko__Nat__Xnat__Xinduct__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.92  0 [] -c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 223.84/223.92  0 [] -c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 223.84/223.92  0 [] c_Orderings_Obot__class_Obot(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] hBOOL(hAPP(V_P,V_nat))|hBOOL(hAPP(V_P,v_sko__List__Xupt__Xinduct__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.92  0 [] c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),V_xs,T_a)=V_xs.
% 223.84/223.92  0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] hBOOL(hAPP(V_P,V_n))| -hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.92  0 [] c_lesse_quals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 223.84/223.92  0 [] c_Nat_Osize__class_Osize(V_c,tc_String_Ochar)=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a).
% 223.84/223.92  0 [] c_Orderings_Oord__class_Omax(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=V_n.
% 223.84/223.92  0 [] c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=V_n.
% 223.84/223.92  0 [] c_List_Oreplicate(V_m,V_x,T_a)!=c_List_Oreplicate(V_n,V_y,T_a)|V_x=V_y|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] V_x=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)=V_n.
% 223.84/223.92  0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat))=V_m.
% 223.84/223.92  0 [] hAPP(hAPP(V_pwr,V_x),c_HOL_Ozero__class_Ozero(tc_nat))=V_r1| -c_Groebner__Basis_Ogb__semiring(V_add,V_mul,V_pwr,V_r0,V_r1,T_a).
% 223.84/223.92  0 [] c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_t,V_s,V_k)),c_Lambda_Osubst(V_u,V_s,V_k)).
% 223.84/223.92  0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=c_Lambda_OdB_OAbs(V_dB_H).
% 223.84/223.92  0 [] c_Lambda_OdB_OAbs(V_dB_H)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2).
% 223.84/223.92  0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_xb),V_xc),t_a)))|hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_xb),V_xc))).
% 223.84/223.92  0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),t_a)))|hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_dB1),V_dB2))).
% 223.84/223.92  0 [] c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a)=hAPP(hAPP(V_f2,V_dB1),V_dB2).
% 223.84/223.92  0 [] c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a)=hAPP(hAPP(hAPP(hAPP(V_f2,V_dB1),V_dB2),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB1,T_a)),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB2,T_a)).
% 223.84/223.92  0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)|V_r=V_s.
% 223.84/223.92  0 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_s),hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_t))| -c_Lambda_Obeta(V_s,V_t).
% 223.84/223.92  0 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_u),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u))| -c_Lambda_Obeta(V_s,V_t).
% 223.84/223.92  0 [] c_Lambda_Oliftn(V_n,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(V_n,V_s,V_k)),c_Lambda_Oliftn(V_n,V_t,V_k)).
% 223.84/223.92  0 [] c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(V_t,V_s,V_k)),c_Lambda_Osubstn(V_u,V_s,V_k)).
% 223.84/223.92  0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB).
% 223.84/223.92  0 [] c_Lambda_OdB_OVar(V_m)=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 223.84/223.92  0 [] c_Lambda_OdB_OVar(V_m)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_ss=c_List_Olist_ONil(tc_Lambda_OdB).
% 223.84/223.92  0 [] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB).
% 223.84/223.92  0 [] c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T,V_e,V_i,V_ts))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 223.84/223.92  0 [] c_Type_Otypings(V_e,V_us,c_Type_Osko__Type__Xvar__app__types__1__1(V_T,V_U,V_e,V_us))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_U)| -c_Type_Otypings(V_e,V_ts,V_Ts)| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_us,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 223.84/223.92  0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OVar(V_nat).
% 223.84/223.92  0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_xd),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f1,V_xd))).
% 223.84/223.92  0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f1,V_nat))).
% 223.84/223.92  0 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k)=V_u.
% 223.84/223.92  0 [] -c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t).
% 223.84/223.92  0 [] c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a)=hAPP(V_f1,V_nat).
% 223.84/223.92  0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OAbs(V_dB_H).
% 223.84/223.92  0 [] c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)).
% 223.84/223.92  0 [] c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a)=hAPP(V_f1,V_nat).
% 223.84/223.92  0 [] V_U=c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(V_T,V_U,V_e,V_us),V_T,tc_Type_Otype,tc_Type_Otype)| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_U)| -c_Type_Otypings(V_e,V_ts,V_Ts)| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_us,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 223.84/223.92  0 [] c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 223.84/223.92  0 [] c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T)| -c_Type_Otypings(V_e,V_ts,V_Ts)| -c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,V_T,tc_Type_Otype,tc_Type_Otype)).
% 223.84/223.92  0 [] c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 223.84/223.92  0 [] c_Type_Otyping(V_e,V_t_H,V_T)| -c_Lambda_Obeta(V_t,V_t_H)| -c_Type_Otyping(V_e,V_t,V_T).
% 223.84/223.92  0 [] hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)!=c_Type_Otype_OAtom(V_nat).
% 223.84/223.92  0 [] c_Type_Osko__Type__Xtype__induct__1__1(V_P)!=hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2)|hBOOL(hAPP(V_P,V_T))|hBOOL(hAPP(V_P,V_T2)).
% 223.84/223.92  0 [] c_Type_Osko__Type__Xtype__induct__1__1(V_P)!=hAPP(hAPP(c_Type_Otype_OFun,V_T1a),V_x)|hBOOL(hAPP(V_P,V_T))|hBOOL(hAPP(V_P,V_T1a)).
% 223.84/223.92  0 [] c_Type_Otype_Otype__rec(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),T_a)=hAPP(hAPP(hAPP(hAPP(V_f2,V_type1),V_type2),c_Type_Otype_Otype__rec(V_f1,V_f2,V_type1,T_a)),c_Type_Otype_Otype__rec(V_f1,V_f2,V_type2,T_a)).
% 223.84/223.92  0 [] c_Type_Otype_Otype__case(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),T_a)=hAPP(hAPP(V_f2,V_type1),V_type2).
% 223.84/223.92  0 [] -hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_xa),V_xb),t_a)))|hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_xa),V_xb))).
% 223.84/223.92  0 [] -hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),t_a)))|hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_type1),V_type2))).
% 223.84/223.92  0 [] c_Type_Otype_OAtom(V_nat)!=hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H).
% 223.84/223.92  0 [] c_Type_Otyping(c_Type_Oshift(V_e,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(V_e,V_t),tc_Type_Otype),V_t,c_Type_Osko__Type__Xabs__typeE__1__2(V_e,V_t))| -c_Type_Otyping(V_e,c_Lambda_OdB_OAbs(V_t),V_T).
% 223.84/223.92  0 [] c_Type_Otyping(c_Type_Oshift(V_e,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(V_T,V_e,V_t),tc_Type_Otype),V_t,c_Type_Osko__Type__Xtyping__elims__3__2(V_T,V_e,V_t))| -c_Type_Otyping(V_e,c_Lambda_OdB_OAbs(V_t),V_T).
% 223.84/223.92  0 [] c_InductTermi_OIT(c_Lambda_Olift(V_t,V_i))| -c_InductTermi_OIT(V_t).
% 223.84/223.92  0 [] c_Lambda_Osubst(c_Lambda_Olift(V_t,V_k),V_s,V_k)=V_t.
% 223.84/223.92  0 [] c_Lambda_Obeta(c_Lambda_Olift(V_r,V_i),c_Lambda_Olift(V_s,V_i))| -c_Lambda_Obeta(V_r,V_s).
% 223.84/223.92  0 [] hAPP(c_Type_Oshift(V_e,V_i,V_T,T_a),V_j)=hAPP(V_e,V_j)| -c_HOL_Oord__class_Oless(V_j,V_i,tc_nat).
% 223.84/223.92  0 [] c_InductTermi_OIT(c_Lambda_Osubst(V_t,V_u,V_i))| -c_Type_Otyping(V_e,V_u,V_U)| -c_InductTermi_OIT(V_u)| -c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),V_t,V_T)| -c_InductTermi_OIT(V_t).
% 223.84/223.92  0 [] c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T,V_e,V_i,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 223.84/223.92  0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a)=c_HOL_Ozero__class_Ozero(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a)=c_HOL_Ozero__class_Ozero(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a)!=c_HOL_Ozero__class_Ozero(T_a).
% 223.84/223.92  0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 223.84/223.92  0 [] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(V_nat),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(V_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.92  0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_m=V_n.
% 223.84/223.92  0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_rs=V_ss.
% 223.84/223.92  0 [] c_Lambda_OdB_OVar(V_m)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|c_Lambda_OdB_OVar(V_m)=V_s.
% 223.84/223.92  0 [] c_InductTermi_OIT(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),c_Lambda_OdB_OVar(V_i)))| -c_InductTermi_OIT(V_t).
% 223.84/223.92  0 [] c_InductTermi_OIT(v_ta____).
% 223.84/223.92  0 [] c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u))| -c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T).
% 223.84/223.92  0 [] c_Type_Oshift(c_Type_Oshift(V_e,V_i,V_U,T_a),c_HOL_Ozero__class_Ozero(tc_nat),V_T,T_a)=c_Type_Oshift(c_Type_Oshift(V_e,c_HOL_Ozero__class_Ozero(tc_nat),V_T,T_a),c_Suc(V_i),V_U,T_a).
% 223.84/223.92  0 [] c_Lambda_Olift(c_Lambda_OdB_OVar(V_i),V_k)=c_Lambda_OdB_OVar(V_i)| -c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 223.84/223.92  0 [] -c_Type_Otyping(V_e_H,V_u,V_U)| -c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)|c_Type_Otyping(V_e_H,c_Lambda_Osubst(V_t,V_u,V_i),V_T).
% 223.84/223.92  0 [] V_T=V_U| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_U)| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 223.84/223.92  0 [] c_Type_Otyping(V_e,V_t,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)),V_T))| -c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T).
% 223.84/223.92  0 [] c_Type_Otyping(V_env,c_Lambda_OdB_OAbs(V_t),hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))| -c_Type_Otyping(c_Type_Oshift(V_env,c_HOL_Ozero__class_Ozero(tc_nat),V_T,tc_Type_Otype),V_t,V_U).
% 223.84/223.92  0 [] c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)).
% 223.84/223.92  0 [] c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_Lambda_Olift(V_t,V_i),V_T)| -c_Type_Otyping(V_e,V_t,V_T).
% 223.84/223.92  0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OVar(V_nat_H)|V_nat=V_nat_H.
% 223.84/223.92  0 [] hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2)!=hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)|V_type1=V_type1_H.
% 223.84/223.92  0 [] hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2)!=hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)|V_type2=V_type2_H.
% 223.84/223.92  0 [] c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U)| -c_Type_Otyping(V_env,V_t,V_T)| -c_Type_Otyping(V_env,V_s,hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U)).
% 223.84/223.92  0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)|V_dB1=V_dB1_H.
% 223.84/223.92  0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)|V_dB2=V_dB2_H.
% 223.84/223.92  0 [] c_Lambda_OdB_OVar(V_nat)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H).
% 223.84/223.92  0 [] hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x)=V_T.
% 223.84/223.92  0 [] hAPP(V_e,V_i)=V_T| -c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T).
% 223.84/223.92  0 [] c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(V_s,V_k)),c_Lambda_Olift(V_t,V_k)).
% 223.84/223.92  0 [] c_Type_Otyping(v_ea____,v_ta____,v_Ta____).
% 223.84/223.92  0 [] c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)).
% 223.84/223.92  0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)!=c_Lambda_OdB_OVar(V_nat).
% 223.84/223.92  0 [] c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_Ta____).
% 223.84/223.92  0 [] c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)).
% 223.84/223.92  0 [] -c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_U____).
% 223.84/223.92  0 [] class_Orderings_Opreorder(tc_fun(T_2,T_1))| -class_Orderings_Opreorder(T_1).
% 223.84/223.92  0 [] class_Orderings_Oorder(tc_fun(T_2,T_1))| -class_Orderings_Oorder(T_1).
% 223.84/223.92  0 [] class_Orderings_Obot(tc_fun(T_2,T_1))| -class_Orderings_Obot(T_1).
% 223.84/223.92  0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 223.84/223.92  0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 223.84/223.92  0 [] class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat).
% 223.84/223.92  0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 223.84/223.92  0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 223.84/223.92  0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 223.84/223.92  0 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 223.84/223.92  0 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 223.84/223.92  0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 223.84/223.92  0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 223.84/223.92  0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 223.84/223.92  0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 223.84/223.92  0 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 223.84/223.92  0 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 223.84/223.92  0 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 223.84/223.92  0 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 223.84/223.92  0 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 223.84/223.92  0 [] class_Nat_Osemiring__char__0(tc_nat).
% 223.84/223.92  0 [] class_Orderings_Opreorder(tc_nat).
% 223.84/223.92  0 [] class_Orderings_Olinorder(tc_nat).
% 223.84/223.92  0 [] class_Orderings_Oorder(tc_nat).
% 223.84/223.92  0 [] class_Orderings_Obot(tc_nat).
% 223.84/223.92  0 [] class_Power_Opower(tc_nat).
% 223.84/223.92  0 [] c_fe_qual(V_x,V_x,T_a).
% 223.84/223.92  0 [] V_X=V_Y| -c_fe_qual(V_X,V_Y,T_a).
% 223.84/223.92  end_of_list.
% 223.84/223.92  
% 223.84/223.92  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 223.84/223.92  
% 223.84/223.92  This ia a non-Horn set with equality.  The strategy will be
% 223.84/223.92  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 223.84/223.92  deletion, with positive clauses in sos and nonpositive
% 223.84/223.92  clauses in usable.
% 223.84/223.92  
% 223.84/223.92     dependent: set(knuth_bendix).
% 223.84/223.92     dependent: set(anl_eq).
% 223.84/223.92     dependent: set(para_from).
% 223.84/223.92     dependent: set(para_into).
% 223.84/223.92     dependent: clear(para_from_right).
% 223.84/223.92     dependent: clear(para_into_right).
% 223.84/223.92     dependent: set(para_from_vars).
% 223.84/223.92     dependent: set(eq_units_both_ways).
% 223.84/223.92     dependent: set(dynamic_demod_all).
% 223.84/223.92     dependent: set(dynamic_demod).
% 223.84/223.92     dependent: set(order_eq).
% 223.84/223.92     dependent: set(back_demod).
% 223.84/223.92     dependent: set(lrpo).
% 223.84/223.92     dependent: set(hyper_res).
% 223.84/223.92     dependent: set(unit_deletion).
% 223.84/223.92     dependent: set(factor).
% 223.84/223.92  
% 223.84/223.92  ------------> process usable:
% 223.84/223.92  ** KEPT (pick-wt=14): 1 [] -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).
% 223.84/223.92  ** KEPT (pick-wt=14): 2 [] -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).
% 223.84/223.92  ** KEPT (pick-wt=22): 3 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 223.84/223.92  ** KEPT (pick-wt=19): 5 [copy,4,factor_simp] -class_OrderedGroup_Opordered__comm__monoid__add(A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 223.84/223.92  ** KEPT (pick-wt=9): 6 [] -c_lesse_quals(A,A,tc_nat)|c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=9): 7 [] c_lesse_quals(A,B,tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=9): 8 [] c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)| -c_lesse_quals(A,B,tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=24): 9 [] -class_OrderedGroup_Opordered__ab__semigroup__add(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A)| -c_lesse_quals(C,E,A)| -c_lesse_quals(B,D,A).
% 223.84/223.92  ** KEPT (pick-wt=22): 10 [] c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat)| -c_lesse_quals(B,D,tc_nat)| -c_lesse_quals(A,C,tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=16): 11 [] -hBOOL(hAPP(A,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),B,tc_nat)))|hBOOL(hAPP(A,C)).
% 223.84/223.92    Following clause subsumed by 11 during input processing: 0 [] -hBOOL(hAPP(A,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),B,tc_nat)))|hBOOL(hAPP(A,C)).
% 223.84/223.92  ** KEPT (pick-wt=13): 12 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ominus__class_Ominus(B,C,A)),C)=B.
% 223.84/223.92  ** KEPT (pick-wt=17): 13 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 223.84/223.92  ** KEPT (pick-wt=17): 14 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A).
% 223.84/223.92  ** KEPT (pick-wt=10): 15 [] A=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=12): 16 [] c_Lambda_Obeta(c_Lambda_Osubst(A,B,C),c_Lambda_Osubst(D,B,C))| -c_Lambda_Obeta(A,D).
% 223.84/223.92  ** KEPT (pick-wt=14): 17 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A)| -c_lesse_quals(B,C,tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=14): 18 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(B,C,tc_nat)| -c_lesse_quals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A).
% 223.84/223.92  ** KEPT (pick-wt=18): 19 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_lesse_quals(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=22): 20 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)| -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_lesse_quals(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 223.84/223.92  ** KEPT (pick-wt=12): 21 [] c_List_Oreplicate(A,B,C)!=c_List_Oreplicate(D,E,C)|A=D.
% 223.84/223.92  ** KEPT (pick-wt=23): 22 [] c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(A,B,tc_nat)),C,tc_nat)=c_HOL_Ominus__class_Ominus(c_Suc(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_lesse_quals(B,A,tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=17): 23 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,C,A),D,A)| -c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 223.84/223.92  ** KEPT (pick-wt=11): 24 [] c_HOL_Ominus__class_Ominus(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_lesse_quals(A,B,tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=11): 25 [] c_HOL_Ominus__class_Ominus(A,B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_lesse_quals(A,B,tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=15): 26 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 223.84/223.92  ** KEPT (pick-wt=15): 27 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Suc(v_sko__Nat__Xnat__Xinduct__1(A))))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.92  ** KEPT (pick-wt=13): 28 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Suc(B),A)=c_HOL_Ozero__class_Ozero(A).
% 223.84/223.92  ** KEPT (pick-wt=14): 30 [copy,29,factor_simp] hBOOL(hAPP(A,B))| -c_HOL_Oord__class_Oless(B,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(A),tc_nat)| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.92  ** KEPT (pick-wt=20): 31 [] c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat)| -c_lesse_quals(A,c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat)| -c_lesse_quals(B,C,tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=20): 32 [] c_lesse_quals(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat)| -c_lesse_quals(C,B,tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=17): 33 [] -class_Orderings_Olinorder(A)|c_lesse_quals(c_Orderings_Oord__class_Omax(B,C,A),D,A)| -c_lesse_quals(C,D,A)| -c_lesse_quals(B,D,A).
% 223.84/223.92    Following clause subsumed by 33 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_lesse_quals(c_Orderings_Oord__class_Omax(B,C,A),D,A)| -c_lesse_quals(C,D,A)| -c_lesse_quals(B,D,A).
% 223.84/223.92    Following clause subsumed by 33 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_lesse_quals(c_Orderings_Oord__class_Omax(B,C,A),D,A)| -c_lesse_quals(C,D,A)| -c_lesse_quals(B,D,A).
% 223.84/223.92  ** KEPT (pick-wt=9): 34 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,c_Orderings_Oord__class_Omax(B,C,A),A).
% 223.84/223.92  ** KEPT (pick-wt=9): 35 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,c_Orderings_Oord__class_Omax(C,B,A),A).
% 223.84/223.92  ** KEPT (pick-wt=7): 36 [] -class_Orderings_Obot(A)|c_lesse_quals(c_Orderings_Obot__class_Obot(A),B,A).
% 223.84/223.92  ** KEPT (pick-wt=22): 37 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)| -class_OrderedGroup_Ocomm__monoid__add(A)|c_lesse_quals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_lesse_quals(B,D,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A).
% 223.84/223.92  ** KEPT (pick-wt=22): 38 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)| -class_OrderedGroup_Ocomm__monoid__add(A)|c_lesse_quals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_lesse_quals(B,C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),D,A).
% 223.84/223.92  ** KEPT (pick-wt=15): 39 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Suc(v_sko__List__Xupt__Xinduct__1(A))))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.92  ** KEPT (pick-wt=8): 40 [] c_Type_Otype_OAtom(A)!=c_Type_Otype_OAtom(B)|A=B.
% 223.84/223.92  ** KEPT (pick-wt=9): 41 [] c_lesse_quals(c_Suc(A),B,tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=9): 42 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_lesse_quals(c_Suc(A),B,tc_nat).
% 223.84/223.92    Following clause subsumed by 41 during input processing: 0 [] c_lesse_quals(c_Suc(A),B,tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 223.84/223.92    Following clause subsumed by 42 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_lesse_quals(c_Suc(A),B,tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=13): 43 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=13): 44 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=13): 45 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 223.84/223.92    Following clause subsumed by 43 during input processing: 0 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 223.84/223.92    Following clause subsumed by 44 during input processing: 0 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=15): 47 [copy,46,flip.1] c_Suc(c_HOL_Ominus__class_Ominus(A,B,tc_nat))=c_HOL_Ominus__class_Ominus(c_Suc(A),B,tc_nat)| -c_lesse_quals(B,A,tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=15): 48 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B).
% 223.84/223.92  ** KEPT (pick-wt=15): 49 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B).
% 223.84/223.92  ** KEPT (pick-wt=21): 50 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)| -c_HOL_Oord__class_Oless(C,B,tc_nat)|c_HOL_Oord__class_Oless(A,D,tc_nat).
% 223.84/223.92    Following clause subsumed by 48 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B).
% 223.84/223.92  ** KEPT (pick-wt=27): 52 [copy,51,flip.2] -class_OrderedGroup_Osemigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,D,A,A))=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A,A).
% 223.84/223.92  ** KEPT (pick-wt=18): 53 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_HOL_Ominus__class_Ominus(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(C,A,tc_nat)| -c_HOL_Oord__class_Oless(C,B,tc_nat).
% 223.84/223.92  ** KEPT (pick-wt=12): 54 [] -class_Nat_Osemiring__char__0(A)|c_Nat_Osemiring__1__class_Oof__nat(B,A)!=c_Nat_Osemiring__1__class_Oof__nat(C,A)|B=C.
% 223.84/223.92  ** KEPT (pick-wt=17): 55 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)|c_lesse_quals(B,D,A)| -c_lesse_quals(B,c_Orderings_Oord__class_Omax(D,C,A),A).
% 223.84/223.92  ** KEPT (pick-wt=31): 56 [] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,C),E))=hAPP(hAPP(B,C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),E))| -c_Groebner__Basis_Ogb__semiring(F,A,B,G,H,I).
% 223.84/223.92  ** KEPT (pick-wt=25): 57 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=c_HOL_Ozero__class_Ozero(A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)|C=c_HOL_Ozero__class_Ozero(A).
% 223.84/223.92  ** KEPT (pick-wt=25): 58 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=c_HOL_Ozero__class_Ozero(A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)|B=c_HOL_Ozero__class_Ozero(A).
% 223.84/223.92  ** KEPT (pick-wt=12): 59 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,C,A)=C| -c_lesse_quals(B,C,A).
% 223.84/223.92  ** KEPT (pick-wt=12): 60 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,C,A)!=C|c_lesse_quals(B,C,A).
% 223.84/223.92  ** KEPT (pick-wt=12): 61 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,C,A)=B| -c_lesse_quals(C,B,A).
% 223.84/223.92  ** KEPT (pick-wt=25): 63 [copy,62,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 223.84/223.92  ** KEPT (pick-wt=25): 64 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)).
% 223.84/223.92  ** KEPT (pick-wt=25): 65 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 223.84/223.92  ** KEPT (pick-wt=25): 66 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)).
% 223.84/223.93  ** KEPT (pick-wt=25): 67 [] -class_OrderedGroup_Oab__semigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 223.84/223.93    Following clause subsumed by 63 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 223.84/223.93  ** KEPT (pick-wt=25): 68 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C).
% 223.84/223.93  ** KEPT (pick-wt=25): 69 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)).
% 223.84/223.93    Following clause subsumed by 63 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 223.84/223.93  ** KEPT (pick-wt=20): 70 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=28): 71 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)=E.
% 223.84/223.93  ** KEPT (pick-wt=13): 72 [] c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_lesse_quals(A,C,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=13): 73 [] c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_lesse_quals(A,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=13): 74 [] c_lesse_quals(A,B,tc_nat)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=13): 75 [] c_lesse_quals(A,B,tc_nat)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 223.84/223.93    Following clause subsumed by 72 during input processing: 0 [] c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_lesse_quals(A,C,tc_nat).
% 223.84/223.93    Following clause subsumed by 73 during input processing: 0 [] c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_lesse_quals(A,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=20): 77 [copy,76,flip.2] -class_OrderedGroup_Opordered__ab__group__add(A)|c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ominus__class_Ominus(D,C,A),A)=c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(B,D,A),C,A).
% 223.84/223.93  ** KEPT (pick-wt=17): 78 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xlist__app__typeE__1__1(C,A,D,B))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,D,B,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 223.84/223.93  ** KEPT (pick-wt=10): 79 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_lesse_quals(C,B,A).
% 223.84/223.93  ** KEPT (pick-wt=10): 80 [] -class_Orderings_Olinorder(A)| -c_lesse_quals(B,B,A)| -c_HOL_Oord__class_Oless(B,B,A).
% 223.84/223.93    Following clause subsumed by 79 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,B,A)|c_lesse_quals(B,B,A).
% 223.84/223.93  ** KEPT (pick-wt=10): 81 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(C,B,A).
% 223.84/223.93    Following clause subsumed by 79 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)|c_HOL_Oord__class_Oless(C,B,A).
% 223.84/223.93    Following clause subsumed by 81 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 223.84/223.93    Following clause subsumed by 79 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_lesse_quals(C,B,A).
% 223.84/223.93  ** KEPT (pick-wt=10): 82 [] -class_Orderings_Opreorder(A)| -c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 223.84/223.93  ** KEPT (pick-wt=15): 83 [] hBOOL(hAPP(A,B))|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(A),tc_nat)| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.93  ** KEPT (pick-wt=9): 84 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Type_Osko__Type__Xtype__induct__1__1(A))).
% 223.84/223.93  ** KEPT (pick-wt=22): 85 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)| -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A).
% 223.84/223.93  ** KEPT (pick-wt=14): 86 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_HOL_Ominus__class_Ominus(A,C,tc_nat),tc_nat)| -c_lesse_quals(C,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=14): 87 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat)| -c_lesse_quals(A,C,tc_nat).
% 223.84/223.93    Following clause subsumed by 87 during input processing: 0 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat)| -c_lesse_quals(A,C,tc_nat)| -c_lesse_quals(B,C,tc_nat)| -c_lesse_quals(B,A,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=22): 88 [] c_lesse_quals(A,B,tc_nat)| -c_lesse_quals(c_HOL_Ominus__class_Ominus(A,C,tc_nat),c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)| -c_lesse_quals(C,B,tc_nat)| -c_lesse_quals(C,A,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=21): 89 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lesse_quals(B,D,A).
% 223.84/223.93  ** KEPT (pick-wt=14): 90 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,D,A)|B=C.
% 223.84/223.93  ** KEPT (pick-wt=14): 91 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)!=c_HOL_Ominus__class_Ominus(C,D,A)|C=D.
% 223.84/223.93  ** KEPT (pick-wt=20): 92 [] c_HOL_Ominus__class_Ominus(A,B,tc_nat)!=c_HOL_Ominus__class_Ominus(C,B,tc_nat)| -c_lesse_quals(B,C,tc_nat)| -c_lesse_quals(B,A,tc_nat)|A=C.
% 223.84/223.93  ** KEPT (pick-wt=19): 93 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=19): 94 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|A=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.93  ** KEPT (pick-wt=13): 95 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_HOL_Oord__class_Oless(B,C,A).
% 223.84/223.93  ** KEPT (pick-wt=13): 96 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 223.84/223.93    Following clause subsumed by 95 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_HOL_Oord__class_Oless(B,C,A).
% 223.84/223.93    Following clause subsumed by 96 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 223.84/223.93  ** KEPT (pick-wt=13): 97 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(B,D,A),C,A).
% 223.84/223.93  ** KEPT (pick-wt=13): 98 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(D,B,A),C,A).
% 223.84/223.93  ** KEPT (pick-wt=13): 99 [] c_Lambda_OdB_OAbs(A)!=c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB)|c_Lambda_OdB_OAbs(A)=B.
% 223.84/223.93  ** KEPT (pick-wt=22): 100 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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).
% 223.84/223.93  ** KEPT (pick-wt=26): 101 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 223.84/223.93  ** KEPT (pick-wt=23): 102 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(A,C,tc_nat)| -c_lesse_quals(B,C,tc_nat)| -c_lesse_quals(B,A,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=23): 104 [copy,103,flip.2] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),C,c_HOL_Ozero__class_Ozero(A),A,A))=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A).
% 223.84/223.93  ** KEPT (pick-wt=22): 105 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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).
% 223.84/223.93  ** KEPT (pick-wt=22): 106 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 223.84/223.93  ** KEPT (pick-wt=18): 107 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat)| -c_lesse_quals(B,A,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=13): 108 [] c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat)|c_Suc(A)=B| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=9): 109 [] -c_lesse_quals(A,B,tc_nat)| -c_lesse_quals(c_Suc(B),A,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=16): 110 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 223.84/223.93  ** KEPT (pick-wt=16): 111 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B)|A=C.
% 223.84/223.93    Following clause subsumed by 110 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 223.84/223.93  ** KEPT (pick-wt=20): 112 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)|C=D.
% 223.84/223.93  ** KEPT (pick-wt=18): 113 [] -class_OrderedGroup_Ocancel__ab__semigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)|C=D.
% 223.84/223.93  ** KEPT (pick-wt=18): 114 [] -class_OrderedGroup_Ocancel__semigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)|C=D.
% 223.84/223.93  ** KEPT (pick-wt=18): 115 [] -class_OrderedGroup_Ocancel__semigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C)|B=D.
% 223.84/223.93  ** KEPT (pick-wt=13): 116 [] c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(C)|B=c_List_Olist_ONil(tc_Lambda_OdB).
% 223.84/223.93  ** KEPT (pick-wt=16): 117 [] c_lesse_quals(A,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),C,tc_nat),tc_nat)| -c_lesse_quals(C,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=30): 118 [] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E)=hAPP(hAPP(B,hAPP(hAPP(A,C),E)),hAPP(hAPP(A,D),E))| -c_Groebner__Basis_Ogb__semiring(F,B,A,G,H,I).
% 223.84/223.93  ** KEPT (pick-wt=30): 120 [copy,119,flip.1] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,C),E))=hAPP(hAPP(B,C),hAPP(hAPP(A,D),E))| -c_Groebner__Basis_Ogb__semiring(A,B,F,G,H,I).
% 223.84/223.93  ** KEPT (pick-wt=18): 121 [] hAPP(hAPP(A,B),C)=hAPP(hAPP(A,C),B)| -c_Groebner__Basis_Ogb__semiring(D,A,E,F,G,H).
% 223.84/223.93  ** KEPT (pick-wt=26): 123 [copy,122,flip.1] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(E,A,F,G,H,I).
% 223.84/223.93  ** KEPT (pick-wt=14): 124 [] hAPP(hAPP(A,B),C)=C| -c_Groebner__Basis_Ogb__semiring(D,A,E,F,B,G).
% 223.84/223.93  ** KEPT (pick-wt=14): 125 [] hAPP(hAPP(A,B),C)=B| -c_Groebner__Basis_Ogb__semiring(D,A,E,B,F,G).
% 223.84/223.93  ** KEPT (pick-wt=18): 126 [] hAPP(hAPP(A,B),C)=hAPP(hAPP(A,C),B)| -c_Groebner__Basis_Ogb__semiring(A,D,E,F,G,H).
% 223.84/223.93  ** KEPT (pick-wt=26): 128 [copy,127,flip.1] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(A,E,F,G,H,I).
% 223.84/223.93  ** KEPT (pick-wt=14): 129 [] hAPP(hAPP(A,B),C)=C| -c_Groebner__Basis_Ogb__semiring(A,D,E,B,F,G).
% 223.84/223.93    Following clause subsumed by 128 during input processing: 0 [flip.1] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(A,E,F,G,H,I).
% 223.84/223.93    Following clause subsumed by 126 during input processing: 0 [] hAPP(hAPP(A,B),C)=hAPP(hAPP(A,C),B)| -c_Groebner__Basis_Ogb__semiring(A,D,E,F,G,H).
% 223.84/223.93  ** KEPT (pick-wt=26): 130 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,hAPP(hAPP(A,B),D)),C)| -c_Groebner__Basis_Ogb__semiring(A,E,F,G,H,I).
% 223.84/223.93  ** KEPT (pick-wt=26): 131 [] hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))=hAPP(hAPP(A,C),hAPP(hAPP(A,B),D))| -c_Groebner__Basis_Ogb__semiring(A,E,F,G,H,I).
% 223.84/223.93    Following clause subsumed by 128 during input processing: 0 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(A,E,F,G,H,I).
% 223.84/223.93  ** KEPT (pick-wt=34): 132 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E))=hAPP(hAPP(A,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,C),E))| -c_Groebner__Basis_Ogb__semiring(A,F,G,H,I,J).
% 223.84/223.93  ** KEPT (pick-wt=8): 133 [] c_Suc(A)!=c_Suc(B)|A=B.
% 223.84/223.93    Following clause subsumed by 133 during input processing: 0 [] c_Suc(A)!=c_Suc(B)|A=B.
% 223.84/223.93  ** KEPT (pick-wt=17): 134 [] -class_OrderedGroup_Oab__semigroup__add(A)|c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,C,A,A)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,B,A,A).
% 223.84/223.93  ** KEPT (pick-wt=17): 135 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 223.84/223.93  ** KEPT (pick-wt=17): 136 [] -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(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A).
% 223.84/223.93  ** KEPT (pick-wt=17): 137 [] -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(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A).
% 223.84/223.93  ** KEPT (pick-wt=17): 138 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 223.84/223.93  ** KEPT (pick-wt=20): 139 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.93  ** KEPT (pick-wt=18): 140 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=21): 141 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A).
% 223.84/223.93  ** KEPT (pick-wt=23): 142 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),C,A,A))=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A).
% 223.84/223.93  ** KEPT (pick-wt=13): 143 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_Orderings_Oord__class_Omax(D,B,A),C,A).
% 223.84/223.93  ** KEPT (pick-wt=13): 144 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_Orderings_Oord__class_Omax(B,D,A),C,A).
% 223.84/223.93  ** KEPT (pick-wt=13): 145 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_lesse_quals(B,D,A).
% 223.84/223.93  ** KEPT (pick-wt=13): 146 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_lesse_quals(B,C,A).
% 223.84/223.93    Following clause subsumed by 145 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_lesse_quals(B,D,A).
% 223.84/223.93    Following clause subsumed by 146 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_lesse_quals(B,C,A).
% 223.84/223.93    Following clause subsumed by 143 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_Orderings_Oord__class_Omax(D,B,A),C,A).
% 223.84/223.93    Following clause subsumed by 144 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_Orderings_Oord__class_Omax(B,D,A),C,A).
% 223.84/223.93  ** KEPT (pick-wt=16): 147 [] c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_lesse_quals(c_HOL_Ominus__class_Ominus(A,C,tc_nat),B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=16): 148 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)| -c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=15): 149 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 223.84/223.93  ** KEPT (pick-wt=17): 150 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(D,C,A),A).
% 223.84/223.93  ** KEPT (pick-wt=25): 151 [] c_InductTermi_OIT(c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B),C,tc_Lambda_OdB,tc_Lambda_OdB))| -c_InductTermi_OIT(B)| -c_InductTermi_OIT(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_Lambda_OdB,tc_Lambda_OdB)).
% 223.84/223.93  ** KEPT (pick-wt=8): 152 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OAbs(B)|A=B.
% 223.84/223.93  ** KEPT (pick-wt=22): 153 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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).
% 223.84/223.93  ** KEPT (pick-wt=22): 154 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 223.84/223.93  ** KEPT (pick-wt=12): 155 [] A=B|c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=12): 156 [] A=B| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 223.84/223.93    Following clause subsumed by 155 during input processing: 0 [] A=B| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)|c_HOL_Oord__class_Oless(A,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=13): 157 [] c_Lambda_OdB_OAbs(A)!=c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB)|C=c_List_Olist_ONil(tc_Lambda_OdB).
% 223.84/223.93  ** KEPT (pick-wt=23): 159 [copy,158,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ominus__class_Ominus(B,C,tc_nat))=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat)| -c_lesse_quals(C,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=23): 161 [copy,160,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(A,B,tc_nat)),C)=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat)| -c_lesse_quals(B,A,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=21): 162 [] c_HOL_Ominus__class_Ominus(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat)| -c_lesse_quals(C,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=11): 163 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=16): 164 [] c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,C,B,tc_Lambda_OdB,tc_Lambda_OdB))| -c_Lambda_Obeta(A,C).
% 223.84/223.93  ** KEPT (pick-wt=14): 165 [] -class_Orderings_Opreorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_lesse_quals(C,B,A)| -c_lesse_quals(B,C,A).
% 223.84/223.93  ** KEPT (pick-wt=4): 166 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 223.84/223.93    Following clause subsumed by 166 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=6): 167 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 223.84/223.93  ** KEPT (pick-wt=6): 168 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 223.84/223.93  ** KEPT (pick-wt=6): 169 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 223.84/223.93  ** KEPT (pick-wt=20): 170 [] -c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),tc_nat)|c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),A,tc_nat)=B.
% 223.84/223.93  ** KEPT (pick-wt=22): 171 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),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).
% 223.84/223.93  ** KEPT (pick-wt=13): 172 [] -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.
% 223.84/223.93  ** KEPT (pick-wt=13): 173 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A).
% 223.84/223.93  ** KEPT (pick-wt=11): 174 [] A=B| -c_lesse_quals(B,A,tc_nat)| -c_lesse_quals(A,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=13): 175 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(C,B,A)| -c_lesse_quals(B,C,A).
% 223.84/223.93    Following clause subsumed by 173 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)|C=B.
% 223.84/223.93    Following clause subsumed by 175 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(C,B,A)| -c_lesse_quals(B,C,A).
% 223.84/223.93    Following clause subsumed by 175 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_lesse_quals(B,C,A)| -c_lesse_quals(C,B,A).
% 223.84/223.93    Following clause subsumed by 173 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).
% 223.84/223.93    Following clause subsumed by 173 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).
% 223.84/223.93  ** KEPT (pick-wt=14): 176 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A).
% 223.84/223.93  ** KEPT (pick-wt=14): 177 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,C,A).
% 223.84/223.93  ** KEPT (pick-wt=8): 178 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,B,A)=B.
% 223.84/223.93  ** KEPT (pick-wt=24): 179 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A)| -c_HOL_Oord__class_Oless(C,E,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 223.84/223.93  ** KEPT (pick-wt=22): 180 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat)| -c_HOL_Oord__class_Oless(B,D,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=8): 181 [] c_lesse_quals(A,B,tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 223.84/223.93    Following clause subsumed by 181 during input processing: 0 [] c_lesse_quals(A,B,tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=10): 182 [] -class_Orderings_Oorder(A)|c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(B,C,A).
% 223.84/223.93  ** KEPT (pick-wt=10): 183 [] -class_Orderings_Opreorder(A)|c_lesse_quals(B,C,A)| -c_HOL_Oord__class_Oless(B,C,A).
% 223.84/223.93  ** KEPT (pick-wt=18): 184 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(C),D,tc_Lambda_OdB,tc_Lambda_OdB)|B=D.
% 223.84/223.93  ** KEPT (pick-wt=18): 185 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(C),D,tc_Lambda_OdB,tc_Lambda_OdB)|A=C.
% 223.84/223.93  ** KEPT (pick-wt=13): 186 [] c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(C)|A=c_Lambda_OdB_OAbs(C).
% 223.84/223.93  ** KEPT (pick-wt=23): 187 [] c_HOL_Ominus__class_Ominus(A,c_Suc(c_HOL_Ominus__class_Ominus(B,C,tc_nat)),tc_nat)=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),c_Suc(B),tc_nat)| -c_lesse_quals(C,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=14): 188 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A).
% 223.84/223.93  ** KEPT (pick-wt=14): 189 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,C,A).
% 223.84/223.93  ** KEPT (pick-wt=14): 190 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=14): 191 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A).
% 223.84/223.93  ** KEPT (pick-wt=13): 192 [] c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat)| -c_HOL_Oord__class_Oless(C,B,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=20): 193 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A)| -c_lesse_quals(B,D,A).
% 223.84/223.93  ** KEPT (pick-wt=20): 194 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A).
% 223.84/223.93  ** KEPT (pick-wt=20): 195 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A)| -c_lesse_quals(C,D,A).
% 223.84/223.93  ** KEPT (pick-wt=20): 196 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A).
% 223.84/223.93  ** KEPT (pick-wt=20): 197 [] -class_OrderedGroup_Opordered__ab__semigroup__add(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A)| -c_lesse_quals(B,D,A).
% 223.84/223.93  ** KEPT (pick-wt=20): 198 [] -class_OrderedGroup_Opordered__ab__semigroup__add(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A)| -c_lesse_quals(C,D,A).
% 223.84/223.93  ** KEPT (pick-wt=18): 199 [] c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat)| -c_lesse_quals(A,C,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=18): 200 [] c_lesse_quals(A,B,tc_nat)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=18): 201 [] c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat)| -c_lesse_quals(B,C,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=20): 202 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_List_Ofoldl(c_Lambda_OdB_OApp,C,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)|hAPP(hAPP(c_Lambda_OdB_OApp,A),B)=C.
% 223.84/223.93  ** KEPT (pick-wt=26): 203 [] hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))=hAPP(hAPP(A,C),hAPP(hAPP(A,B),D))| -c_Groebner__Basis_Ogb__semiring(E,A,F,G,H,I).
% 223.84/223.93    Following clause subsumed by 123 during input processing: 0 [flip.1] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(E,A,F,G,H,I).
% 223.84/223.93    Following clause subsumed by 123 during input processing: 0 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(E,A,F,G,H,I).
% 223.84/223.93  ** KEPT (pick-wt=26): 204 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,hAPP(hAPP(A,B),D)),C)| -c_Groebner__Basis_Ogb__semiring(E,A,F,G,H,I).
% 223.84/223.93    Following clause subsumed by 203 during input processing: 0 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E))=hAPP(hAPP(A,D),hAPP(hAPP(A,hAPP(hAPP(A,B),C)),E))| -c_Groebner__Basis_Ogb__semiring(F,A,G,H,I,J).
% 223.84/223.93    Following clause subsumed by 123 during input processing: 0 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E))=hAPP(hAPP(A,B),hAPP(hAPP(A,C),hAPP(hAPP(A,D),E)))| -c_Groebner__Basis_Ogb__semiring(F,A,G,H,I,J).
% 223.84/223.93  ** KEPT (pick-wt=34): 205 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E))=hAPP(hAPP(A,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,C),E))| -c_Groebner__Basis_Ogb__semiring(F,A,G,H,I,J).
% 223.84/223.93  ** KEPT (pick-wt=14): 206 [] hAPP(hAPP(A,B),C)=B| -c_Groebner__Basis_Ogb__semiring(D,A,E,F,C,G).
% 223.84/223.93    Following clause subsumed by 124 during input processing: 0 [] hAPP(hAPP(A,B),C)=C| -c_Groebner__Basis_Ogb__semiring(D,A,E,F,B,G).
% 223.84/223.93  ** KEPT (pick-wt=14): 207 [] hAPP(hAPP(A,B),C)=C| -c_Groebner__Basis_Ogb__semiring(D,A,E,C,F,G).
% 223.84/223.93    Following clause subsumed by 125 during input processing: 0 [] hAPP(hAPP(A,B),C)=B| -c_Groebner__Basis_Ogb__semiring(D,A,E,B,F,G).
% 223.84/223.93  ** KEPT (pick-wt=30): 208 [] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E)=hAPP(hAPP(B,hAPP(hAPP(A,C),E)),hAPP(hAPP(A,D),E))| -c_Groebner__Basis_Ogb__semiring(B,A,F,G,H,I).
% 223.84/223.93    Following clause subsumed by 121 during input processing: 0 [] hAPP(hAPP(A,B),C)=hAPP(hAPP(A,C),B)| -c_Groebner__Basis_Ogb__semiring(D,A,E,F,G,H).
% 223.84/223.93  ** KEPT (pick-wt=14): 209 [] hAPP(hAPP(A,B),C)=B| -c_Groebner__Basis_Ogb__semiring(A,D,E,C,F,G).
% 223.84/223.93    Following clause subsumed by 129 during input processing: 0 [] hAPP(hAPP(A,B),C)=C| -c_Groebner__Basis_Ogb__semiring(A,D,E,B,F,G).
% 223.84/223.93  ** KEPT (pick-wt=22): 210 [] hAPP(hAPP(A,B),B)=hAPP(hAPP(C,hAPP(hAPP(A,D),D)),B)| -c_Groebner__Basis_Ogb__semiring(A,C,E,F,D,G).
% 223.84/223.93  ** KEPT (pick-wt=26): 211 [] hAPP(hAPP(A,B),hAPP(hAPP(C,D),B))=hAPP(hAPP(C,hAPP(hAPP(A,D),E)),B)| -c_Groebner__Basis_Ogb__semiring(A,C,F,G,E,H).
% 223.84/223.93  ** KEPT (pick-wt=26): 212 [] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),D)=hAPP(hAPP(B,hAPP(hAPP(A,C),E)),D)| -c_Groebner__Basis_Ogb__semiring(A,B,F,G,E,H).
% 223.84/223.93  ** KEPT (pick-wt=30): 213 [] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,E),D))=hAPP(hAPP(B,hAPP(hAPP(A,C),E)),D)| -c_Groebner__Basis_Ogb__semiring(A,B,F,G,H,I).
% 223.84/223.93  ** KEPT (pick-wt=15): 214 [] -hBOOL(hAPP(A,c_Type_Otype_Otype__case(B,C,c_Type_Otype_OAtom(D),t_a)))|hBOOL(hAPP(A,hAPP(B,D))).
% 223.84/223.93    Following clause subsumed by 214 during input processing: 0 [] -hBOOL(hAPP(A,c_Type_Otype_Otype__case(B,C,c_Type_Otype_OAtom(D),t_a)))|hBOOL(hAPP(A,hAPP(B,D))).
% 223.84/223.93  ** KEPT (pick-wt=19): 215 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=19): 216 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.93  ** KEPT (pick-wt=5): 217 [] c_InductTermi_OIT(c_Lambda_OdB_OAbs(A))| -c_InductTermi_OIT(A).
% 223.84/223.93  ** KEPT (pick-wt=35): 218 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)).
% 223.84/223.93  ** KEPT (pick-wt=9): 219 [] -class_Ring__and__Field_Oordered__semidom(A)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_HOL_Ozero__class_Ozero(A),A).
% 223.84/223.93  ** KEPT (pick-wt=11): 220 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,C,A)=c_Orderings_Oord__class_Omax(C,B,A).
% 223.84/223.93  ** KEPT (pick-wt=29): 221 [] -class_Ring__and__Field_Oordered__semidom(A)|c_Power_Opower__class_Opower(B,C,A)!=c_Power_Opower__class_Opower(D,C,A)|B=D| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),D,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 223.84/223.93  ** KEPT (pick-wt=12): 222 [] c_Lambda_Oliftn(A,c_Lambda_OdB_OVar(B),C)=c_Lambda_OdB_OVar(B)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=13): 223 [] c_HOL_Ominus__class_Ominus(A,c_HOL_Ominus__class_Ominus(A,B,tc_nat),tc_nat)=B| -c_lesse_quals(B,A,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=13): 224 [] A=c_Suc(B)|c_lesse_quals(A,B,tc_nat)| -c_lesse_quals(A,c_Suc(B),tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=9): 225 [] -c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=26): 226 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Orderings_Oord__class_Omax(B,C,A)),D)=c_Orderings_Oord__class_Omax(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A).
% 223.84/223.93  ** KEPT (pick-wt=26): 227 [] -class_Ring__and__Field_Oordered__semidom(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)!=c_Power_Opower__class_Opower(D,c_Suc(C),A)|B=D| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),D,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),B,A).
% 223.84/223.93  ** KEPT (pick-wt=17): 228 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(B,C,A),D,A)=c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,A),A).
% 223.84/223.93  ** KEPT (pick-wt=17): 229 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(C,D,A),A)=c_Orderings_Oord__class_Omax(C,c_Orderings_Oord__class_Omax(B,D,A),A).
% 223.84/223.93  ** KEPT (pick-wt=9): 230 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A).
% 223.84/223.93    Following clause subsumed by 230 during input processing: 0 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A).
% 223.84/223.93  ** KEPT (pick-wt=8): 231 [] c_Lambda_Obeta(c_Lambda_OdB_OAbs(A),c_Lambda_OdB_OAbs(B))| -c_Lambda_Obeta(A,B).
% 223.84/223.93  ** KEPT (pick-wt=14): 232 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Omax(B,c_Orderings_Oord__class_Omax(B,C,A),A)=c_Orderings_Oord__class_Omax(B,C,A).
% 223.84/223.93  ** KEPT (pick-wt=13): 233 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A)=B.
% 223.84/223.93  ** KEPT (pick-wt=24): 234 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A)| -c_HOL_Oord__class_Oless(C,E,A)| -c_lesse_quals(B,D,A).
% 223.84/223.93  ** KEPT (pick-wt=24): 235 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A)| -c_lesse_quals(C,E,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 223.84/223.93  ** KEPT (pick-wt=10): 236 [] c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=10): 237 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat).
% 223.84/223.93    Following clause subsumed by 236 during input processing: 0 [] c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 223.84/223.93    Following clause subsumed by 44 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 223.84/223.93    Following clause subsumed by 43 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=17): 238 [] -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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A).
% 223.84/223.93  ** KEPT (pick-wt=17): 239 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 223.84/223.93  ** KEPT (pick-wt=18): 241 [copy,240,flip.1] hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(A,B,C)),c_Type_Osko__Type__Xtyping__elims__3__2(A,B,C))=A| -c_Type_Otyping(B,c_Lambda_OdB_OAbs(C),A).
% 223.84/223.93  ** KEPT (pick-wt=19): 242 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 223.84/223.93  ** KEPT (pick-wt=13): 243 [] -class_Ring__and__Field_Oring__1__no__zero__divisors(A)|c_Power_Opower__class_Opower(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 223.84/223.93  ** KEPT (pick-wt=15): 244 [] -class_OrderedGroup_Olordered__ab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 223.84/223.93  ** KEPT (pick-wt=11): 245 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 223.84/223.93  ** KEPT (pick-wt=9): 246 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 223.84/223.93  ** KEPT (pick-wt=9): 247 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 223.84/223.93    Following clause subsumed by 246 during input processing: 0 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 223.84/223.93  ** KEPT (pick-wt=9): 248 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 223.84/223.93  ** KEPT (pick-wt=16): 250 [copy,249,flip.3] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=B|C=c_HOL_Ozero__class_Ozero(A).
% 223.84/223.93  ** KEPT (pick-wt=13): 251 [] -class_OrderedGroup_Olordered__ab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 223.84/223.93  ** KEPT (pick-wt=14): 252 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 223.84/223.93  ** KEPT (pick-wt=12): 253 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 223.84/223.93  ** KEPT (pick-wt=12): 254 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 223.84/223.93  ** KEPT (pick-wt=11): 255 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 223.84/223.93  ** KEPT (pick-wt=11): 256 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 223.84/223.93  ** KEPT (pick-wt=13): 258 [copy,257,flip.3] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 223.84/223.93  ** KEPT (pick-wt=11): 259 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 223.84/223.93  ** KEPT (pick-wt=11): 260 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 223.84/223.93  ** KEPT (pick-wt=11): 261 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 223.84/223.93  ** KEPT (pick-wt=11): 262 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 223.84/223.93    Following clause subsumed by 255 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 223.84/223.93    Following clause subsumed by 166 during input processing: 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=5): 263 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.93    Following clause subsumed by 263 during input processing: 0 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=17): 264 [] c_HOL_Ominus__class_Ominus(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Ominus__class_Ominus(B,A,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=A.
% 223.84/223.93  ** KEPT (pick-wt=9): 265 [] A=c_HOL_Ozero__class_Ozero(tc_nat)| -c_lesse_quals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=13): 266 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=13): 267 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=12): 269 [copy,268,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.93    Following clause subsumed by 269 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.93    Following clause subsumed by 263 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.93    Following clause subsumed by 263 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=19): 271 [copy,270,flip.2] -class_OrderedGroup_Omonoid__add(A)|c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(A),A,A)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A,A).
% 223.84/223.93  ** KEPT (pick-wt=15): 273 [copy,272,flip.2] -c_lesse_quals(A,B,tc_nat)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(B,A,tc_nat)),A)=B.
% 223.84/223.93  ** KEPT (pick-wt=15): 274 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ominus__class_Ominus(B,A,tc_nat))=B| -c_lesse_quals(A,B,tc_nat).
% 223.84/223.93    Following clause subsumed by 273 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(A,B,tc_nat)),B)=A| -c_lesse_quals(B,A,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=23): 275 [] hAPP(hAPP(A,B),hAPP(hAPP(C,B),D))=hAPP(hAPP(C,B),c_Suc(D))| -c_Groebner__Basis_Ogb__semiring(E,A,C,F,G,H).
% 223.84/223.93  ** KEPT (pick-wt=23): 276 [] hAPP(hAPP(A,hAPP(hAPP(B,C),D)),C)=hAPP(hAPP(B,C),c_Suc(D))| -c_Groebner__Basis_Ogb__semiring(E,A,B,F,G,H).
% 223.84/223.93  ** KEPT (pick-wt=23): 277 [] hAPP(hAPP(A,B),c_Suc(C))=hAPP(hAPP(D,B),hAPP(hAPP(A,B),C))| -c_Groebner__Basis_Ogb__semiring(E,D,A,F,G,H).
% 223.84/223.93    Following clause subsumed by 277 during input processing: 0 [] hAPP(hAPP(A,B),c_Suc(C))=hAPP(hAPP(D,B),hAPP(hAPP(A,B),C))| -c_Groebner__Basis_Ogb__semiring(E,D,A,F,G,H).
% 223.84/223.93    Following clause subsumed by 159 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ominus__class_Ominus(B,C,tc_nat))=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat)| -c_lesse_quals(C,B,tc_nat).
% 223.84/223.93    Following clause subsumed by 161 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(A,B,tc_nat)),C)=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat)| -c_lesse_quals(B,A,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=23): 278 [] -class_Ring__and__Field_Oordered__semidom(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lesse_quals(c_Power_Opower__class_Opower(B,c_Suc(D),A),c_Power_Opower__class_Opower(C,c_Suc(D),A),A).
% 223.84/223.93  ** KEPT (pick-wt=14): 279 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=14): 280 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A).
% 223.84/223.93  ** KEPT (pick-wt=11): 281 [] c_List_Oreplicate(A,B,C)!=c_List_Olist_ONil(C)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=11): 282 [] c_List_Olist_ONil(A)!=c_List_Oreplicate(B,C,A)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=9): 283 [] c_lesse_quals(A,B,tc_nat)| -c_lesse_quals(c_Suc(A),B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=9): 284 [] c_lesse_quals(A,c_Suc(B),tc_nat)| -c_lesse_quals(A,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=17): 285 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xlist__app__typeD__1__1(C,A,D,B))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,D,B,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 223.84/223.93  ** KEPT (pick-wt=5): 286 [] -c_lesse_quals(c_Suc(A),A,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=22): 287 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,C,tc_nat),c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)| -c_lesse_quals(C,B,tc_nat)| -c_lesse_quals(C,A,tc_nat).
% 223.84/223.93    Following clause subsumed by 107 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat)| -c_lesse_quals(B,C,tc_nat)| -c_lesse_quals(B,A,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=20): 288 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 223.84/223.93  ** KEPT (pick-wt=12): 289 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,C)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=16): 290 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OAbs(E),t_a)))|hBOOL(hAPP(A,hAPP(D,E))).
% 223.84/223.93    Following clause subsumed by 290 during input processing: 0 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OAbs(E),t_a)))|hBOOL(hAPP(A,hAPP(D,E))).
% 223.84/223.93  ** KEPT (pick-wt=8): 291 [] c_InductTermi_OIT(c_Lambda_Osubst(A,c_Lambda_OdB_OVar(B),C))| -c_InductTermi_OIT(A).
% 223.84/223.93  ** KEPT (pick-wt=17): 292 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 223.84/223.93  ** KEPT (pick-wt=17): 293 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A).
% 223.84/223.93  ** KEPT (pick-wt=9): 294 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=9): 295 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=21): 296 [] -class_Ring__and__Field_Oring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ominus__class_Ominus(B,C,tc_nat),A)=c_HOL_Ominus__class_Ominus(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A)| -c_lesse_quals(C,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=16): 297 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat)| -c_HOL_Oord__class_Oless(A,c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=16): 298 [] c_HOL_Oord__class_Oless(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=4): 299 [] c_Suc(A)!=A.
% 223.84/223.93    Following clause subsumed by 299 during input processing: 0 [flip.1] c_Suc(A)!=A.
% 223.84/223.93  ** KEPT (pick-wt=20): 300 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 223.84/223.93  ** KEPT (pick-wt=20): 301 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 223.84/223.93  ** KEPT (pick-wt=20): 302 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A).
% 223.84/223.93  ** KEPT (pick-wt=20): 303 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A)| -c_HOL_Oord__class_Oless(C,D,A).
% 223.84/223.93  ** KEPT (pick-wt=20): 304 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A)| -c_HOL_Oord__class_Oless(C,D,A).
% 223.84/223.93  ** KEPT (pick-wt=20): 305 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A).
% 223.84/223.93  ** KEPT (pick-wt=18): 306 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=18): 307 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=18): 308 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=14): 309 [] -class_Orderings_Oorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(B,D,A)| -c_lesse_quals(D,C,A).
% 223.84/223.93  ** KEPT (pick-wt=14): 310 [] -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).
% 223.84/223.93  ** KEPT (pick-wt=14): 311 [] -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).
% 223.84/223.93  ** KEPT (pick-wt=22): 312 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_lesse_quals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lesse_quals(B,c_HOL_Ozero__class_Ozero(A),A).
% 223.84/223.93  ** KEPT (pick-wt=14): 313 [] -class_Orderings_Opreorder(A)|c_lesse_quals(B,C,A)| -c_lesse_quals(D,C,A)| -c_lesse_quals(B,D,A).
% 223.84/223.93  ** KEPT (pick-wt=12): 314 [] c_lesse_quals(A,B,tc_nat)| -c_lesse_quals(C,B,tc_nat)| -c_lesse_quals(A,C,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=6): 315 [] -class_Orderings_Oorder(A)|c_lesse_quals(B,B,A).
% 223.84/223.93  ** KEPT (pick-wt=6): 316 [] -class_Orderings_Opreorder(A)|c_lesse_quals(B,B,A).
% 223.84/223.93  ** KEPT (pick-wt=14): 317 [] -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).
% 223.84/223.93  ** KEPT (pick-wt=14): 318 [] -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).
% 223.84/223.93  ** KEPT (pick-wt=24): 319 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_lesse_quals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_lesse_quals(E,D,A)| -c_lesse_quals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E),A).
% 223.84/223.93  ** KEPT (pick-wt=16): 320 [] hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)))| -c_HOL_Oord__class_Oless(B,C,tc_nat)| -hBOOL(hAPP(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat))).
% 223.84/223.93  ** KEPT (pick-wt=12): 321 [] A=B| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)| -c_lesse_quals(B,A,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=12): 322 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(B,A,tc_nat),tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=12): 323 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,A,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=9): 324 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=9): 325 [] c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=14): 326 [] c_Suc(c_HOL_Ominus__class_Ominus(A,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))=A| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=21): 327 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)).
% 223.84/223.93  ** KEPT (pick-wt=17): 328 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=19): 329 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,E,A)|c_lesse_quals(E,D,A)| -c_lesse_quals(C,B,A).
% 223.84/223.93  ** KEPT (pick-wt=19): 330 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,E,A)|c_lesse_quals(C,B,A)| -c_lesse_quals(E,D,A).
% 223.84/223.93  ** KEPT (pick-wt=19): 331 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,E,A)|c_HOL_Oord__class_Oless(D,E,A)| -c_HOL_Oord__class_Oless(B,C,A).
% 223.84/223.93  ** KEPT (pick-wt=19): 332 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,E,A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(D,E,A).
% 223.84/223.93  ** KEPT (pick-wt=13): 333 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,c_Suc(B),tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=20): 334 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.93  ** KEPT (pick-wt=18): 335 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=13): 336 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|C=B| -c_lesse_quals(B,C,A).
% 223.84/223.93    Following clause subsumed by 336 during input processing: 0 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,C,A)|C=B.
% 223.84/223.93  ** KEPT (pick-wt=11): 337 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|A=B| -c_lesse_quals(A,B,tc_nat).
% 223.84/223.93    Following clause subsumed by 337 during input processing: 0 [] A=B|c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_lesse_quals(A,B,tc_nat).
% 223.84/223.93    Following clause subsumed by 337 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|A=B| -c_lesse_quals(A,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=13): 338 [] -class_Orderings_Oorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,C,A).
% 223.84/223.93    Following clause subsumed by 338 during input processing: 0 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|B=C| -c_lesse_quals(B,C,A).
% 223.84/223.93    Following clause subsumed by 338 during input processing: 0 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|B=C| -c_lesse_quals(B,C,A).
% 223.84/223.93    Following clause subsumed by 338 during input processing: 0 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,C,A)|B=C.
% 223.84/223.93  ** KEPT (pick-wt=13): 339 [] -class_Orderings_Olinorder(A)|B=C| -c_lesse_quals(B,C,A)|c_HOL_Oord__class_Oless(B,C,A).
% 223.84/223.93    Following clause subsumed by 339 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)| -c_lesse_quals(B,C,A).
% 223.84/223.93  ** KEPT (pick-wt=10): 340 [] c_lesse_quals(A,B,tc_nat)| -c_lesse_quals(c_Suc(A),c_Suc(B),tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=10): 341 [] c_lesse_quals(c_Suc(A),c_Suc(B),tc_nat)| -c_lesse_quals(A,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=10): 342 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 223.84/223.93  ** KEPT (pick-wt=10): 343 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 223.84/223.93  ** KEPT (pick-wt=10): 344 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,C,A)|c_lesse_quals(C,B,A).
% 223.84/223.93  ** KEPT (pick-wt=10): 345 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 223.84/223.93    Following clause subsumed by 345 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 223.84/223.93  ** KEPT (pick-wt=10): 347 [copy,346,factor_simp] hBOOL(hAPP(A,v_sko__Nat__Xnat__Xinduct__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.93  ** KEPT (pick-wt=5): 348 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 223.84/223.93    Following clause subsumed by 348 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=10): 350 [copy,349,factor_simp] hBOOL(hAPP(A,v_sko__List__Xupt__Xinduct__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.93  ** KEPT (pick-wt=14): 351 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.93  ** KEPT (pick-wt=16): 352 [] c_List_Oreplicate(A,B,C)!=c_List_Oreplicate(D,E,C)|B=E|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=15): 353 [] hAPP(hAPP(A,B),c_HOL_Ozero__class_Ozero(tc_nat))=C| -c_Groebner__Basis_Ogb__semiring(D,E,A,F,C,G).
% 223.84/223.93  ** KEPT (pick-wt=8): 354 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 223.84/223.93  ** KEPT (pick-wt=8): 355 [] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 223.84/223.93  ** KEPT (pick-wt=21): 356 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,hAPP(hAPP(c_Lambda_OdB_OApp,E),F),t_a)))|hBOOL(hAPP(A,hAPP(hAPP(C,E),F))).
% 223.84/223.93    Following clause subsumed by 356 during input processing: 0 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,hAPP(hAPP(c_Lambda_OdB_OApp,E),F),t_a)))|hBOOL(hAPP(A,hAPP(hAPP(C,E),F))).
% 223.84/223.93  ** KEPT (pick-wt=16): 357 [] c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,C,B,tc_Lambda_OdB,tc_Lambda_OdB)|A=C.
% 223.84/223.93  ** KEPT (pick-wt=14): 358 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),hAPP(hAPP(c_Lambda_OdB_OApp,A),C))| -c_Lambda_Obeta(B,C).
% 223.84/223.93  ** KEPT (pick-wt=14): 359 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),hAPP(hAPP(c_Lambda_OdB_OApp,C),B))| -c_Lambda_Obeta(A,C).
% 223.84/223.93  ** KEPT (pick-wt=15): 360 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(C),D,tc_Lambda_OdB,tc_Lambda_OdB).
% 223.84/223.93  ** KEPT (pick-wt=13): 361 [] c_Lambda_OdB_OVar(A)!=c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB)|C=c_List_Olist_ONil(tc_Lambda_OdB).
% 223.84/223.93  ** KEPT (pick-wt=14): 362 [] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(C),D,tc_Lambda_OdB,tc_Lambda_OdB).
% 223.84/223.93  ** KEPT (pick-wt=18): 363 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xvar__app__typesE__1__1(C,A,D,B))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(D),B,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 223.84/223.93  ** KEPT (pick-wt=37): 364 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xvar__app__types__1__1(C,D,A,B))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(E),F,tc_Lambda_OdB,tc_Lambda_OdB),D)| -c_Type_Otypings(A,F,G)| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(E),F,tc_Lambda_OdB,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 223.84/223.93  ** KEPT (pick-wt=5): 365 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 223.84/223.93  ** KEPT (pick-wt=16): 366 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OVar(E),t_a)))|hBOOL(hAPP(A,hAPP(B,E))).
% 223.84/223.93    Following clause subsumed by 366 during input processing: 0 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OVar(E),t_a)))|hBOOL(hAPP(A,hAPP(B,E))).
% 223.84/223.93  ** KEPT (pick-wt=4): 367 [] -c_Lambda_Obeta(c_Lambda_OdB_OVar(A),B).
% 223.84/223.93  ** KEPT (pick-wt=5): 368 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 223.84/223.93  ** KEPT (pick-wt=41): 370 [copy,369,flip.1] c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(A,B,C,D),A,tc_Type_Otype,tc_Type_Otype)=B| -c_Type_Otyping(C,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(E),F,tc_Lambda_OdB,tc_Lambda_OdB),B)| -c_Type_Otypings(C,F,G)| -c_Type_Otyping(C,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(E),F,tc_Lambda_OdB,tc_Lambda_OdB),D,tc_Lambda_OdB,tc_Lambda_OdB),A).
% 223.84/223.93  ** KEPT (pick-wt=22): 371 [] c_Type_Otyping(A,B,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(C,A,B,D),C,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,B,D,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 223.84/223.93  ** KEPT (pick-wt=22): 372 [] c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB),D)| -c_Type_Otypings(A,C,E)| -c_Type_Otyping(A,B,c_List_Ofoldr(c_Type_Otype_OFun,E,D,tc_Type_Otype,tc_Type_Otype)).
% 223.84/223.93  ** KEPT (pick-wt=22): 373 [] c_Type_Otyping(A,B,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(C,A,B,D),C,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,B,D,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 223.84/223.93  ** KEPT (pick-wt=11): 374 [] c_Type_Otyping(A,B,C)| -c_Lambda_Obeta(D,B)| -c_Type_Otyping(A,D,C).
% 223.84/223.93  ** KEPT (pick-wt=8): 375 [] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=c_Type_Otype_OAtom(C).
% 223.84/223.93  ** KEPT (pick-wt=12): 377 [copy,376,factor_simp] c_Type_Osko__Type__Xtype__induct__1__1(A)!=hAPP(hAPP(c_Type_Otype_OFun,B),C)|hBOOL(hAPP(A,C)).
% 223.84/223.93  ** KEPT (pick-wt=12): 379 [copy,378,factor_simp] c_Type_Osko__Type__Xtype__induct__1__1(A)!=hAPP(hAPP(c_Type_Otype_OFun,B),C)|hBOOL(hAPP(A,B)).
% 223.84/223.93  ** KEPT (pick-wt=20): 380 [] -hBOOL(hAPP(A,c_Type_Otype_Otype__case(B,C,hAPP(hAPP(c_Type_Otype_OFun,D),E),t_a)))|hBOOL(hAPP(A,hAPP(hAPP(C,D),E))).
% 223.84/223.93    Following clause subsumed by 380 during input processing: 0 [] -hBOOL(hAPP(A,c_Type_Otype_Otype__case(B,C,hAPP(hAPP(c_Type_Otype_OFun,D),E),t_a)))|hBOOL(hAPP(A,hAPP(hAPP(C,D),E))).
% 223.84/223.93  ** KEPT (pick-wt=8): 381 [] c_Type_Otype_OAtom(A)!=hAPP(hAPP(c_Type_Otype_OFun,B),C).
% 223.84/223.93  ** KEPT (pick-wt=18): 382 [] c_Type_Otyping(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xabs__typeE__1__1(A,B),tc_Type_Otype),B,c_Type_Osko__Type__Xabs__typeE__1__2(A,B))| -c_Type_Otyping(A,c_Lambda_OdB_OAbs(B),C).
% 223.84/223.93  ** KEPT (pick-wt=20): 383 [] c_Type_Otyping(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(B,A,C),tc_Type_Otype),C,c_Type_Osko__Type__Xtyping__elims__3__2(B,A,C))| -c_Type_Otyping(A,c_Lambda_OdB_OAbs(C),B).
% 223.84/223.93  ** KEPT (pick-wt=6): 384 [] c_InductTermi_OIT(c_Lambda_Olift(A,B))| -c_InductTermi_OIT(A).
% 223.84/223.93  ** KEPT (pick-wt=10): 385 [] c_Lambda_Obeta(c_Lambda_Olift(A,B),c_Lambda_Olift(C,B))| -c_Lambda_Obeta(A,C).
% 223.84/223.93  ** KEPT (pick-wt=15): 386 [] hAPP(c_Type_Oshift(A,B,C,D),E)=hAPP(A,E)| -c_HOL_Oord__class_Oless(E,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=21): 387 [] c_InductTermi_OIT(c_Lambda_Osubst(A,B,C))| -c_Type_Otyping(D,B,E)| -c_InductTermi_OIT(B)| -c_Type_Otyping(c_Type_Oshift(D,C,E,tc_Type_Otype),A,F)| -c_InductTermi_OIT(A).
% 223.84/223.93  ** KEPT (pick-wt=24): 388 [] c_Type_Otyping(A,c_Lambda_OdB_OVar(B),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(C,A,B,D),C,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(B),D,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 223.84/223.93  ** KEPT (pick-wt=20): 389 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=16): 390 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=16): 391 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A)!=c_HOL_Ozero__class_Ozero(A).
% 223.84/223.93  ** KEPT (pick-wt=9): 392 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Ozero__class_Ozero(A).
% 223.84/223.93  ** KEPT (pick-wt=18): 393 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(C),D,tc_Lambda_OdB,tc_Lambda_OdB)|A=C.
% 223.84/223.93  ** KEPT (pick-wt=18): 394 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(C),D,tc_Lambda_OdB,tc_Lambda_OdB)|B=D.
% 223.84/223.93  ** KEPT (pick-wt=13): 395 [] c_Lambda_OdB_OVar(A)!=c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB)|c_Lambda_OdB_OVar(A)=B.
% 223.84/223.93  ** KEPT (pick-wt=9): 396 [] c_InductTermi_OIT(hAPP(hAPP(c_Lambda_OdB_OApp,A),c_Lambda_OdB_OVar(B)))| -c_InductTermi_OIT(A).
% 223.84/223.93  ** KEPT (pick-wt=16): 397 [] c_Type_Otyping(A,B,c_Type_Osko__Type__Xtyping__elims__2__1(C,A,D,B))| -c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,D),B),C).
% 223.84/223.93  ** KEPT (pick-wt=11): 398 [] c_Lambda_Olift(c_Lambda_OdB_OVar(A),B)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 223.84/223.93  ** KEPT (pick-wt=19): 399 [] -c_Type_Otyping(A,B,C)| -c_Type_Otyping(c_Type_Oshift(A,D,C,tc_Type_Otype),E,F)|c_Type_Otyping(A,c_Lambda_Osubst(E,B,D),F).
% 223.84/223.93  ** KEPT (pick-wt=23): 400 [] A=B| -c_Type_Otyping(C,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(D),E,tc_Lambda_OdB,tc_Lambda_OdB),B)| -c_Type_Otyping(C,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(D),E,tc_Lambda_OdB,tc_Lambda_OdB),A).
% 223.84/223.94  ** KEPT (pick-wt=20): 401 [] c_Type_Otyping(A,B,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(C,A,B,D)),C))| -c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),D),C).
% 223.84/223.94  ** KEPT (pick-wt=18): 402 [] c_Type_Otyping(A,c_Lambda_OdB_OAbs(B),hAPP(hAPP(c_Type_Otype_OFun,C),D))| -c_Type_Otyping(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),C,tc_Type_Otype),B,D).
% 223.84/223.94  ** KEPT (pick-wt=14): 403 [] c_Type_Otyping(c_Type_Oshift(A,B,C,tc_Type_Otype),c_Lambda_Olift(D,B),E)| -c_Type_Otyping(A,D,E).
% 223.84/223.94  ** KEPT (pick-wt=8): 404 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OVar(B)|A=B.
% 223.84/223.94  ** KEPT (pick-wt=14): 405 [] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=hAPP(hAPP(c_Type_Otype_OFun,C),D)|A=C.
% 223.84/223.94  ** KEPT (pick-wt=14): 406 [] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=hAPP(hAPP(c_Type_Otype_OFun,C),D)|B=D.
% 223.84/223.94  ** KEPT (pick-wt=20): 407 [] c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),D)| -c_Type_Otyping(A,C,E)| -c_Type_Otyping(A,B,hAPP(hAPP(c_Type_Otype_OFun,E),D)).
% 223.84/223.94  ** KEPT (pick-wt=14): 408 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|A=C.
% 223.84/223.94  ** KEPT (pick-wt=14): 409 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|B=D.
% 223.84/223.94  ** KEPT (pick-wt=8): 410 [] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 223.84/223.94  ** KEPT (pick-wt=10): 411 [] hAPP(A,B)=C| -c_Type_Otyping(A,c_Lambda_OdB_OVar(B),C).
% 223.84/223.94  ** KEPT (pick-wt=8): 412 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 223.84/223.94  ** KEPT (pick-wt=22): 413 [] -c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_U____).
% 223.84/223.94  ** KEPT (pick-wt=6): 414 [] class_Orderings_Opreorder(tc_fun(A,B))| -class_Orderings_Opreorder(B).
% 223.84/223.94  ** KEPT (pick-wt=6): 415 [] class_Orderings_Oorder(tc_fun(A,B))| -class_Orderings_Oorder(B).
% 223.84/223.94  ** KEPT (pick-wt=6): 416 [] class_Orderings_Obot(tc_fun(A,B))| -class_Orderings_Obot(B).
% 223.84/223.94  ** KEPT (pick-wt=7): 417 [] A=B| -c_fe_qual(A,B,C).
% 223.84/223.94  8 back subsumes 6.
% 223.84/223.94  81 back subsumes 80.
% 223.84/223.94    Following clause subsumed by 355 during input processing: 0 [copy,354,flip.1] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 223.84/223.94    Following clause subsumed by 354 during input processing: 0 [copy,355,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 223.84/223.94  ** KEPT (pick-wt=15): 455 [copy,360,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(C),D,tc_Lambda_OdB,tc_Lambda_OdB).
% 223.84/223.94  ** KEPT (pick-wt=14): 456 [copy,362,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(C)),D).
% 223.84/223.94    Following clause subsumed by 368 during input processing: 0 [copy,365,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 223.84/223.94    Following clause subsumed by 365 during input processing: 0 [copy,368,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 223.84/223.94    Following clause subsumed by 381 during input processing: 0 [copy,375,flip.1] c_Type_Otype_OAtom(A)!=hAPP(hAPP(c_Type_Otype_OFun,B),C).
% 223.84/223.94    Following clause subsumed by 375 during input processing: 0 [copy,381,flip.1] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=c_Type_Otype_OAtom(C).
% 223.84/223.94    Following clause subsumed by 412 during input processing: 0 [copy,410,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 223.84/223.94    Following clause subsumed by 410 during input processing: 0 [copy,412,flip.1] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 223.84/223.94    Following clause subsumed by 360 during input processing: 0 [copy,455,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(C),D,tc_Lambda_OdB,tc_Lambda_OdB).
% 223.84/223.94    Following clause subsumed by 362 during input processing: 0 [copy,456,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(C),D,tc_Lambda_OdB,tc_Lambda_OdB).
% 223.84/223.94  
% 223.84/223.94  ------------> process sos:
% 223.84/223.94  ** KEPT (pick-wt=3): 459 [] A=A.
% 223.84/223.94  ** KEPT (pick-wt=8): 460 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_Suc(A),tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=13): 461 [] c_Lambda_Osubstn(A,B,C)=c_Lambda_Osubst(A,c_Lambda_Oliftn(C,B,c_HOL_Ozero__class_Ozero(tc_nat)),C).
% 223.84/223.94  ** KEPT (pick-wt=15): 462 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,C)=c_Lambda_OdB_OVar(A)|A=C|c_HOL_Oord__class_Oless(C,A,tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=12): 464 [copy,463,flip.1] c_Suc(c_Orderings_Oord__class_Omax(A,B,tc_nat))=c_Orderings_Oord__class_Omax(c_Suc(A),c_Suc(B),tc_nat).
% 223.84/223.94  ---> New Demodulator: 465 [new_demod,464] c_Suc(c_Orderings_Oord__class_Omax(A,B,tc_nat))=c_Orderings_Oord__class_Omax(c_Suc(A),c_Suc(B),tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=11): 466 [] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(C,D).
% 223.84/223.94  ** KEPT (pick-wt=13): 467 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.94  ---> New Demodulator: 468 [new_demod,467] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.94  ** KEPT (pick-wt=15): 470 [copy,469,flip.1] c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)).
% 223.84/223.94  ---> New Demodulator: 471 [new_demod,470] c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)).
% 223.84/223.94  ** KEPT (pick-wt=15): 473 [copy,472,demod,471] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)).
% 223.84/223.94  ** KEPT (pick-wt=10): 475 [copy,474,demod,471] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)),tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=10): 477 [copy,476,demod,471] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_Suc(A)),tc_nat).
% 223.84/223.94    Following clause subsumed by 475 during input processing: 0 [demod,471] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)),tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=13): 478 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 223.84/223.94  ** KEPT (pick-wt=8): 479 [] c_List_Odrop(A,c_List_Olist_ONil(B),B)=c_List_Olist_ONil(B).
% 223.84/223.94  ---> New Demodulator: 480 [new_demod,479] c_List_Odrop(A,c_List_Olist_ONil(B),B)=c_List_Olist_ONil(B).
% 223.84/223.94  ** KEPT (pick-wt=12): 481 [] c_Lambda_Oliftn(c_Suc(A),B,C)=c_Lambda_Olift(c_Lambda_Oliftn(A,B,C),C).
% 223.84/223.94  ** KEPT (pick-wt=23): 482 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)).
% 223.84/223.94  ** KEPT (pick-wt=23): 483 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)).
% 223.84/223.94  ---> New Demodulator: 484 [new_demod,483] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)).
% 223.84/223.94  ** KEPT (pick-wt=7): 486 [copy,485,unit_del,166] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,A)=B.
% 223.84/223.94  ---> New Demodulator: 487 [new_demod,486] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,A)=B.
% 223.84/223.94  ** KEPT (pick-wt=9): 488 [] c_List_Ofoldr(A,c_List_Olist_ONil(B),C,B,D)=C.
% 223.84/223.94  ---> New Demodulator: 489 [new_demod,488] c_List_Ofoldr(A,c_List_Olist_ONil(B),C,B,D)=C.
% 223.84/223.94  ** KEPT (pick-wt=13): 491 [copy,490,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.94  ---> New Demodulator: 492 [new_demod,491] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.94  ** KEPT (pick-wt=12): 493 [] c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=17): 494 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat).
% 223.84/223.94    Following clause subsumed by 473 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)).
% 223.84/223.94  ** KEPT (pick-wt=19): 495 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat)=c_HOL_Ominus__class_Ominus(A,C,tc_nat).
% 223.84/223.94  ---> New Demodulator: 496 [new_demod,495] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat)=c_HOL_Ominus__class_Ominus(A,C,tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=19): 497 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat)=c_HOL_Ominus__class_Ominus(B,C,tc_nat).
% 223.84/223.94  ---> New Demodulator: 498 [new_demod,497] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat)=c_HOL_Ominus__class_Ominus(B,C,tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=6): 499 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat).
% 223.84/223.94    Following clause subsumed by 499 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=25): 501 [copy,500,demod,484,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(B,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))=c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),tc_Lambda_OdB).
% 223.84/223.94  ---> New Demodulator: 502 [new_demod,501] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(B,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))=c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),tc_Lambda_OdB).
% 223.84/223.94  ** KEPT (pick-wt=11): 504 [copy,503,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OAbs(A).
% 223.84/223.94  ---> New Demodulator: 505 [new_demod,504] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OAbs(A).
% 223.84/223.94  ** KEPT (pick-wt=7): 506 [] c_lesse_quals(c_HOL_Ominus__class_Ominus(A,B,tc_nat),A,tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=15): 507 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,C,tc_nat),B,tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=9): 508 [] c_lesse_quals(c_Suc(A),B,tc_nat)|c_lesse_quals(B,A,tc_nat).
% 223.84/223.94    Following clause subsumed by 499 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=9): 509 [] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 223.84/223.94  ---> New Demodulator: 510 [new_demod,509] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 223.84/223.94  ** KEPT (pick-wt=15): 511 [] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,C)=c_Lambda_OdB_OVar(A)|A=C|c_HOL_Oord__class_Oless(C,A,tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 512 [] c_InductTermi_OIT(v_s____).
% 223.84/223.94  ** KEPT (pick-wt=11): 513 [] c_HOL_Ominus__class_Ominus(c_Suc(A),c_Suc(B),tc_nat)=c_HOL_Ominus__class_Ominus(A,B,tc_nat).
% 223.84/223.94  ---> New Demodulator: 514 [new_demod,513] c_HOL_Ominus__class_Ominus(c_Suc(A),c_Suc(B),tc_nat)=c_HOL_Ominus__class_Ominus(A,B,tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=10): 515 [] c_Type_Otype_Otype__rec(A,B,c_Type_Otype_OAtom(C),D)=hAPP(A,C).
% 223.84/223.94  ** KEPT (pick-wt=8): 516 [] c_List_Olist_ONil(A)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),B,A).
% 223.84/223.94    Following clause subsumed by 459 during input processing: 0 [demod,468] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.94  ** KEPT (pick-wt=17): 517 [] c_Lambda_Oliftn(A,c_Lambda_OdB_OVar(B),C)=c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A))|c_HOL_Oord__class_Oless(B,C,tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=12): 518 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B),c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.94  ** KEPT (pick-wt=9): 519 [] c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=9): 520 [] c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),tc_nat).
% 223.84/223.94    Following clause subsumed by 519 during input processing: 0 [] c_lesse_quals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=14): 521 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(A,B,tc_nat)),B)=c_Orderings_Oord__class_Omax(A,B,tc_nat).
% 223.84/223.94  ---> New Demodulator: 522 [new_demod,521] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(A,B,tc_nat)),B)=c_Orderings_Oord__class_Omax(A,B,tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=11): 523 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 223.84/223.94    Following clause subsumed by 523 during input processing: 0 [] hBOOL(hAPP(hAPP(A,B),C))|c_HOL_Oord__class_Oless(B,C,tc_nat)|C=B|c_HOL_Oord__class_Oless(C,B,tc_nat).
% 223.84/223.94    Following clause subsumed by 523 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 223.84/223.94  ** KEPT (pick-wt=5): 524 [] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 223.84/223.94    Following clause subsumed by 524 during input processing: 0 [] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=17): 525 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(A),B,tc_nat),c_Suc(C),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat).
% 223.84/223.94  ---> New Demodulator: 526 [new_demod,525] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(A),B,tc_nat),c_Suc(C),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=15): 527 [] c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(A),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.94  ** KEPT (pick-wt=6): 528 [] c_lesse_quals(c_Suc(A),c_Suc(A),tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=15): 530 [copy,529,flip.1] c_List_Oreplicate(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,D)=c_List_Odrop(B,c_List_Oreplicate(A,C,D),D).
% 223.84/223.94  ---> New Demodulator: 531 [new_demod,530] c_List_Oreplicate(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,D)=c_List_Odrop(B,c_List_Oreplicate(A,C,D),D).
% 223.84/223.94  ** KEPT (pick-wt=8): 532 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Olist_ONil(B).
% 223.84/223.94    Following clause subsumed by 459 during input processing: 0 [demod,510] c_Lambda_OdB_OAbs(A)=c_Lambda_OdB_OAbs(A).
% 223.84/223.94  ** KEPT (pick-wt=11): 534 [copy,533,unit_del,166] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.94  ---> New Demodulator: 535 [new_demod,534] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.94    Following clause subsumed by 524 during input processing: 0 [unit_del,166] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=9): 536 [] c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=11): 537 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat)=A.
% 223.84/223.94  ---> New Demodulator: 538 [new_demod,537] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat)=A.
% 223.84/223.94  ** KEPT (pick-wt=11): 539 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat)=B.
% 223.84/223.94  ---> New Demodulator: 540 [new_demod,539] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat)=B.
% 223.84/223.94  ** KEPT (pick-wt=10): 541 [] c_Type_Otype_Otype__case(A,B,c_Type_Otype_OAtom(C),D)=hAPP(A,C).
% 223.84/223.94  ** KEPT (pick-wt=6): 542 [] c_lesse_quals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=7): 543 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 223.84/223.94  ---> New Demodulator: 544 [new_demod,543] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 223.84/223.94  ** KEPT (pick-wt=9): 545 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=7): 546 [] c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 223.84/223.94  ---> New Demodulator: 547 [new_demod,546] c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 223.84/223.94  ** KEPT (pick-wt=7): 548 [] c_HOL_Ominus__class_Ominus(A,A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=17): 550 [copy,549,flip.1] c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,D)=c_List_Odrop(A,c_List_Odrop(B,C,D),D).
% 223.84/223.94  ---> New Demodulator: 551 [new_demod,550] c_List_Odrop(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,D)=c_List_Odrop(A,c_List_Odrop(B,C,D),D).
% 223.84/223.94  ** KEPT (pick-wt=18): 552 [] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(hAPP(C,D),c_Lambda_OdB_OdB__rec(A,B,C,D,E)).
% 223.84/223.94  ** KEPT (pick-wt=11): 553 [] c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.94  ---> New Demodulator: 554 [new_demod,553] c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.94  ** KEPT (pick-wt=4): 555 [] c_lesse_quals(A,A,tc_nat).
% 223.84/223.94    Following clause subsumed by 555 during input processing: 0 [] c_lesse_quals(A,A,tc_nat).
% 223.84/223.94    Following clause subsumed by 459 during input processing: 0 [demod,492] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 223.84/223.94  ** KEPT (pick-wt=15): 556 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ominus__class_Ominus(B,A,tc_nat))=B|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 223.84/223.94    Following clause subsumed by 459 during input processing: 0 [demod,510] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)=hAPP(hAPP(c_Lambda_OdB_OApp,A),B).
% 223.84/223.94  ** KEPT (pick-wt=22): 558 [copy,557,demod,484] c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(B)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))).
% 223.84/223.94  ** KEPT (pick-wt=13): 559 [] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(A))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.94  ** KEPT (pick-wt=8): 560 [] c_lesse_quals(A,B,tc_nat)|c_lesse_quals(B,A,tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=11): 561 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.94  ---> New Demodulator: 562 [new_demod,561] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=5): 563 [] c_Orderings_Obot__class_Obot(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.94  ---> New Demodulator: 564 [new_demod,563] c_Orderings_Obot__class_Obot(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=7): 565 [] c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 223.84/223.94  ---> New Demodulator: 566 [new_demod,565] c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 223.84/223.94  ** KEPT (pick-wt=8): 567 [] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.94  ---> New Demodulator: 568 [new_demod,567] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=5): 569 [] c_lesse_quals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=6): 570 [] c_Nat_Osize__class_Osize(A,tc_String_Ochar)=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=11): 571 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),C,B).
% 223.84/223.94  ** KEPT (pick-wt=7): 572 [] c_Orderings_Oord__class_Omax(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 223.84/223.94  ---> New Demodulator: 573 [new_demod,572] c_Orderings_Oord__class_Omax(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 223.84/223.94  ** KEPT (pick-wt=7): 574 [] c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=A.
% 223.84/223.94  ---> New Demodulator: 575 [new_demod,574] c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=A.
% 223.84/223.94  ** KEPT (pick-wt=9): 577 [copy,576,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 223.84/223.94  ---> New Demodulator: 578 [new_demod,577] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 223.84/223.94  ** KEPT (pick-wt=9): 579 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 223.84/223.94  ---> New Demodulator: 580 [new_demod,579] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 223.84/223.94    Following clause subsumed by 459 during input processing: 0 [demod,578] A=A.
% 223.84/223.94  ** KEPT (pick-wt=20): 582 [copy,581,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(A,B,C)),c_Lambda_Osubst(D,B,C))=c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C).
% 223.84/223.94  ---> New Demodulator: 583 [new_demod,582] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(A,B,C)),c_Lambda_Osubst(D,B,C))=c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C).
% 223.84/223.94  ** KEPT (pick-wt=16): 584 [] c_Lambda_OdB_OdB__case(A,B,C,hAPP(hAPP(c_Lambda_OdB_OApp,D),E),F)=hAPP(hAPP(B,D),E).
% 223.84/223.94  ** KEPT (pick-wt=30): 586 [copy,585,flip.1] hAPP(hAPP(hAPP(hAPP(A,B),C),c_Lambda_OdB_OdB__rec(D,A,E,B,F)),c_Lambda_OdB_OdB__rec(D,A,E,C,F))=c_Lambda_OdB_OdB__rec(D,A,E,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),F).
% 223.84/223.94  ---> New Demodulator: 587 [new_demod,586] hAPP(hAPP(hAPP(hAPP(A,B),C),c_Lambda_OdB_OdB__rec(D,A,E,B,F)),c_Lambda_OdB_OdB__rec(D,A,E,C,F))=c_Lambda_OdB_OdB__rec(D,A,E,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),F).
% 223.84/223.94  ** KEPT (pick-wt=20): 589 [copy,588,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(A,B,C)),c_Lambda_Oliftn(A,D,C))=c_Lambda_Oliftn(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),D),C).
% 223.84/223.94  ---> New Demodulator: 590 [new_demod,589] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(A,B,C)),c_Lambda_Oliftn(A,D,C))=c_Lambda_Oliftn(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),D),C).
% 223.84/223.94  ** KEPT (pick-wt=20): 592 [copy,591,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(A,B,C)),c_Lambda_Osubstn(D,B,C))=c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C).
% 223.84/223.94  ---> New Demodulator: 593 [new_demod,592] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(A,B,C)),c_Lambda_Osubstn(D,B,C))=c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C).
% 223.84/223.94    Following clause subsumed by 459 during input processing: 0 [demod,510] c_Lambda_OdB_OVar(A)=c_Lambda_OdB_OVar(A).
% 223.84/223.94    Following clause subsumed by 459 during input processing: 0 [demod,487] B=B.
% 223.84/223.94  ** KEPT (pick-wt=11): 594 [] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 223.84/223.94  ** KEPT (pick-wt=3): 595 [] c_InductTermi_OIT(c_Lambda_OdB_OVar(A)).
% 223.84/223.94  ** KEPT (pick-wt=11): 596 [] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 223.84/223.94  ** KEPT (pick-wt=27): 598 [copy,597,flip.1] hAPP(hAPP(hAPP(hAPP(A,B),C),c_Type_Otype_Otype__rec(D,A,B,E)),c_Type_Otype_Otype__rec(D,A,C,E))=c_Type_Otype_Otype__rec(D,A,hAPP(hAPP(c_Type_Otype_OFun,B),C),E).
% 223.84/223.94  ---> New Demodulator: 599 [new_demod,598] hAPP(hAPP(hAPP(hAPP(A,B),C),c_Type_Otype_Otype__rec(D,A,B,E)),c_Type_Otype_Otype__rec(D,A,C,E))=c_Type_Otype_Otype__rec(D,A,hAPP(hAPP(c_Type_Otype_OFun,B),C),E).
% 223.84/223.94  ** KEPT (pick-wt=15): 600 [] c_Type_Otype_Otype__case(A,B,hAPP(hAPP(c_Type_Otype_OFun,C),D),E)=hAPP(hAPP(B,C),D).
% 223.84/223.94  ** KEPT (pick-wt=8): 601 [] c_Lambda_Osubst(c_Lambda_Olift(A,B),C,B)=A.
% 223.84/223.94  ---> New Demodulator: 602 [new_demod,601] c_Lambda_Osubst(c_Lambda_Olift(A,B),C,B)=A.
% 223.84/223.94  ** KEPT (pick-wt=7): 603 [] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(A),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.94  ---> New Demodulator: 604 [new_demod,603] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(A),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=6): 605 [] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(A))=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.94  ---> New Demodulator: 606 [new_demod,605] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(A))=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 607 [] c_InductTermi_OIT(v_ta____).
% 223.84/223.94  ** KEPT (pick-wt=22): 608 [] c_Type_Oshift(c_Type_Oshift(A,B,C,D),c_HOL_Ozero__class_Ozero(tc_nat),E,D)=c_Type_Oshift(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),E,D),c_Suc(B),C,D).
% 223.84/223.94  ** KEPT (pick-wt=8): 609 [] c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)).
% 223.84/223.94  ** KEPT (pick-wt=9): 610 [] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 223.84/223.94  ---> New Demodulator: 611 [new_demod,610] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 223.84/223.94  ** KEPT (pick-wt=17): 613 [copy,612,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(A,B)),c_Lambda_Olift(C,B))=c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,A),C),B).
% 223.84/223.94  ---> New Demodulator: 614 [new_demod,613] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Olift(A,B)),c_Lambda_Olift(C,B))=c_Lambda_Olift(hAPP(hAPP(c_Lambda_OdB_OApp,A),C),B).
% 223.84/223.94  ** KEPT (pick-wt=4): 615 [] c_Type_Otyping(v_ea____,v_ta____,v_Ta____).
% 223.84/223.94  ** KEPT (pick-wt=7): 616 [] c_Type_Otyping(A,c_Lambda_OdB_OVar(B),hAPP(A,B)).
% 223.84/223.94  ** KEPT (pick-wt=16): 617 [] c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_Ta____).
% 223.84/223.94  ** KEPT (pick-wt=19): 618 [] c_Type_Otyping(c_Type_Oshift(v_ea____,c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____),tc_Type_Otype),c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)).
% 223.84/223.94  ** KEPT (pick-wt=2): 619 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 620 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 621 [] class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 622 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 623 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 624 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 625 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 626 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 627 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 628 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 629 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 630 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 631 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 632 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 633 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 634 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 635 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 636 [] class_Nat_Osemiring__char__0(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 637 [] class_Orderings_Opreorder(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 638 [] class_Orderings_Olinorder(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 639 [] class_Orderings_Oorder(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 640 [] class_Orderings_Obot(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=2): 641 [] class_Power_Opower(tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=4): 642 [] c_fe_qual(A,A,B).
% 223.84/223.94    Following clause subsumed by 459 during input processing: 0 [copy,459,flip.1] A=A.
% 223.84/223.94  459 back subsumes 458.
% 223.84/223.94  459 back subsumes 446.
% 223.84/223.94  459 back subsumes 445.
% 223.84/223.94  459 back subsumes 444.
% 223.84/223.94  459 back subsumes 441.
% 223.84/223.94  459 back subsumes 440.
% 223.84/223.94  459 back subsumes 439.
% 223.84/223.94  459 back subsumes 438.
% 223.84/223.94  459 back subsumes 430.
% 223.84/223.94  ** KEPT (pick-wt=13): 643 [copy,461,flip.1] c_Lambda_Osubst(A,c_Lambda_Oliftn(B,C,c_HOL_Ozero__class_Ozero(tc_nat)),B)=c_Lambda_Osubstn(A,C,B).
% 223.84/223.94  >>>> Starting back demodulation with 465.
% 223.84/223.94  ** KEPT (pick-wt=11): 644 [copy,466,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__case(C,D,A,c_Lambda_OdB_OAbs(B),E).
% 223.84/223.94  >>>> Starting back demodulation with 468.
% 223.84/223.94  >>>> Starting back demodulation with 471.
% 223.84/223.94  ** KEPT (pick-wt=15): 645 [copy,473,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B).
% 223.84/223.94    Following clause subsumed by 478 during input processing: 0 [copy,478,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 223.84/223.94  >>>> Starting back demodulation with 480.
% 223.84/223.94  ** KEPT (pick-wt=12): 646 [copy,481,flip.1] c_Lambda_Olift(c_Lambda_Oliftn(A,B,C),C)=c_Lambda_Oliftn(c_Suc(A),B,C).
% 223.84/223.94    Following clause subsumed by 482 during input processing: 0 [copy,482,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)).
% 223.84/223.94  >>>> Starting back demodulation with 484.
% 223.84/223.94  >>>> Starting back demodulation with 487.
% 223.84/223.94  >>>> Starting back demodulation with 489.
% 223.84/223.94  >>>> Starting back demodulation with 492.
% 223.84/223.94  ** KEPT (pick-wt=12): 647 [copy,493,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat).
% 223.84/223.94  ** KEPT (pick-wt=17): 648 [copy,494,flip.1] c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat).
% 223.84/223.94  >>>> Starting back demodulation with 496.
% 223.84/223.94  >>>> Starting back demodulation with 498.
% 223.84/223.94  >>>> Starting back demodulation with 502.
% 223.84/223.94  >>>> Starting back demodulation with 505.
% 223.84/223.94    Following clause subsumed by 507 during input processing: 0 [copy,507,flip.1] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,C,tc_nat),B,tc_nat).
% 223.84/223.94  >>>> Starting back demodulation with 510.
% 223.84/223.94      >> back demodulating 504 with 510.
% 223.84/223.94      >> back demodulating 202 with 510.
% 223.84/223.94  >>>> Starting back demodulation with 514.
% 223.84/223.94  ** KEPT (pick-wt=10): 649 [copy,515,flip.1] hAPP(A,B)=c_Type_Otype_Otype__rec(A,C,c_Type_Otype_OAtom(B),D).
% 223.84/223.94    Following clause subsumed by 532 during input processing: 0 [copy,516,flip.1] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Olist_ONil(B).
% 223.84/223.94  >>>> Starting back demodulation with 522.
% 223.84/223.94      >> back demodulating 273 with 522.
% 223.84/223.94  >>>> Starting back demodulation with 526.
% 223.84/223.94  ** KEPT (pick-wt=15): 651 [copy,527,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(A),tc_Lambda_OdB).
% 223.84/223.94  >>>> Starting back demodulation with 531.
% 223.84/223.94    Following clause subsumed by 516 during input processing: 0 [copy,532,flip.1] c_List_Olist_ONil(A)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),B,A).
% 223.84/223.94  >>>> Starting back demodulation with 535.
% 223.84/223.94  >>>> Starting back demodulation with 538.
% 223.84/223.94      >> back demodulating 170 with 538.
% 223.84/223.94  >>>> Starting back demodulation with 540.
% 223.84/223.94      >> back demodulating 11 with 540.
% 223.84/223.94  ** KEPT (pick-wt=10): 652 [copy,541,flip.1] hAPP(A,B)=c_Type_Otype_Otype__case(A,C,c_Type_Otype_OAtom(B),D).
% 223.84/223.94  >>>> Starting back demodulation with 544.
% 223.84/223.94  >>>> Starting back demodulation with 547.
% 223.84/223.94  ** KEPT (pick-wt=7): 653 [copy,548,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ominus__class_Ominus(A,A,tc_nat).
% 223.84/223.94  >>>> Starting back demodulation with 551.
% 223.84/223.94  ** KEPT (pick-wt=18): 654 [copy,552,flip.1] hAPP(hAPP(A,B),c_Lambda_OdB_OdB__rec(C,D,A,B,E))=c_Lambda_OdB_OdB__rec(C,D,A,c_Lambda_OdB_OAbs(B),E).
% 223.84/223.94  >>>> Starting back demodulation with 554.
% 223.84/223.94  555 back subsumes 542.
% 223.84/223.94  555 back subsumes 528.
% 223.84/223.94  555 back subsumes 428.
% 223.84/223.94  ** KEPT (pick-wt=22): 655 [copy,558,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(B)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))))=c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,A),B)).
% 223.84/223.94  ** KEPT (pick-wt=13): 656 [copy,559,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(A)).
% 223.84/223.94  >>>> Starting back demodulation with 562.
% 223.84/223.94  >>>> Starting back demodulation with 564.
% 223.84/223.94  >>>> Starting back demodulation with 566.
% 223.84/223.94  >>>> Starting back demodulation with 568.
% 223.84/223.94  ** KEPT (pick-wt=6): 657 [copy,570,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)=c_Nat_Osize__class_Osize(A,tc_String_Ochar).
% 223.84/223.94    Following clause subsumed by 571 during input processing: 0 [copy,571,flip.1] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),C,B).
% 223.84/223.94  >>>> Starting back demodulation with 573.
% 223.84/223.94  >>>> Starting back demodulation with 575.
% 223.84/223.94  >>>> Starting back demodulation with 578.
% 223.84/223.94      >> back demodulating 561 with 578.
% 223.84/223.94      >> back demodulating 467 with 578.
% 223.84/223.94  >>>> Starting back demodulation with 580.
% 223.84/223.94      >> back demodulating 491 with 580.
% 223.84/223.94  >>>> Starting back demodulation with 583.
% 223.84/223.94  ** KEPT (pick-wt=16): 658 [copy,584,flip.1] hAPP(hAPP(A,B),C)=c_Lambda_OdB_OdB__case(D,A,E,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),F).
% 223.84/223.94  >>>> Starting back demodulation with 587.
% 223.84/223.94  >>>> Starting back demodulation with 590.
% 223.84/223.94  >>>> Starting back demodulation with 593.
% 223.84/223.94  ** KEPT (pick-wt=11): 659 [copy,594,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__rec(A,C,D,c_Lambda_OdB_OVar(B),E).
% 223.84/223.94  ** KEPT (pick-wt=11): 660 [copy,596,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__case(A,C,D,c_Lambda_OdB_OVar(B),E).
% 223.84/223.94  >>>> Starting back demodulation with 599.
% 223.84/223.94  ** KEPT (pick-wt=15): 661 [copy,600,flip.1] hAPP(hAPP(A,B),C)=c_Type_Otype_Otype__case(D,A,hAPP(hAPP(c_Type_Otype_OFun,B),C),E).
% 223.84/223.94  >>>> Starting back demodulation with 602.
% 223.84/223.94  >>>> Starting back demodulation with 604.
% 223.84/223.94  >>>> Starting back demodulation with 606.
% 223.84/223.94  ** KEPT (pick-wt=22): 662 [copy,608,flip.1] c_Type_Oshift(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),B,C),c_Suc(D),E,C)=c_Type_Oshift(c_Type_Oshift(A,D,E,C),c_HOL_Ozero__class_Ozero(tc_nat),B,C).
% 223.84/223.94  >>>> Starting back demodulation with 611.
% 223.84/223.94  >>>> Starting back demodulation with 614.
% 223.84/223.94    Following clause subsumed by 461 during input processing: 0 [copy,643,flip.1] c_Lambda_Osubstn(A,B,C)=c_Lambda_Osubst(A,c_Lambda_Oliftn(C,B,c_HOL_Ozero__class_Ozero(tc_nat)),C).
% 223.84/223.94    Following clause subsumed by 466 during input processing: 0 [copy,644,flip.1] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(C,D).
% 223.84/223.94    Following clause subsumed by 473 during input processing: 0 [copy,645,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B)).
% 223.84/223.94    Following clause subsumed by 481 during input processing: 0 [copy,646,flip.1] c_Lambda_Oliftn(c_Suc(A),B,C)=c_Lambda_Olift(c_Lambda_Oliftn(A,B,C),C).
% 223.84/223.94    Following clause subsumed by 493 during input processing: 0 [copy,647,flip.1] c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.94    Following clause subsumed by 494 during input processing: 0 [copy,648,flip.1] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat).
% 223.84/223.94    Following clause subsumed by 515 during input processing: 0 [copy,649,flip.1] c_Type_Otype_Otype__rec(A,B,c_Type_Otype_OAtom(C),D)=hAPP(A,C).
% 223.84/223.94    Following clause subsumed by 527 during input processing: 0 [copy,651,flip.1] c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(A),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.94    Following clause subsumed by 541 during input processing: 0 [copy,652,flip.1] c_Type_Otype_Otype__case(A,B,c_Type_Otype_OAtom(C),D)=hAPP(A,C).
% 223.84/223.94    Following clause subsumed by 548 during input processing: 0 [copy,653,flip.1] c_HOL_Ominus__class_Ominus(A,A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 223.84/223.94    Following clause subsumed by 552 during input processing: 0 [copy,654,flip.1] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(hAPP(C,D),c_Lambda_OdB_OdB__rec(A,B,C,D,E)).
% 223.84/223.94    Following clause subsumed by 558 during input processing: 0 [copy,655,flip.1] c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(B)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))).
% 223.84/223.94    Following clause subsumed by 559 during input processing: 0 [copy,656,flip.1] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(A))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 223.84/223.94    Following clause subsumed by 570 during input processing: 0 [copy,657,flip.1] c_Nat_Osize__class_Osize(A,tc_String_Ochar)=c_HOL_Ozero__class_Ozero(tc_nat).
% 224.36/224.49    Following clause subsumed by 584 during input processing: 0 [copy,658,flip.1] c_Lambda_OdB_OdB__case(A,B,C,hAPP(hAPP(c_Lambda_OdB_OApp,D),E),F)=hAPP(hAPP(B,D),E).
% 224.36/224.49    Following clause subsumed by 594 during input processing: 0 [copy,659,flip.1] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 224.36/224.49    Following clause subsumed by 596 during input processing: 0 [copy,660,flip.1] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 224.36/224.49    Following clause subsumed by 600 during input processing: 0 [copy,661,flip.1] c_Type_Otype_Otype__case(A,B,hAPP(hAPP(c_Type_Otype_OFun,C),D),E)=hAPP(hAPP(B,C),D).
% 224.36/224.49    Following clause subsumed by 608 during input processing: 0 [copy,662,flip.1] c_Type_Oshift(c_Type_Oshift(A,B,C,D),c_HOL_Ozero__class_Ozero(tc_nat),E,D)=c_Type_Oshift(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),E,D),c_Suc(B),C,D).
% 224.36/224.49  
% 224.36/224.49  ======= end of input processing =======
% 224.36/224.49  
% 224.36/224.49  =========== start of search ===========
% 224.36/224.49  
% 224.36/224.49  
% 224.36/224.49  Resetting weight limit to 2.
% 224.36/224.49  
% 224.36/224.49  
% 224.36/224.49  Resetting weight limit to 2.
% 224.36/224.49  
% 224.36/224.49  sos_size=135
% 224.36/224.49  
% 224.36/224.49  Search stopped because sos empty.
% 224.36/224.49  
% 224.36/224.49  
% 224.36/224.49  Search stopped because sos empty.
% 224.36/224.49  
% 224.36/224.49  ============ end of search ============
% 224.36/224.49  
% 224.36/224.49  -------------- statistics -------------
% 224.36/224.49  clauses given                136
% 224.36/224.49  clauses generated          71021
% 224.36/224.49  clauses kept                 577
% 224.36/224.49  clauses forward subsumed     143
% 224.36/224.49  clauses back subsumed         14
% 224.36/224.49  Kbytes malloced             9765
% 224.36/224.49  
% 224.36/224.49  ----------- times (seconds) -----------
% 224.36/224.49  user CPU time          0.58          (0 hr, 0 min, 0 sec)
% 224.36/224.49  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 224.36/224.49  wall-clock time      224             (0 hr, 3 min, 44 sec)
% 224.36/224.49  
% 224.36/224.49  Process 15296 finished Wed Jul 27 09:13:09 2022
% 224.36/224.49  Otter interrupted
% 224.36/224.49  PROOF NOT FOUND
%------------------------------------------------------------------------------